%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP181^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 08:56:13 AM UTC 2026
% Result : Theorem 71.77s 11.46s
% Output : Refutation 71.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP181^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n003.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:28:55 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.48 ---- Original DTF file ---
% 0.32/0.48 thf(spec,logic,$$dhol).
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 % File : ITP181^2 : TPTP v9.2.1. Released v7.5.0.
% 0.32/0.48 % Domain : Interactive Theorem Proving
% 0.32/0.48 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_189__3410182_1
% 0.32/0.48 % Version : Especial.
% 0.32/0.48 % English :
% 0.32/0.48
% 0.32/0.48 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.32/0.48 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.32/0.48 % Source : [Des21]
% 0.32/0.48 % Names : Strong_Late_Sim_SC/prob_189__3410182_1 [Des21]
% 0.32/0.48
% 0.32/0.48 % Status : Theorem
% 0.32/0.48 % Rating : 0.00 v7.5.0
% 0.32/0.48 % Syntax : Number of formulae : 325 ( 140 unt; 51 typ; 0 def)
% 0.32/0.48 % Number of atoms : 728 ( 237 equ; 0 cnn)
% 0.32/0.48 % Maximal formula atoms : 17 ( 2 avg)
% 0.32/0.48 % Number of connectives : 3990 ( 134 ~; 5 |; 49 &;3424 @)
% 0.32/0.48 % ( 0 <=>; 378 =>; 0 <=; 0 <~>)
% 0.32/0.48 % Maximal formula depth : 28 ( 9 avg)
% 0.32/0.48 % Number of types : 6 ( 5 usr)
% 0.32/0.48 % Number of type conns : 151 ( 151 >; 0 *; 0 +; 0 <<)
% 0.32/0.48 % Number of symbols : 47 ( 46 usr; 9 con; 0-5 aty)
% 0.32/0.48 % Number of variables : 1252 ( 28 ^;1186 !; 13 ?;1252 :)
% 0.32/0.48 % ( 25 !>; 0 ?*; 0 @-; 0 @+)
% 0.32/0.48 % SPC : TH1_THM_EQU_NAR
% 0.32/0.48
% 0.32/0.48 % Comments : This file was generated by Sledgehammer 2021-02-23 16:15:47.705
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 % Could-be-implicit typings (8)
% 0.32/0.48 thf(ty_t_Late__Semantics_Oresidual,type,
% 0.32/0.48 late_residual: $tType ).
% 0.32/0.48
% 0.32/0.48 thf(ty_t_Late__Semantics_Osubject,type,
% 0.32/0.48 late_subject: $tType ).
% 0.32/0.48
% 0.32/0.48 thf(ty_t_Late__Semantics_OfreeRes,type,
% 0.32/0.48 late_freeRes: $tType ).
% 0.32/0.48
% 0.32/0.48 thf(ty_t_Product__Type_Oprod,type,
% 0.32/0.48 product_prod: $tType > $tType > $tType ).
% 0.32/0.48
% 0.32/0.48 thf(ty_t_Nominal_Onoption,type,
% 0.32/0.48 noption: $tType > $tType ).
% 0.32/0.48
% 0.32/0.48 thf(ty_t_Agent_Oname,type,
% 0.32/0.48 name: $tType ).
% 0.32/0.48
% 0.32/0.48 thf(ty_t_Agent_Opi,type,
% 0.32/0.48 pi: $tType ).
% 0.32/0.48
% 0.32/0.48 thf(ty_t_Set_Oset,type,
% 0.32/0.48 set: $tType > $tType ).
% 0.32/0.48
% 0.32/0.48 % Explicit typings (43)
% 0.32/0.48 thf(sy_cl_HOL_Otype,type,
% 0.32/0.48 type:
% 0.32/0.48 !>[A: $tType] : $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Agent_Ofs__name,type,
% 0.32/0.48 fs_name:
% 0.32/0.48 !>[A: $tType] : $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Orderings_Oord,type,
% 0.32/0.48 ord:
% 0.32/0.48 !>[A: $tType] : $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Orderings_Oorder,type,
% 0.32/0.48 order:
% 0.32/0.48 !>[A: $tType] : $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Orderings_Olinorder,type,
% 0.32/0.48 linorder:
% 0.32/0.48 !>[A: $tType] : $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_cl_Orderings_Opreorder,type,
% 0.32/0.48 preorder:
% 0.32/0.48 !>[A: $tType] : $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Agent_Opi_OInput,type,
% 0.32/0.48 input: name > name > pi > pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.32/0.48 mismatch: name > name > pi > pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Agent_Opi_OOutput,type,
% 0.32/0.48 output: name > name > pi > pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Agent_Opi_OPar,type,
% 0.32/0.48 par: pi > pi > pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.32/0.48 piNil: pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Agent_Opi_ORes,type,
% 0.32/0.48 res: name > pi > pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Agent_Opi_OSum,type,
% 0.32/0.48 sum: pi > pi > pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Agent_Opi_OTau,type,
% 0.32/0.48 tau: pi > pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Agent_Osubs,type,
% 0.32/0.48 subs: pi > name > name > pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.32/0.48 late_OutputR: name > name > late_freeRes ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.32/0.48 late_TauR: late_freeRes ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 0.32/0.48 late_freeRes_rec:
% 0.32/0.48 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.32/0.48 late_BoundR: late_subject > name > pi > late_residual ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.32/0.48 late_FreeR: late_freeRes > pi > late_residual ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.32/0.48 late_BoundOutputS: name > late_subject ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.32/0.48 late_InputS: name > late_subject ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 0.32/0.48 late_subject_rec:
% 0.32/0.48 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.32/0.48 late_transitions: pi > late_residual > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Nominal_Oabs__fun,type,
% 0.32/0.48 abs_fun:
% 0.32/0.48 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Nominal_Ofresh,type,
% 0.32/0.48 fresh:
% 0.32/0.48 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.32/0.48 ord_less_eq:
% 0.32/0.48 !>[A: $tType] : ( A > A > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Product__Type_OPair,type,
% 0.32/0.48 product_Pair:
% 0.32/0.48 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.32/0.48 produc2004651681e_prod:
% 0.32/0.48 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.32/0.48 product_rec_prod:
% 0.32/0.48 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Rel_Oeqvt,type,
% 0.32/0.48 eqvt:
% 0.32/0.48 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Relation_OId,type,
% 0.32/0.48 id:
% 0.32/0.48 !>[A: $tType] : ( set @ ( product_prod @ A @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Set_OCollect,type,
% 0.32/0.48 collect:
% 0.32/0.48 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.32/0.48 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.32/0.48 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 0.32/0.48
% 0.32/0.48 thf(sy_c_member,type,
% 0.32/0.48 member:
% 0.32/0.48 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v_P,type,
% 0.32/0.48 p: pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v_PQ____,type,
% 0.32/0.48 pq: pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v_Q,type,
% 0.32/0.48 q: pi ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v_Rel,type,
% 0.32/0.48 rel: set @ ( product_prod @ pi @ pi ) ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v_a____,type,
% 0.32/0.48 a: late_subject ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v_x,type,
% 0.32/0.48 x: name ).
% 0.32/0.48
% 0.32/0.48 thf(sy_v_y____,type,
% 0.32/0.48 y: name ).
% 0.32/0.48
% 0.32/0.48 % Relevant facts (256)
% 0.32/0.48 thf(fact_0_Eqvt,axiom,
% 0.32/0.48 eqvt @ pi @ rel ).
% 0.32/0.48
% 0.32/0.48 % Eqvt
% 0.32/0.48 thf(fact_1_Bound_Ohyps_I5_J,axiom,
% 0.32/0.48 fresh @ name @ ( product_prod @ name @ ( product_prod @ pi @ pi ) ) @ y @ ( product_Pair @ name @ ( product_prod @ pi @ pi ) @ x @ ( product_Pair @ pi @ pi @ p @ q ) ) ).
% 0.32/0.48
% 0.32/0.48 % Bound.hyps(5)
% 0.32/0.48 thf(fact_2_Bound_Ohyps_I4_J,axiom,
% 0.32/0.48 fresh @ name @ late_subject @ y @ a ).
% 0.32/0.48
% 0.32/0.48 % Bound.hyps(4)
% 0.32/0.48 thf(fact_3_Bound_Ohyps_I3_J,axiom,
% 0.32/0.48 fresh @ name @ pi @ y @ ( res @ x @ ( sum @ p @ q ) ) ).
% 0.32/0.48
% 0.32/0.48 % Bound.hyps(3)
% 0.32/0.48 thf(fact_4_Bound_Ohyps_I2_J,axiom,
% 0.32/0.48 fresh @ name @ pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) ).
% 0.32/0.48
% 0.32/0.48 % Bound.hyps(2)
% 0.32/0.48 thf(fact_5_Bound_Ohyps_I1_J,axiom,
% 0.32/0.48 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ a @ y @ pq ) ).
% 0.32/0.48
% 0.32/0.48 % Bound.hyps(1)
% 0.32/0.48 thf(fact_6_fresh__prod,axiom,
% 0.32/0.48 ! [A: $tType,X: $tType,B: $tType,A2: X,X2: A,Y: B] :
% 0.32/0.48 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X2 @ Y ) )
% 0.32/0.48 = ( ( fresh @ X @ A @ A2 @ X2 )
% 0.32/0.48 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % fresh_prod
% 0.32/0.48 thf(fact_7_pi_Ofresh_I7_J,axiom,
% 0.32/0.48 ! [A2: name,X22: pi,X1: pi] :
% 0.32/0.48 ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 0.32/0.48 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.32/0.48 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.fresh(7)
% 0.32/0.48 thf(fact_8_transitions_OResB,axiom,
% 0.32/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.32/0.48 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.32/0.48 => ( ( Y != X2 )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.32/0.48 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.32/0.48 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % transitions.ResB
% 0.32/0.48 thf(fact_9_freshBoundDerivative_I1_J,axiom,
% 0.32/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/0.48 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % freshBoundDerivative(1)
% 0.32/0.48 thf(fact_10_Late__Semantics_OResB,axiom,
% 0.32/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.32/0.48 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 0.32/0.48 => ( ( Y != X2 )
% 0.32/0.48 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics.ResB
% 0.32/0.48 thf(fact_11_fresh__prodD_I2_J,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,C: $tType,A2: A,X2: B,Y: C] :
% 0.32/0.48 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X2 @ Y ) )
% 0.32/0.48 => ( fresh @ A @ C @ A2 @ Y ) ) ).
% 0.32/0.48
% 0.32/0.48 % fresh_prodD(2)
% 0.32/0.48 thf(fact_12_fresh__prodD_I1_J,axiom,
% 0.32/0.48 ! [C: $tType,A: $tType,B: $tType,A2: A,X2: B,Y: C] :
% 0.32/0.48 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X2 @ Y ) )
% 0.32/0.48 => ( fresh @ A @ B @ A2 @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % fresh_prodD(1)
% 0.32/0.48 thf(fact_13_freshBoundDerivative_I2_J,axiom,
% 0.32/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/0.48 => ( ( Y != X2 )
% 0.32/0.48 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % freshBoundDerivative(2)
% 0.32/0.48 thf(fact_14_prod_Oinject,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 0.32/0.48 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 0.32/0.48 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.32/0.48 = ( ( X1 = Y1 )
% 0.32/0.48 & ( X22 = Y2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod.inject
% 0.32/0.48 thf(fact_15_old_Oprod_Oinject,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.32/0.48 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.32/0.48 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.32/0.48 = ( ( A2 = A3 )
% 0.32/0.48 & ( B2 = B3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % old.prod.inject
% 0.32/0.48 thf(fact_16_pi_Odistinct_I81_J,axiom,
% 0.32/0.48 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.32/0.48 ( ( sum @ Pi1 @ Pi2 )
% 0.32/0.48 != ( res @ Name @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(81)
% 0.32/0.48 thf(fact_17_freshResidual,axiom,
% 0.32/0.48 ! [P: pi,Rs: late_residual,X2: name] :
% 0.32/0.48 ( ( late_transitions @ P @ Rs )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.32/0.48 => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % freshResidual
% 0.32/0.48 thf(fact_18_old_Oprod_Oinducts,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.32/0.48 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.32/0.48 => ( P @ Prod ) ) ).
% 0.32/0.48
% 0.32/0.48 % old.prod.inducts
% 0.32/0.48 thf(fact_19_old_Oprod_Oexhaust,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.32/0.48 ~ ! [A4: A,B4: B] :
% 0.32/0.48 ( Y
% 0.32/0.48 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 0.32/0.48
% 0.32/0.48 % old.prod.exhaust
% 0.32/0.48 thf(fact_20_Pair__inject,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.32/0.48 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.32/0.48 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.32/0.48 => ~ ( ( A2 = A3 )
% 0.32/0.48 => ( B2 != B3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Pair_inject
% 0.32/0.48 thf(fact_21_prod__cases,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 0.32/0.48 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.32/0.48 => ( P @ P3 ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod_cases
% 0.32/0.48 thf(fact_22_surj__pair,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 0.32/0.48 ? [X3: A,Y3: B] :
% 0.32/0.48 ( P3
% 0.32/0.48 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 0.32/0.48
% 0.32/0.48 % surj_pair
% 0.32/0.48 thf(fact_23_name__exists__fresh,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( fs_name @ A )
% 0.32/0.48 => ! [X2: A] :
% 0.32/0.48 ~ ! [C2: name] :
% 0.32/0.48 ~ ( fresh @ name @ A @ C2 @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % name_exists_fresh
% 0.32/0.48 thf(fact_24_pi_Oinject_I6_J,axiom,
% 0.32/0.48 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.32/0.48 ( ( ( sum @ X22 @ X1 )
% 0.32/0.48 = ( sum @ Y2 @ Y1 ) )
% 0.32/0.48 = ( ( X22 = Y2 )
% 0.32/0.48 & ( X1 = Y1 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.inject(6)
% 0.32/0.48 thf(fact_25_prod__induct7,axiom,
% 0.32/0.48 ! [G: $tType,F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.32/0.48 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F,G2: G] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) )
% 0.32/0.48 => ( P @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod_induct7
% 0.32/0.48 thf(fact_26_prod__induct6,axiom,
% 0.32/0.48 ! [F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 0.32/0.48 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) )
% 0.32/0.48 => ( P @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod_induct6
% 0.32/0.48 thf(fact_27_prod__induct5,axiom,
% 0.32/0.48 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.32/0.48 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.32/0.48 => ( P @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod_induct5
% 0.32/0.48 thf(fact_28_prod__induct4,axiom,
% 0.32/0.48 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.32/0.48 ( ! [A4: A,B4: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 0.32/0.48 => ( P @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod_induct4
% 0.32/0.48 thf(fact_29_prod__induct3,axiom,
% 0.32/0.48 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.32/0.48 ( ! [A4: A,B4: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 0.32/0.48 => ( P @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod_induct3
% 0.32/0.48 thf(fact_30_prod__cases7,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.32/0.48 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F,G2: G] :
% 0.32/0.48 ( Y
% 0.32/0.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod_cases7
% 0.32/0.48 thf(fact_31_prod__cases6,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 0.32/0.48 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F] :
% 0.32/0.48 ( Y
% 0.32/0.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod_cases6
% 0.32/0.48 thf(fact_32_prod__cases5,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.32/0.48 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E] :
% 0.32/0.48 ( Y
% 0.32/0.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod_cases5
% 0.32/0.48 thf(fact_33_prod__cases4,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.32/0.48 ~ ! [A4: A,B4: B,C2: C,D2: D] :
% 0.32/0.48 ( Y
% 0.32/0.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod_cases4
% 0.32/0.48 thf(fact_34_prod__cases3,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.32/0.48 ~ ! [A4: A,B4: B,C2: C] :
% 0.32/0.48 ( Y
% 0.32/0.48 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod_cases3
% 0.32/0.48 thf(fact_35_freshRes,axiom,
% 0.32/0.48 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 0.32/0.48
% 0.32/0.48 % freshRes
% 0.32/0.48 thf(fact_36_Sum2,axiom,
% 0.32/0.48 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.32/0.48 ( ( late_transitions @ Q @ Rs )
% 0.32/0.48 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.32/0.48
% 0.32/0.48 % Sum2
% 0.32/0.48 thf(fact_37_Sum1,axiom,
% 0.32/0.48 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ Rs )
% 0.32/0.48 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.32/0.48
% 0.32/0.48 % Sum1
% 0.32/0.48 thf(fact_38_sumCases_H,axiom,
% 0.32/0.48 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.32/0.48 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.32/0.48 => ( ~ ( late_transitions @ P @ Rs )
% 0.32/0.48 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sumCases'
% 0.32/0.48 thf(fact_39_sumCases,axiom,
% 0.32/0.48 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.32/0.48 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.32/0.48 => ( ~ ( late_transitions @ P @ Rs )
% 0.32/0.48 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sumCases
% 0.32/0.48 thf(fact_40_old_Oprod_Orec,axiom,
% 0.32/0.48 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.32/0.48 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.32/0.48 = ( F1 @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % old.prod.rec
% 0.32/0.48 thf(fact_41_internal__case__prod__conv,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 0.32/0.48 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.32/0.48 = ( C3 @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % internal_case_prod_conv
% 0.32/0.48 thf(fact_42_Id,axiom,
% 0.32/0.48 ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ rel ).
% 0.32/0.48
% 0.32/0.48 % Id
% 0.32/0.48 thf(fact_43_transitions_OPar2B,axiom,
% 0.32/0.48 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.32/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.32/0.48 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.32/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % transitions.Par2B
% 0.32/0.48 thf(fact_44_transitions_OPar1B,axiom,
% 0.32/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.32/0.48 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 0.32/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % transitions.Par1B
% 0.32/0.48 thf(fact_45_mem__Collect__eq,axiom,
% 0.32/0.48 ! [A: $tType,A2: A,P: A > $o] :
% 0.32/0.48 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.32/0.48 = ( P @ A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % mem_Collect_eq
% 0.32/0.48 thf(fact_46_Collect__mem__eq,axiom,
% 0.32/0.48 ! [A: $tType,A5: set @ A] :
% 0.32/0.48 ( ( collect @ A
% 0.32/0.48 @ ^ [X4: A] : ( member @ A @ X4 @ A5 ) )
% 0.32/0.48 = A5 ) ).
% 0.32/0.48
% 0.32/0.48 % Collect_mem_eq
% 0.32/0.48 thf(fact_47_Collect__cong,axiom,
% 0.32/0.48 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/0.48 ( ! [X3: A] :
% 0.32/0.48 ( ( P @ X3 )
% 0.32/0.48 = ( Q @ X3 ) )
% 0.32/0.48 => ( ( collect @ A @ P )
% 0.32/0.48 = ( collect @ A @ Q ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Collect_cong
% 0.32/0.48 thf(fact_48_parCasesB_H,axiom,
% 0.32/0.48 ! [P: pi,Q: pi,B2: late_subject,Y: name,P2: pi] :
% 0.32/0.48 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 0.32/0.48 => ( ! [P4: pi,A4: late_subject,X3: name,P5: pi,Q3: pi] :
% 0.32/0.48 ( ( ( par @ P @ Q )
% 0.32/0.48 = ( par @ P4 @ Q3 ) )
% 0.32/0.48 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 0.32/0.48 = ( late_BoundR @ A4 @ X3 @ ( par @ P5 @ Q3 ) ) )
% 0.32/0.48 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X3 @ P5 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X3 @ P4 )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X3 @ Q3 )
% 0.32/0.48 => ~ ( fresh @ name @ late_subject @ X3 @ A4 ) ) ) ) ) )
% 0.32/0.48 => ~ ! [Q3: pi,A4: late_subject,X3: name,Q4: pi,P4: pi] :
% 0.32/0.48 ( ( ( par @ P @ Q )
% 0.32/0.48 = ( par @ P4 @ Q3 ) )
% 0.32/0.48 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 0.32/0.48 = ( late_BoundR @ A4 @ X3 @ ( par @ P4 @ Q4 ) ) )
% 0.32/0.48 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A4 @ X3 @ Q4 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X3 @ P4 )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X3 @ Q3 )
% 0.32/0.48 => ~ ( fresh @ name @ late_subject @ X3 @ A4 ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % parCasesB'
% 0.32/0.48 thf(fact_49_inputIneqTrans,axiom,
% 0.32/0.48 ! [A2: name,X2: name,P: pi,B2: late_subject,Y: name,P2: pi] :
% 0.32/0.48 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 0.32/0.48 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inputIneqTrans
% 0.32/0.48 thf(fact_50_resTauBoundTrans,axiom,
% 0.32/0.48 ! [X2: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % resTauBoundTrans
% 0.32/0.48 thf(fact_51_residual_Ostrong__inducts,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( fs_name @ A )
% 0.32/0.48 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 0.32/0.48 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: A] :
% 0.32/0.48 ( ( fresh @ name @ A @ Name2 @ Z2 )
% 0.32/0.48 => ( ( fresh @ name @ late_subject @ Name2 @ Subject )
% 0.32/0.48 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.32/0.48 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.32/0.48 => ( P @ Z @ Residual ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % residual.strong_inducts
% 0.32/0.48 thf(fact_52_residual_Ostrong__induct,axiom,
% 0.32/0.48 ! [N: $tType] :
% 0.32/0.48 ( ( fs_name @ N )
% 0.32/0.48 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 0.32/0.48 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: N] :
% 0.32/0.48 ( ( fresh @ name @ N @ Name2 @ Z2 )
% 0.32/0.48 => ( ( fresh @ name @ late_subject @ Name2 @ Subject )
% 0.32/0.48 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.32/0.48 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.32/0.48 => ( P @ Z @ Residual ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % residual.strong_induct
% 0.32/0.48 thf(fact_53_pi_Ofresh_I8_J,axiom,
% 0.32/0.48 ! [A2: name,X22: pi,X1: pi] :
% 0.32/0.48 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 0.32/0.48 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 0.32/0.48 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.fresh(8)
% 0.32/0.48 thf(fact_54_pi_Ofresh_I3_J,axiom,
% 0.32/0.48 ! [A2: name,X1: pi] :
% 0.32/0.48 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 0.32/0.48 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.fresh(3)
% 0.32/0.48 thf(fact_55_residual_Ofresh_I2_J,axiom,
% 0.32/0.48 ! [A2: name,X22: late_freeRes,X1: pi] :
% 0.32/0.48 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 0.32/0.48 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 0.32/0.48 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % residual.fresh(2)
% 0.32/0.48 thf(fact_56_residual_Oinject_I2_J,axiom,
% 0.32/0.48 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.32/0.48 ( ( ( late_FreeR @ X22 @ X1 )
% 0.32/0.48 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.32/0.48 = ( ( X22 = Y2 )
% 0.32/0.48 & ( X1 = Y1 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % residual.inject(2)
% 0.32/0.48 thf(fact_57_pi_Odistinct_I35_J,axiom,
% 0.32/0.48 ! [Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 0.32/0.48 ( ( tau @ Pi4 )
% 0.32/0.48 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(35)
% 0.32/0.48 thf(fact_58_pi_Odistinct_I43_J,axiom,
% 0.32/0.48 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.32/0.48 ( ( tau @ Pi4 )
% 0.32/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(43)
% 0.32/0.48 thf(fact_59_pi_Odistinct_I55_J,axiom,
% 0.32/0.48 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.32/0.48 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.32/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(55)
% 0.32/0.48 thf(fact_60_pi_Oinject_I2_J,axiom,
% 0.32/0.48 ! [X1: pi,Y1: pi] :
% 0.32/0.48 ( ( ( tau @ X1 )
% 0.32/0.48 = ( tau @ Y1 ) )
% 0.32/0.48 = ( X1 = Y1 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.inject(2)
% 0.32/0.48 thf(fact_61_pi_Oinject_I7_J,axiom,
% 0.32/0.48 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.32/0.48 ( ( ( par @ X22 @ X1 )
% 0.32/0.48 = ( par @ Y2 @ Y1 ) )
% 0.32/0.48 = ( ( X22 = Y2 )
% 0.32/0.48 & ( X1 = Y1 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.inject(7)
% 0.32/0.48 thf(fact_62_Par2F,axiom,
% 0.32/0.48 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.32/0.48 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.32/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Par2F
% 0.32/0.48 thf(fact_63_Par1F,axiom,
% 0.32/0.48 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.32/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Par1F
% 0.32/0.48 thf(fact_64_inputFreeTrans,axiom,
% 0.32/0.48 ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inputFreeTrans
% 0.32/0.48 thf(fact_65_resInputFreeTrans,axiom,
% 0.32/0.48 ! [X2: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % resInputFreeTrans
% 0.32/0.48 thf(fact_66_pi_Odistinct_I85_J,axiom,
% 0.32/0.48 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.32/0.48 ( ( par @ Pi1 @ Pi2 )
% 0.32/0.48 != ( res @ Name @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(85)
% 0.32/0.48 thf(fact_67_pi_Odistinct_I79_J,axiom,
% 0.32/0.48 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.32/0.48 ( ( sum @ Pi1 @ Pi2 )
% 0.32/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(79)
% 0.32/0.48 thf(fact_68_residual_Odistinct_I1_J,axiom,
% 0.32/0.48 ! [Subject2: late_subject,Name3: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
% 0.32/0.48 ( ( late_BoundR @ Subject2 @ Name3 @ Pi4 )
% 0.32/0.48 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % residual.distinct(1)
% 0.32/0.48 thf(fact_69_residual_Oinducts,axiom,
% 0.32/0.48 ! [P: late_residual > $o,Residual: late_residual] :
% 0.32/0.48 ( ! [Subject: late_subject,Name2: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) )
% 0.32/0.48 => ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.32/0.48 => ( P @ Residual ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % residual.inducts
% 0.32/0.48 thf(fact_70_pi_Odistinct_I57_J,axiom,
% 0.32/0.48 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 0.32/0.48 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.32/0.48 != ( res @ Name @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(57)
% 0.32/0.48 thf(fact_71_pi_Odistinct_I45_J,axiom,
% 0.32/0.48 ! [Pi4: pi,Name: name,Pi: pi] :
% 0.32/0.48 ( ( tau @ Pi4 )
% 0.32/0.48 != ( res @ Name @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(45)
% 0.32/0.48 thf(fact_72_pi_Odistinct_I53_J,axiom,
% 0.32/0.48 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.32/0.48 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.32/0.48 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(53)
% 0.32/0.48 thf(fact_73_pi_Odistinct_I41_J,axiom,
% 0.32/0.48 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.32/0.48 ( ( tau @ Pi4 )
% 0.32/0.48 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(41)
% 0.32/0.48 thf(fact_74_resCasesF,axiom,
% 0.32/0.48 ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
% 0.32/0.48 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.32/0.48 => ( ! [P5: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 0.32/0.48 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 0.32/0.48 => ( F3 @ ( res @ X2 @ P5 ) ) ) )
% 0.32/0.48 => ( F3 @ XP ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % resCasesF
% 0.32/0.48 thf(fact_75_resCasesF_H,axiom,
% 0.32/0.48 ! [X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.32/0.48 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.32/0.48 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.32/0.48 ( ( ( res @ X2 @ P )
% 0.32/0.48 = ( res @ Y3 @ P4 ) )
% 0.32/0.48 => ( ( ( late_FreeR @ Alpha @ P2 )
% 0.32/0.48 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.32/0.48 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.32/0.48 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % resCasesF'
% 0.32/0.48 thf(fact_76_ResF,axiom,
% 0.32/0.48 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.32/0.48 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 0.32/0.48 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ResF
% 0.32/0.48 thf(fact_77_freshFreeDerivative_I2_J,axiom,
% 0.32/0.48 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/0.48 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % freshFreeDerivative(2)
% 0.32/0.48 thf(fact_78_freshFreeDerivative_I1_J,axiom,
% 0.32/0.48 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/0.48 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % freshFreeDerivative(1)
% 0.32/0.48 thf(fact_79_resTrans_I2_J,axiom,
% 0.32/0.48 ! [X2: name,Y: name,P: pi,Rs: late_residual] :
% 0.32/0.48 ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y @ P ) ) @ Rs ) ).
% 0.32/0.48
% 0.32/0.48 % resTrans(2)
% 0.32/0.48 thf(fact_80_tauBoundTrans,axiom,
% 0.32/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X2 @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % tauBoundTrans
% 0.32/0.48 thf(fact_81_Late__Semantics_OPar1B,axiom,
% 0.32/0.48 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.32/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics.Par1B
% 0.32/0.48 thf(fact_82_Late__Semantics_OPar2B,axiom,
% 0.32/0.48 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 0.32/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.32/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics.Par2B
% 0.32/0.48 thf(fact_83_parCasesB,axiom,
% 0.32/0.48 ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 0.32/0.48 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.32/0.48 => ( ! [P5: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P5 ) )
% 0.32/0.48 => ( Prop @ ( par @ P5 @ Q ) ) )
% 0.32/0.48 => ( ! [Q4: pi] :
% 0.32/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q4 ) )
% 0.32/0.48 => ( Prop @ ( par @ P @ Q4 ) ) )
% 0.32/0.48 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % parCasesB
% 0.32/0.48 thf(fact_84_IdI,axiom,
% 0.32/0.48 ! [A: $tType,A2: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( id @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % IdI
% 0.32/0.48 thf(fact_85_pair__in__Id__conv,axiom,
% 0.32/0.48 ! [A: $tType,A2: A,B2: A] :
% 0.32/0.48 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 0.32/0.48 = ( A2 = B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pair_in_Id_conv
% 0.32/0.48 thf(fact_86_subsetI,axiom,
% 0.32/0.48 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.32/0.48 ( ! [X3: A] :
% 0.32/0.48 ( ( member @ A @ X3 @ A5 )
% 0.32/0.48 => ( member @ A @ X3 @ B5 ) )
% 0.32/0.48 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 0.32/0.48
% 0.32/0.48 % subsetI
% 0.32/0.48 thf(fact_87_subset__antisym,axiom,
% 0.32/0.48 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.32/0.48 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 0.32/0.48 => ( A5 = B5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_antisym
% 0.32/0.48 thf(fact_88_order__refl,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( preorder @ A )
% 0.32/0.48 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % order_refl
% 0.32/0.48 thf(fact_89_IdE,axiom,
% 0.32/0.48 ! [A: $tType,P3: product_prod @ A @ A] :
% 0.32/0.48 ( ( member @ ( product_prod @ A @ A ) @ P3 @ ( id @ A ) )
% 0.32/0.48 => ~ ! [X3: A] :
% 0.32/0.48 ( P3
% 0.32/0.48 != ( product_Pair @ A @ A @ X3 @ X3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % IdE
% 0.32/0.48 thf(fact_90_IdD,axiom,
% 0.32/0.48 ! [A: $tType,A2: A,B2: A] :
% 0.32/0.48 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 0.32/0.48 => ( A2 = B2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % IdD
% 0.32/0.48 thf(fact_91_subrelI,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.32/0.48 ( ! [X3: A,Y3: B] :
% 0.32/0.48 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R )
% 0.32/0.48 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ S ) )
% 0.32/0.48 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 0.32/0.48
% 0.32/0.48 % subrelI
% 0.32/0.48 thf(fact_92_dual__order_Oantisym,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [B2: A,A2: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/0.48 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48 => ( A2 = B2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % dual_order.antisym
% 0.32/0.48 thf(fact_93_dual__order_Oeq__iff,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.32/0.48 = ( ^ [A6: A,B6: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ B6 @ A6 )
% 0.32/0.48 & ( ord_less_eq @ A @ A6 @ B6 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % dual_order.eq_iff
% 0.32/0.48 thf(fact_94_dual__order_Otrans,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [B2: A,A2: A,C3: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/0.48 => ( ( ord_less_eq @ A @ C3 @ B2 )
% 0.32/0.48 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % dual_order.trans
% 0.32/0.48 thf(fact_95_linorder__wlog,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.32/0.48 ( ! [A4: A,B4: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.32/0.48 => ( P @ A4 @ B4 ) )
% 0.32/0.48 => ( ! [A4: A,B4: A] :
% 0.32/0.48 ( ( P @ B4 @ A4 )
% 0.32/0.48 => ( P @ A4 @ B4 ) )
% 0.32/0.48 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % linorder_wlog
% 0.32/0.48 thf(fact_96_dual__order_Orefl,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % dual_order.refl
% 0.32/0.48 thf(fact_97_order__trans,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( preorder @ A )
% 0.32/0.48 => ! [X2: A,Y: A,Z: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/0.48 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.32/0.48 => ( ord_less_eq @ A @ X2 @ Z ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % order_trans
% 0.32/0.48 thf(fact_98_order__class_Oorder_Oantisym,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [A2: A,B2: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/0.48 => ( A2 = B2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % order_class.order.antisym
% 0.32/0.48 thf(fact_99_ord__le__eq__trans,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [A2: A,B2: A,C3: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48 => ( ( B2 = C3 )
% 0.32/0.48 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ord_le_eq_trans
% 0.32/0.48 thf(fact_100_ord__eq__le__trans,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [A2: A,B2: A,C3: A] :
% 0.32/0.48 ( ( A2 = B2 )
% 0.32/0.48 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 0.32/0.48 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ord_eq_le_trans
% 0.32/0.48 thf(fact_101_order__class_Oorder_Oeq__iff,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.32/0.48 = ( ^ [A6: A,B6: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.32/0.48 & ( ord_less_eq @ A @ B6 @ A6 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % order_class.order.eq_iff
% 0.32/0.48 thf(fact_102_antisym__conv,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [Y: A,X2: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ Y @ X2 )
% 0.32/0.48 => ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/0.48 = ( X2 = Y ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % antisym_conv
% 0.32/0.48 thf(fact_103_le__cases3,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ! [X2: A,Y: A,Z: A] :
% 0.32/0.48 ( ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/0.48 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.32/0.48 => ( ( ( ord_less_eq @ A @ Y @ X2 )
% 0.32/0.48 => ~ ( ord_less_eq @ A @ X2 @ Z ) )
% 0.32/0.48 => ( ( ( ord_less_eq @ A @ X2 @ Z )
% 0.32/0.48 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.32/0.48 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.32/0.48 => ~ ( ord_less_eq @ A @ Y @ X2 ) )
% 0.32/0.48 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.32/0.48 => ~ ( ord_less_eq @ A @ Z @ X2 ) )
% 0.32/0.48 => ~ ( ( ord_less_eq @ A @ Z @ X2 )
% 0.32/0.48 => ~ ( ord_less_eq @ A @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_cases3
% 0.32/0.48 thf(fact_104_order_Otrans,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [A2: A,B2: A,C3: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 0.32/0.48 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % order.trans
% 0.32/0.48 thf(fact_105_le__cases,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ! [X2: A,Y: A] :
% 0.32/0.48 ( ~ ( ord_less_eq @ A @ X2 @ Y )
% 0.32/0.48 => ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_cases
% 0.32/0.48 thf(fact_106_eq__refl,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( preorder @ A )
% 0.32/0.48 => ! [X2: A,Y: A] :
% 0.32/0.48 ( ( X2 = Y )
% 0.32/0.48 => ( ord_less_eq @ A @ X2 @ Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % eq_refl
% 0.32/0.48 thf(fact_107_linear,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ! [X2: A,Y: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/0.48 | ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % linear
% 0.32/0.48 thf(fact_108_antisym,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [X2: A,Y: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/0.48 => ( ( ord_less_eq @ A @ Y @ X2 )
% 0.32/0.48 => ( X2 = Y ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % antisym
% 0.32/0.48 thf(fact_109_eq__iff,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.32/0.48 = ( ^ [X4: A,Y5: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.32/0.48 & ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % eq_iff
% 0.32/0.48 thf(fact_110_ord__le__eq__subst,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType] :
% 0.32/0.48 ( ( ( ord @ B )
% 0.32/0.48 & ( ord @ A ) )
% 0.32/0.48 => ! [A2: A,B2: A,F4: A > B,C3: B] :
% 0.32/0.48 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48 => ( ( ( F4 @ B2 )
% 0.32/0.48 = C3 )
% 0.32/0.48 => ( ! [X3: A,Y3: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/0.48 => ( ord_less_eq @ B @ ( F4 @ X3 ) @ ( F4 @ Y3 ) ) )
% 0.32/0.48 => ( ord_less_eq @ B @ ( F4 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ord_le_eq_subst
% 0.32/0.48 thf(fact_111_ord__eq__le__subst,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType] :
% 0.32/0.48 ( ( ( ord @ B )
% 0.32/0.48 & ( ord @ A ) )
% 0.32/0.48 => ! [A2: A,F4: B > A,B2: B,C3: B] :
% 0.32/0.48 ( ( A2
% 0.32/0.48 = ( F4 @ B2 ) )
% 0.32/0.48 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 0.32/0.48 => ( ! [X3: B,Y3: B] :
% 0.32/0.48 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.32/0.48 => ( ord_less_eq @ A @ ( F4 @ X3 ) @ ( F4 @ Y3 ) ) )
% 0.32/0.48 => ( ord_less_eq @ A @ A2 @ ( F4 @ C3 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ord_eq_le_subst
% 0.32/0.48 thf(fact_112_order__subst2,axiom,
% 0.32/0.48 ! [A: $tType,C: $tType] :
% 0.32/0.48 ( ( ( order @ C )
% 0.32/0.48 & ( order @ A ) )
% 0.32/0.48 => ! [A2: A,B2: A,F4: A > C,C3: C] :
% 0.32/0.48 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/0.48 => ( ( ord_less_eq @ C @ ( F4 @ B2 ) @ C3 )
% 0.32/0.48 => ( ! [X3: A,Y3: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.32/0.48 => ( ord_less_eq @ C @ ( F4 @ X3 ) @ ( F4 @ Y3 ) ) )
% 0.32/0.48 => ( ord_less_eq @ C @ ( F4 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % order_subst2
% 0.32/0.48 thf(fact_113_order__subst1,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType] :
% 0.32/0.48 ( ( ( order @ B )
% 0.32/0.48 & ( order @ A ) )
% 0.32/0.48 => ! [A2: A,F4: B > A,B2: B,C3: B] :
% 0.32/0.48 ( ( ord_less_eq @ A @ A2 @ ( F4 @ B2 ) )
% 0.32/0.48 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 0.32/0.48 => ( ! [X3: B,Y3: B] :
% 0.32/0.48 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.32/0.48 => ( ord_less_eq @ A @ ( F4 @ X3 ) @ ( F4 @ Y3 ) ) )
% 0.32/0.48 => ( ord_less_eq @ A @ A2 @ ( F4 @ C3 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % order_subst1
% 0.32/0.48 thf(fact_114_le__fun__def,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( ord @ B )
% 0.32/0.48 => ( ( ord_less_eq @ ( A > B ) )
% 0.32/0.48 = ( ^ [F5: A > B,G3: A > B] :
% 0.32/0.48 ! [X4: A] : ( ord_less_eq @ B @ ( F5 @ X4 ) @ ( G3 @ X4 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_fun_def
% 0.32/0.48 thf(fact_115_le__funI,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( ord @ B )
% 0.32/0.48 => ! [F4: A > B,G4: A > B] :
% 0.32/0.48 ( ! [X3: A] : ( ord_less_eq @ B @ ( F4 @ X3 ) @ ( G4 @ X3 ) )
% 0.32/0.48 => ( ord_less_eq @ ( A > B ) @ F4 @ G4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_funI
% 0.32/0.48 thf(fact_116_le__funE,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( ord @ B )
% 0.32/0.48 => ! [F4: A > B,G4: A > B,X2: A] :
% 0.32/0.48 ( ( ord_less_eq @ ( A > B ) @ F4 @ G4 )
% 0.32/0.48 => ( ord_less_eq @ B @ ( F4 @ X2 ) @ ( G4 @ X2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_funE
% 0.32/0.48 thf(fact_117_le__funD,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( ord @ B )
% 0.32/0.48 => ! [F4: A > B,G4: A > B,X2: A] :
% 0.32/0.48 ( ( ord_less_eq @ ( A > B ) @ F4 @ G4 )
% 0.32/0.48 => ( ord_less_eq @ B @ ( F4 @ X2 ) @ ( G4 @ X2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_funD
% 0.32/0.48 thf(fact_118_Collect__mono__iff,axiom,
% 0.32/0.48 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.32/0.48 = ( ! [X4: A] :
% 0.32/0.48 ( ( P @ X4 )
% 0.32/0.48 => ( Q @ X4 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Collect_mono_iff
% 0.32/0.48 thf(fact_119_set__eq__subset,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ^ [Y4: set @ A,Z3: set @ A] : ( Y4 = Z3 ) )
% 0.32/0.48 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 0.32/0.48 & ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % set_eq_subset
% 0.32/0.48 thf(fact_120_subset__trans,axiom,
% 0.32/0.48 ! [A: $tType,A5: set @ A,B5: set @ A,C4: set @ A] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.32/0.48 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 0.32/0.48 => ( ord_less_eq @ ( set @ A ) @ A5 @ C4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_trans
% 0.32/0.48 thf(fact_121_Collect__mono,axiom,
% 0.32/0.48 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/0.48 ( ! [X3: A] :
% 0.32/0.48 ( ( P @ X3 )
% 0.32/0.48 => ( Q @ X3 ) )
% 0.32/0.48 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Collect_mono
% 0.32/0.48 thf(fact_122_subset__refl,axiom,
% 0.32/0.48 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A5 @ A5 ) ).
% 0.32/0.48
% 0.32/0.48 % subset_refl
% 0.32/0.48 thf(fact_123_subset__iff,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ A ) )
% 0.32/0.48 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.32/0.48 ! [T2: A] :
% 0.32/0.48 ( ( member @ A @ T2 @ A7 )
% 0.32/0.48 => ( member @ A @ T2 @ B7 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_iff
% 0.32/0.48 thf(fact_124_equalityD2,axiom,
% 0.32/0.48 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.32/0.48 ( ( A5 = B5 )
% 0.32/0.48 => ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ).
% 0.32/0.48
% 0.32/0.48 % equalityD2
% 0.32/0.48 thf(fact_125_equalityD1,axiom,
% 0.32/0.48 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.32/0.48 ( ( A5 = B5 )
% 0.32/0.48 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 0.32/0.48
% 0.32/0.48 % equalityD1
% 0.32/0.48 thf(fact_126_subset__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ A ) )
% 0.32/0.48 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.32/0.48 ! [X4: A] :
% 0.32/0.48 ( ( member @ A @ X4 @ A7 )
% 0.32/0.48 => ( member @ A @ X4 @ B7 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_eq
% 0.32/0.48 thf(fact_127_equalityE,axiom,
% 0.32/0.48 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 0.32/0.48 ( ( A5 = B5 )
% 0.32/0.48 => ~ ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.32/0.48 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % equalityE
% 0.32/0.48 thf(fact_128_subsetD,axiom,
% 0.32/0.48 ! [A: $tType,A5: set @ A,B5: set @ A,C3: A] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.32/0.48 => ( ( member @ A @ C3 @ A5 )
% 0.32/0.48 => ( member @ A @ C3 @ B5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subsetD
% 0.32/0.48 thf(fact_129_in__mono,axiom,
% 0.32/0.48 ! [A: $tType,A5: set @ A,B5: set @ A,X2: A] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.32/0.48 => ( ( member @ A @ X2 @ A5 )
% 0.32/0.48 => ( member @ A @ X2 @ B5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % in_mono
% 0.32/0.48 thf(fact_130_resInputBoundOutputTrans,axiom,
% 0.32/0.48 ! [X2: name,A2: name,Y: name,P: pi,B2: name,Z: name,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % resInputBoundOutputTrans
% 0.32/0.48 thf(fact_131_resTauOutputTrans,axiom,
% 0.32/0.48 ! [X2: name,P: pi,A2: name,B2: name,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % resTauOutputTrans
% 0.32/0.48 thf(fact_132_simCasesCont,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( fs_name @ A )
% 0.32/0.48 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 0.32/0.48 ( ( eqvt @ pi @ Rel )
% 0.32/0.48 => ( ! [A4: late_subject,X3: name,Q4: pi] :
% 0.32/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X3 @ Q4 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X3 @ P )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X3 @ Q )
% 0.32/0.48 => ( ( fresh @ name @ late_subject @ X3 @ A4 )
% 0.32/0.48 => ( ( fresh @ name @ A @ X3 @ C4 )
% 0.32/0.48 => ? [P6: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X3 @ P6 ) )
% 0.32/0.48 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ X3 @ Rel ) ) ) ) ) ) )
% 0.32/0.48 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.32/0.48 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.32/0.48 => ? [P6: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.32/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.32/0.48 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % simCasesCont
% 0.32/0.48 thf(fact_133_residual_Ofresh_I1_J,axiom,
% 0.32/0.48 ! [A2: name,X32: late_subject,X1: name,X22: pi] :
% 0.32/0.48 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 0.32/0.48 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 0.32/0.48 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % residual.fresh(1)
% 0.32/0.48 thf(fact_134_resCases_H,axiom,
% 0.32/0.48 ! [X2: name,P: pi,Rs: late_residual] :
% 0.32/0.48 ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 0.32/0.48 => ( ! [P4: pi,A4: name,B4: name] :
% 0.32/0.48 ( ( ( res @ X2 @ P )
% 0.32/0.48 = ( res @ B4 @ P4 ) )
% 0.32/0.48 => ! [P5: pi] :
% 0.32/0.48 ( ( Rs
% 0.32/0.48 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 0.32/0.48 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 0.32/0.48 => ( A4 = B4 ) ) ) )
% 0.32/0.48 => ( ! [P4: pi,A4: late_subject,X3: name,P5: pi,Y3: name] :
% 0.32/0.48 ( ( ( res @ X2 @ P )
% 0.32/0.48 = ( res @ Y3 @ P4 ) )
% 0.32/0.48 => ( ( Rs
% 0.32/0.48 = ( late_BoundR @ A4 @ X3 @ ( res @ Y3 @ P5 ) ) )
% 0.32/0.48 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X3 @ P5 ) )
% 0.32/0.48 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.32/0.48 => ( ( Y3 != X3 )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X3 @ P4 )
% 0.32/0.48 => ~ ( fresh @ name @ late_subject @ X3 @ A4 ) ) ) ) ) ) )
% 0.32/0.48 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.32/0.48 ( ( ( res @ X2 @ P )
% 0.32/0.48 = ( res @ Y3 @ P4 ) )
% 0.32/0.48 => ( ( Rs
% 0.32/0.48 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.32/0.48 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.32/0.48 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % resCases'
% 0.32/0.48 thf(fact_135_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.32/0.48 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 0.32/0.48 ( ( ( late_OutputR @ X22 @ X1 )
% 0.32/0.48 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.32/0.48 = ( ( X22 = Y2 )
% 0.32/0.48 & ( X1 = Y1 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics.freeRes.inject
% 0.32/0.48 thf(fact_136_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.32/0.48 ! [X1: name,Y1: name] :
% 0.32/0.48 ( ( ( late_BoundOutputS @ X1 )
% 0.32/0.48 = ( late_BoundOutputS @ Y1 ) )
% 0.32/0.48 = ( X1 = Y1 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics.subject.inject(2)
% 0.32/0.48 thf(fact_137_subject_Ofresh_I2_J,axiom,
% 0.32/0.48 ! [A2: name,X1: name] :
% 0.32/0.48 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 0.32/0.48 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.32/0.48
% 0.32/0.48 % subject.fresh(2)
% 0.32/0.48 thf(fact_138_freeRes_Ofresh_I1_J,axiom,
% 0.32/0.48 ! [A2: name,X22: name,X1: name] :
% 0.32/0.48 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 0.32/0.48 = ( ( fresh @ name @ name @ A2 @ X22 )
% 0.32/0.48 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % freeRes.fresh(1)
% 0.32/0.48 thf(fact_139_pi_Ofresh_I9_J,axiom,
% 0.32/0.48 ! [A2: name,X1: name,X22: pi] :
% 0.32/0.48 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 0.32/0.48 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.fresh(9)
% 0.32/0.48 thf(fact_140_pi_Ofresh_I4_J,axiom,
% 0.32/0.48 ! [A2: name,X32: name,X1: name,X22: pi] :
% 0.32/0.48 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X22 ) )
% 0.32/0.48 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.32/0.48 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.fresh(4)
% 0.32/0.48 thf(fact_141_monotonic,axiom,
% 0.32/0.48 ! [P: pi,A5: set @ ( product_prod @ pi @ pi ),P2: pi,B5: set @ ( product_prod @ pi @ pi )] :
% 0.32/0.48 ( ( strong743114133lation @ P @ A5 @ P2 )
% 0.32/0.48 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A5 @ B5 )
% 0.32/0.48 => ( strong743114133lation @ P @ B5 @ P2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % monotonic
% 0.32/0.48 thf(fact_142_abs__fun__eq1,axiom,
% 0.32/0.48 ! [X: $tType,A: $tType,A2: X,X2: A,Y: A] :
% 0.32/0.48 ( ( ( abs_fun @ X @ A @ A2 @ X2 )
% 0.32/0.48 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 0.32/0.48 = ( X2 = Y ) ) ).
% 0.32/0.48
% 0.32/0.48 % abs_fun_eq1
% 0.32/0.48 thf(fact_143_derivativeMonotonic,axiom,
% 0.32/0.48 ! [P: pi,Q: pi,A2: late_subject,X2: name,A5: set @ ( product_prod @ pi @ pi ),B5: set @ ( product_prod @ pi @ pi )] :
% 0.32/0.48 ( ( strong2129052853vative @ P @ Q @ A2 @ X2 @ A5 )
% 0.32/0.48 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A5 @ B5 )
% 0.32/0.48 => ( strong2129052853vative @ P @ Q @ A2 @ X2 @ B5 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % derivativeMonotonic
% 0.32/0.48 thf(fact_144_pi_Oinject_I8_J,axiom,
% 0.32/0.48 ! [X1: name,X22: pi,Y1: name,Y2: pi] :
% 0.32/0.48 ( ( ( res @ X1 @ X22 )
% 0.32/0.48 = ( res @ Y1 @ Y2 ) )
% 0.32/0.48 = ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.32/0.48 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.inject(8)
% 0.32/0.48 thf(fact_145_residual_Oinject_I1_J,axiom,
% 0.32/0.48 ! [X32: late_subject,X1: name,X22: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 0.32/0.48 ( ( ( late_BoundR @ X32 @ X1 @ X22 )
% 0.32/0.48 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 0.32/0.48 = ( ( X32 = Y32 )
% 0.32/0.48 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.32/0.48 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % residual.inject(1)
% 0.32/0.48 thf(fact_146_abs__fresh_I1_J,axiom,
% 0.32/0.48 ! [X5: $tType] :
% 0.32/0.48 ( ( fs_name @ X5 )
% 0.32/0.48 => ! [B2: name,A2: name,X2: X5] :
% 0.32/0.48 ( ( fresh @ name @ ( name > ( noption @ X5 ) ) @ B2 @ ( abs_fun @ name @ X5 @ A2 @ X2 ) )
% 0.32/0.48 = ( ( B2 = A2 )
% 0.32/0.48 | ( fresh @ name @ X5 @ B2 @ X2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % abs_fresh(1)
% 0.32/0.48 thf(fact_147_name__fresh__abs,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( fs_name @ A )
% 0.32/0.48 => ! [B2: name,A2: name,X2: A] :
% 0.32/0.48 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B2 @ ( abs_fun @ name @ A @ A2 @ X2 ) )
% 0.32/0.48 = ( ( B2 = A2 )
% 0.32/0.48 | ( fresh @ name @ A @ B2 @ X2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % name_fresh_abs
% 0.32/0.48 thf(fact_148_pi_Oinject_I3_J,axiom,
% 0.32/0.48 ! [X32: name,X1: name,X22: pi,Y32: name,Y1: name,Y2: pi] :
% 0.32/0.48 ( ( ( input @ X32 @ X1 @ X22 )
% 0.32/0.48 = ( input @ Y32 @ Y1 @ Y2 ) )
% 0.32/0.48 = ( ( X32 = Y32 )
% 0.32/0.48 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 0.32/0.48 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.inject(3)
% 0.32/0.48 thf(fact_149_simE_I1_J,axiom,
% 0.32/0.48 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X2: name,Q2: pi] :
% 0.32/0.48 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.32/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.32/0.48 => ? [P5: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P5 ) )
% 0.32/0.48 & ( strong2129052853vative @ P5 @ Q2 @ A2 @ X2 @ Rel ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % simE(1)
% 0.32/0.48 thf(fact_150_Strong__Late__Sim_Oreflexive,axiom,
% 0.32/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.32/0.48 => ( strong743114133lation @ P @ Rel @ P ) ) ).
% 0.32/0.48
% 0.32/0.48 % Strong_Late_Sim.reflexive
% 0.32/0.48 thf(fact_151_Open,axiom,
% 0.32/0.48 ! [P: pi,A2: name,B2: name,P2: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.32/0.48 => ( ( A2 != B2 )
% 0.32/0.48 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Open
% 0.32/0.48 thf(fact_152_derivativeReflexive,axiom,
% 0.32/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,A2: late_subject,X2: name] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.32/0.48 => ( strong2129052853vative @ P @ P @ A2 @ X2 @ Rel ) ) ).
% 0.32/0.48
% 0.32/0.48 % derivativeReflexive
% 0.32/0.48 thf(fact_153_simE_I2_J,axiom,
% 0.32/0.48 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.32/0.48 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.32/0.48 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.32/0.48 => ? [P5: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 0.32/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % simE(2)
% 0.32/0.48 thf(fact_154_resSimCases,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( fs_name @ A )
% 0.32/0.48 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X2: name,P: pi,C4: A] :
% 0.32/0.48 ( ( eqvt @ pi @ Rel )
% 0.32/0.48 => ( ! [Q4: pi,A4: name] :
% 0.32/0.48 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X2 ) @ Q4 ) )
% 0.32/0.48 => ( ( A4 != X2 )
% 0.32/0.48 => ? [P6: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X2 @ P6 ) )
% 0.32/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.32/0.48 => ( ! [Q4: pi,A4: late_subject,Y3: name] :
% 0.32/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 0.32/0.48 => ( ( fresh @ name @ late_subject @ X2 @ A4 )
% 0.32/0.48 => ( ( X2 != Y3 )
% 0.32/0.48 => ( ( fresh @ name @ A @ Y3 @ C4 )
% 0.32/0.48 => ? [P6: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 0.32/0.48 & ( strong2129052853vative @ P6 @ ( res @ X2 @ Q4 ) @ A4 @ Y3 @ Rel ) ) ) ) ) )
% 0.32/0.48 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.32/0.48 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.32/0.48 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha2 )
% 0.32/0.48 => ? [P6: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.32/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X2 @ Q4 ) ) @ Rel ) ) ) )
% 0.32/0.48 => ( strong743114133lation @ P @ Rel @ ( res @ X2 @ Q ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % resSimCases
% 0.32/0.48 thf(fact_155_simCases,axiom,
% 0.32/0.48 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 0.32/0.48 ( ! [A4: late_subject,Y3: name,Q4: pi] :
% 0.32/0.48 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ Y3 @ P )
% 0.32/0.48 => ? [P6: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 0.32/0.48 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ Y3 @ Rel ) ) ) )
% 0.32/0.48 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.32/0.48 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.32/0.48 => ? [P6: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.32/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.32/0.48 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % simCases
% 0.32/0.48 thf(fact_156_simulation__def,axiom,
% 0.32/0.48 ( strong743114133lation
% 0.32/0.48 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 0.32/0.48 ( ! [A6: late_subject,X4: name,Q6: pi] :
% 0.32/0.48 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A6 @ X4 @ Q6 ) )
% 0.32/0.48 & ( fresh @ name @ pi @ X4 @ P7 ) )
% 0.32/0.48 => ? [P8: pi] :
% 0.32/0.48 ( ( late_transitions @ P7 @ ( late_BoundR @ A6 @ X4 @ P8 ) )
% 0.32/0.48 & ( strong2129052853vative @ P8 @ Q6 @ A6 @ X4 @ Rel2 ) ) )
% 0.32/0.48 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.32/0.48 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.32/0.48 => ? [P8: pi] :
% 0.32/0.48 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 0.32/0.48 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % simulation_def
% 0.32/0.48 thf(fact_157_resCasesB_H,axiom,
% 0.32/0.48 ! [X6: name,P: pi,A2: late_subject,Y6: name,P2: pi] :
% 0.32/0.48 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A2 @ Y6 @ P2 ) )
% 0.32/0.48 => ( ! [P4: pi,A4: name,B4: name] :
% 0.32/0.48 ( ( ( res @ X6 @ P )
% 0.32/0.48 = ( res @ B4 @ P4 ) )
% 0.32/0.48 => ! [P5: pi] :
% 0.32/0.48 ( ( ( late_BoundR @ A2 @ Y6 @ P2 )
% 0.32/0.48 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 0.32/0.48 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 0.32/0.48 => ( A4 = B4 ) ) ) )
% 0.32/0.48 => ~ ! [P4: pi,A4: late_subject,X3: name,P5: pi,Y3: name] :
% 0.32/0.48 ( ( ( res @ X6 @ P )
% 0.32/0.48 = ( res @ Y3 @ P4 ) )
% 0.32/0.48 => ( ( ( late_BoundR @ A2 @ Y6 @ P2 )
% 0.32/0.48 = ( late_BoundR @ A4 @ X3 @ ( res @ Y3 @ P5 ) ) )
% 0.32/0.48 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X3 @ P5 ) )
% 0.32/0.48 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 0.32/0.48 => ( ( Y3 != X3 )
% 0.32/0.48 => ( ( fresh @ name @ pi @ X3 @ P4 )
% 0.32/0.48 => ~ ( fresh @ name @ late_subject @ X3 @ A4 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % resCasesB'
% 0.32/0.48 thf(fact_158_tauOutputTrans,axiom,
% 0.32/0.48 ! [P: pi,A2: name,B2: name,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % tauOutputTrans
% 0.32/0.48 thf(fact_159_inputBoundOutputTrans,axiom,
% 0.32/0.48 ! [A2: name,X2: name,P: pi,B2: name,Y: name,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % inputBoundOutputTrans
% 0.32/0.48 thf(fact_160_sumIdempRight,axiom,
% 0.32/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.32/0.48 => ( strong743114133lation @ ( sum @ P @ P ) @ Rel @ P ) ) ).
% 0.32/0.48
% 0.32/0.48 % sumIdempRight
% 0.32/0.48 thf(fact_161_sumAssocRight,axiom,
% 0.32/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R2: pi] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.32/0.48 => ( strong743114133lation @ ( sum @ P @ ( sum @ Q @ R2 ) ) @ Rel @ ( sum @ ( sum @ P @ Q ) @ R2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sumAssocRight
% 0.32/0.48 thf(fact_162_sumIdempLeft,axiom,
% 0.32/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.32/0.48 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ P ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sumIdempLeft
% 0.32/0.48 thf(fact_163_sumAssocLeft,axiom,
% 0.32/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R2: pi] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.32/0.48 => ( strong743114133lation @ ( sum @ ( sum @ P @ Q ) @ R2 ) @ Rel @ ( sum @ P @ ( sum @ Q @ R2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sumAssocLeft
% 0.32/0.48 thf(fact_164_sumSym,axiom,
% 0.32/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.32/0.48 => ( strong743114133lation @ ( sum @ P @ Q ) @ Rel @ ( sum @ Q @ P ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sumSym
% 0.32/0.48 thf(fact_165_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.32/0.48 ! [X22: name,Y2: name] :
% 0.32/0.48 ( ( ( late_BoundOutputS @ X22 )
% 0.32/0.48 = ( late_BoundOutputS @ Y2 ) )
% 0.32/0.48 = ( X22 = Y2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics1.subject.inject(2)
% 0.32/0.48 thf(fact_166_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.32/0.48 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 0.32/0.48 ( ( ( late_OutputR @ X11 @ X12 )
% 0.32/0.48 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.32/0.48 = ( ( X11 = Y11 )
% 0.32/0.48 & ( X12 = Y12 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics1.freeRes.inject
% 0.32/0.48 thf(fact_167_sumZeroRight,axiom,
% 0.32/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.32/0.48 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ piNil ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % sumZeroRight
% 0.32/0.48 thf(fact_168_sumZeroLeft,axiom,
% 0.32/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.32/0.48 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.32/0.48 => ( strong743114133lation @ ( sum @ P @ piNil ) @ Rel @ P ) ) ).
% 0.32/0.48
% 0.32/0.48 % sumZeroLeft
% 0.32/0.48 thf(fact_169_name__fresh,axiom,
% 0.32/0.48 ( ( fresh @ name @ name )
% 0.32/0.48 = ( ^ [A6: name,B6: name] : ( A6 != B6 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % name_fresh
% 0.32/0.48 thf(fact_170_pi_Ofresh_I1_J,axiom,
% 0.32/0.48 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 0.32/0.48
% 0.32/0.48 % pi.fresh(1)
% 0.32/0.48 thf(fact_171_zeroTrans,axiom,
% 0.32/0.48 ! [Rs: late_residual] :
% 0.32/0.48 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.32/0.48
% 0.32/0.48 % zeroTrans
% 0.32/0.48 thf(fact_172_nilCases_H,axiom,
% 0.32/0.48 ! [Rs: late_residual] :
% 0.32/0.48 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.32/0.48
% 0.32/0.48 % nilCases'
% 0.32/0.48 thf(fact_173_pi_Odistinct_I15_J,axiom,
% 0.32/0.48 ! [Name: name,Pi: pi] :
% 0.32/0.48 ( piNil
% 0.32/0.48 != ( res @ Name @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(15)
% 0.32/0.48 thf(fact_174_pi_Odistinct_I13_J,axiom,
% 0.32/0.48 ! [Pi12: pi,Pi22: pi] :
% 0.32/0.48 ( piNil
% 0.32/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(13)
% 0.32/0.48 thf(fact_175_pi_Odistinct_I11_J,axiom,
% 0.32/0.48 ! [Pi12: pi,Pi22: pi] :
% 0.32/0.48 ( piNil
% 0.32/0.48 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(11)
% 0.32/0.48 thf(fact_176_pi_Odistinct_I5_J,axiom,
% 0.32/0.48 ! [Name1: name,Name22: name,Pi: pi] :
% 0.32/0.48 ( piNil
% 0.32/0.48 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(5)
% 0.32/0.48 thf(fact_177_pi_Odistinct_I3_J,axiom,
% 0.32/0.48 ! [Pi: pi] :
% 0.32/0.48 ( piNil
% 0.32/0.48 != ( tau @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(3)
% 0.32/0.48 thf(fact_178_nilSimRight,axiom,
% 0.32/0.48 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.32/0.48
% 0.32/0.48 % nilSimRight
% 0.32/0.48 thf(fact_179_resZeroTrans,axiom,
% 0.32/0.48 ! [X2: name,Rs: late_residual] :
% 0.32/0.48 ~ ( late_transitions @ ( res @ X2 @ piNil ) @ Rs ) ).
% 0.32/0.48
% 0.32/0.48 % resZeroTrans
% 0.32/0.48 thf(fact_180_nilSim_I2_J,axiom,
% 0.32/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X2: name,P: pi] :
% 0.32/0.48 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X2 @ P ) ) ).
% 0.32/0.48
% 0.32/0.48 % nilSim(2)
% 0.32/0.48 thf(fact_181_nilSim_I1_J,axiom,
% 0.32/0.48 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 0.32/0.48 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.32/0.48
% 0.32/0.48 % nilSim(1)
% 0.32/0.48 thf(fact_182_inputCases_H,axiom,
% 0.32/0.48 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.32/0.48 ( ( late_transitions @ ( input @ A2 @ B2 @ P ) @ Rs )
% 0.32/0.48 => ~ ! [X3: name,A4: name,P4: pi] :
% 0.32/0.48 ( ( ( A2 = A4 )
% 0.32/0.48 & ( ( abs_fun @ name @ pi @ B2 @ P )
% 0.32/0.48 = ( abs_fun @ name @ pi @ X3 @ P4 ) ) )
% 0.32/0.48 => ( ( Rs
% 0.32/0.48 = ( late_BoundR @ ( late_InputS @ A4 ) @ X3 @ P4 ) )
% 0.32/0.48 => ( X3 = A4 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inputCases'
% 0.32/0.48 thf(fact_183_subject_Orecs_I2_J,axiom,
% 0.32/0.48 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 0.32/0.48 ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 0.32/0.48 => ( ! [X13: name] : ( P @ ( F22 @ X13 ) )
% 0.32/0.48 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name3 ) )
% 0.32/0.48 = ( F22 @ Name3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subject.recs(2)
% 0.32/0.48 thf(fact_184_freeRes_Orecs_I1_J,axiom,
% 0.32/0.48 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name12: name,Name23: name] :
% 0.32/0.48 ( ! [X13: name,X23: name] : ( P @ ( F1 @ X13 @ X23 ) )
% 0.32/0.48 => ( ( P @ F22 )
% 0.32/0.48 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name12 @ Name23 ) )
% 0.32/0.48 = ( F1 @ Name12 @ Name23 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % freeRes.recs(1)
% 0.32/0.48 thf(fact_185_subject_Ofresh_I1_J,axiom,
% 0.32/0.48 ! [A2: name,X1: name] :
% 0.32/0.48 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 0.32/0.48 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 0.32/0.48
% 0.32/0.48 % subject.fresh(1)
% 0.32/0.48 thf(fact_186_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.32/0.48 ! [X1: name,X22: name] :
% 0.32/0.48 ( ( late_InputS @ X1 )
% 0.32/0.48 != ( late_BoundOutputS @ X22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics1.subject.distinct(1)
% 0.32/0.48 thf(fact_187_subject_Oexhaust,axiom,
% 0.32/0.48 ! [Y: late_subject] :
% 0.32/0.48 ( ! [X13: name] :
% 0.32/0.48 ( Y
% 0.32/0.48 != ( late_InputS @ X13 ) )
% 0.32/0.48 => ~ ! [X23: name] :
% 0.32/0.48 ( Y
% 0.32/0.48 != ( late_BoundOutputS @ X23 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subject.exhaust
% 0.32/0.48 thf(fact_188_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.32/0.48 ! [Name3: name,Name: name] :
% 0.32/0.48 ( ( late_InputS @ Name3 )
% 0.32/0.48 != ( late_BoundOutputS @ Name ) ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics.subject.distinct(1)
% 0.32/0.48 thf(fact_189_subject_Oinducts,axiom,
% 0.32/0.48 ! [P: late_subject > $o,Subject2: late_subject] :
% 0.32/0.48 ( ! [Name2: name] : ( P @ ( late_InputS @ Name2 ) )
% 0.32/0.48 => ( ! [Name2: name] : ( P @ ( late_BoundOutputS @ Name2 ) )
% 0.32/0.48 => ( P @ Subject2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subject.inducts
% 0.32/0.48 thf(fact_190_subject_Ostrong__induct_H,axiom,
% 0.32/0.48 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject2: late_subject] :
% 0.32/0.48 ( ! [Name2: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name2 ) )
% 0.32/0.48 => ( ! [Name2: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name2 ) )
% 0.32/0.48 => ( P @ Z @ Subject2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subject.strong_induct'
% 0.32/0.48 thf(fact_191_subject_Ostrong__inducts,axiom,
% 0.32/0.48 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject2: late_subject] :
% 0.32/0.48 ( ! [Name2: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name2 ) )
% 0.32/0.48 => ( ! [Name2: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name2 ) )
% 0.32/0.48 => ( P @ Z @ Subject2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subject.strong_inducts
% 0.32/0.48 thf(fact_192_subject_Orecs_I1_J,axiom,
% 0.32/0.48 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 0.32/0.48 ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 0.32/0.48 => ( ! [X13: name] : ( P @ ( F22 @ X13 ) )
% 0.32/0.48 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name3 ) )
% 0.32/0.48 = ( F1 @ Name3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subject.recs(1)
% 0.32/0.48 thf(fact_193_Late__Semantics_OInput,axiom,
% 0.32/0.48 ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics.Input
% 0.32/0.48 thf(fact_194_transitions_OInput,axiom,
% 0.32/0.48 ! [X2: name,A2: name,P: pi] :
% 0.32/0.48 ( ( X2 != A2 )
% 0.32/0.48 => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % transitions.Input
% 0.32/0.48 thf(fact_195_resOutputInputTrans,axiom,
% 0.32/0.48 ! [X2: name,A2: name,B2: name,P: pi,C3: name,Y: name,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C3 ) @ Y @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % resOutputInputTrans
% 0.32/0.48 thf(fact_196_resOutputOutputTrans,axiom,
% 0.32/0.48 ! [X2: name,A2: name,P: pi,B2: name,Y: name,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ X2 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B2 @ Y ) @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % resOutputOutputTrans
% 0.32/0.48 thf(fact_197_Late__Semantics_OClose1,axiom,
% 0.32/0.48 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.32/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.32/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.32/0.48 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics.Close1
% 0.32/0.48 thf(fact_198_subst__identity,axiom,
% 0.32/0.48 ! [P: pi,A2: name] :
% 0.32/0.48 ( ( subs @ P @ A2 @ A2 )
% 0.32/0.48 = P ) ).
% 0.32/0.48
% 0.32/0.48 % subst_identity
% 0.32/0.48 thf(fact_199_simps_I9_J,axiom,
% 0.32/0.48 ! [X2: name,C3: name,D3: name,P: pi] :
% 0.32/0.48 ( ( X2 != C3 )
% 0.32/0.48 => ( ( X2 != D3 )
% 0.32/0.48 => ( ( subs @ ( res @ X2 @ P ) @ C3 @ D3 )
% 0.32/0.48 = ( res @ X2 @ ( subs @ P @ C3 @ D3 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % simps(9)
% 0.32/0.48 thf(fact_200_simps_I8_J,axiom,
% 0.32/0.48 ! [P: pi,Q: pi,C3: name,D3: name] :
% 0.32/0.48 ( ( subs @ ( par @ P @ Q ) @ C3 @ D3 )
% 0.32/0.48 = ( par @ ( subs @ P @ C3 @ D3 ) @ ( subs @ Q @ C3 @ D3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % simps(8)
% 0.32/0.48 thf(fact_201_substTrans,axiom,
% 0.32/0.48 ! [B2: name,P: pi,A2: name,C3: name] :
% 0.32/0.48 ( ( fresh @ name @ pi @ B2 @ P )
% 0.32/0.48 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C3 )
% 0.32/0.48 = ( subs @ P @ A2 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % substTrans
% 0.32/0.48 thf(fact_202_simps_I7_J,axiom,
% 0.32/0.48 ! [P: pi,Q: pi,C3: name,D3: name] :
% 0.32/0.48 ( ( subs @ ( sum @ P @ Q ) @ C3 @ D3 )
% 0.32/0.48 = ( sum @ ( subs @ P @ C3 @ D3 ) @ ( subs @ Q @ C3 @ D3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % simps(7)
% 0.32/0.48 thf(fact_203_simps_I2_J,axiom,
% 0.32/0.48 ! [P: pi,C3: name,D3: name] :
% 0.32/0.48 ( ( subs @ ( tau @ P ) @ C3 @ D3 )
% 0.32/0.48 = ( tau @ ( subs @ P @ C3 @ D3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % simps(2)
% 0.32/0.48 thf(fact_204_simps_I1_J,axiom,
% 0.32/0.48 ! [C3: name,D3: name] :
% 0.32/0.48 ( ( subs @ piNil @ C3 @ D3 )
% 0.32/0.48 = piNil ) ).
% 0.32/0.48
% 0.32/0.48 % simps(1)
% 0.32/0.48 thf(fact_205_freeRes_Ofresh_I2_J,axiom,
% 0.32/0.48 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 0.32/0.48
% 0.32/0.48 % freeRes.fresh(2)
% 0.32/0.48 thf(fact_206_pi_Ofresh_I2_J,axiom,
% 0.32/0.48 ! [A2: name,X32: name,X22: name,X1: pi] :
% 0.32/0.48 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X22 @ X1 ) )
% 0.32/0.48 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.32/0.48 & ( fresh @ name @ name @ A2 @ X22 )
% 0.32/0.48 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.fresh(2)
% 0.32/0.48 thf(fact_207_resOutputTauTrans,axiom,
% 0.32/0.48 ! [X2: name,A2: name,B2: name,P: pi,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % resOutputTauTrans
% 0.32/0.48 thf(fact_208_outputTauTrans,axiom,
% 0.32/0.48 ! [A2: name,B2: name,P: pi,P2: pi] :
% 0.32/0.48 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % outputTauTrans
% 0.32/0.48 thf(fact_209_pi_Odistinct_I31_J,axiom,
% 0.32/0.48 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 0.32/0.48 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.32/0.48 != ( res @ Name @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(31)
% 0.32/0.48 thf(fact_210_pi_Odistinct_I29_J,axiom,
% 0.32/0.48 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.32/0.48 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.32/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(29)
% 0.32/0.48 thf(fact_211_pi_Odistinct_I27_J,axiom,
% 0.32/0.48 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.32/0.48 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.32/0.48 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(27)
% 0.32/0.48 thf(fact_212_pi_Oinject_I1_J,axiom,
% 0.32/0.48 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.32/0.48 ( ( ( output @ X32 @ X22 @ X1 )
% 0.32/0.48 = ( output @ Y32 @ Y2 @ Y1 ) )
% 0.32/0.48 = ( ( X32 = Y32 )
% 0.32/0.48 & ( X22 = Y2 )
% 0.32/0.48 & ( X1 = Y1 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.inject(1)
% 0.32/0.48 thf(fact_213_freeRes_Ostrong__inducts,axiom,
% 0.32/0.48 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 0.32/0.48 ( ! [Name13: name,Name24: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name24 ) )
% 0.32/0.48 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 0.32/0.48 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % freeRes.strong_inducts
% 0.32/0.48 thf(fact_214_freeRes_Ostrong__induct_H,axiom,
% 0.32/0.48 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 0.32/0.48 ( ! [Name13: name,Name24: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name24 ) )
% 0.32/0.48 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 0.32/0.48 => ( P @ Z @ FreeRes3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % freeRes.strong_induct'
% 0.32/0.48 thf(fact_215_freeRes_Oinducts,axiom,
% 0.32/0.48 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.32/0.48 ( ! [Name13: name,Name24: name] : ( P @ ( late_OutputR @ Name13 @ Name24 ) )
% 0.32/0.48 => ( ( P @ late_TauR )
% 0.32/0.48 => ( P @ FreeRes3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % freeRes.inducts
% 0.32/0.48 thf(fact_216_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.32/0.48 ! [Name12: name,Name23: name] :
% 0.32/0.48 ( ( late_OutputR @ Name12 @ Name23 )
% 0.32/0.48 != late_TauR ) ).
% 0.32/0.48
% 0.32/0.48 % Late_Semantics.freeRes.distinct(1)
% 0.32/0.48 thf(fact_217_pi_Odistinct_I19_J,axiom,
% 0.32/0.48 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 0.32/0.48 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.32/0.48 != ( tau @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(19)
% 0.32/0.48 thf(fact_218_pi_Odistinct_I21_J,axiom,
% 0.32/0.48 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 0.32/0.48 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.32/0.48 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(21)
% 0.32/0.48 thf(fact_219_pi_Odistinct_I1_J,axiom,
% 0.32/0.48 ! [Name1: name,Name22: name,Pi: pi] :
% 0.32/0.48 ( piNil
% 0.32/0.48 != ( output @ Name1 @ Name22 @ Pi ) ) ).
% 0.32/0.48
% 0.32/0.48 % pi.distinct(1)
% 0.32/0.48 thf(fact_220_fresh__fact2,axiom,
% 0.32/0.48 ! [A2: name,B2: name,P: pi] :
% 0.32/0.48 ( ( A2 != B2 )
% 0.32/0.48 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % fresh_fact2
% 0.32/0.48 thf(fact_221_fresh__fact1,axiom,
% 0.32/0.48 ! [A2: name,P: pi,C3: name,B2: name] :
% 0.32/0.48 ( ( fresh @ name @ pi @ A2 @ P )
% 0.32/0.48 => ( ( A2 != C3 )
% 0.32/0.48 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % fresh_fact1
% 0.32/0.48 thf(fact_222_forget,axiom,
% 0.32/0.48 ! [A2: name,P: pi,B2: name] :
% 0.32/0.48 ( ( fresh @ name @ pi @ A2 @ P )
% 0.32/0.49 => ( ( subs @ P @ A2 @ B2 )
% 0.32/0.49 = P ) ) ).
% 0.32/0.49
% 0.32/0.49 % forget
% 0.32/0.49 thf(fact_223_freeRes_Oexhaust,axiom,
% 0.32/0.49 ! [Y: late_freeRes] :
% 0.32/0.49 ( ! [X112: name,X122: name] :
% 0.32/0.49 ( Y
% 0.32/0.49 != ( late_OutputR @ X112 @ X122 ) )
% 0.32/0.49 => ( Y = late_TauR ) ) ).
% 0.32/0.49
% 0.32/0.49 % freeRes.exhaust
% 0.32/0.49 thf(fact_224_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.32/0.49 ! [X11: name,X12: name] :
% 0.32/0.49 ( ( late_OutputR @ X11 @ X12 )
% 0.32/0.49 != late_TauR ) ).
% 0.32/0.49
% 0.32/0.49 % Late_Semantics1.freeRes.distinct(1)
% 0.32/0.49 thf(fact_225_substRes3,axiom,
% 0.32/0.49 ! [B2: name,P: pi,A2: name] :
% 0.32/0.49 ( ( fresh @ name @ pi @ B2 @ P )
% 0.32/0.49 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 0.32/0.49 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % substRes3
% 0.32/0.49 thf(fact_226_substRes2,axiom,
% 0.32/0.49 ! [B2: name,P: pi,A2: name] :
% 0.32/0.49 ( ( fresh @ name @ pi @ B2 @ P )
% 0.32/0.49 => ( ( res @ A2 @ P )
% 0.32/0.49 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % substRes2
% 0.32/0.49 thf(fact_227_resTrans_I1_J,axiom,
% 0.32/0.49 ! [X2: name,B2: name,P: pi,Rs: late_residual] :
% 0.32/0.49 ~ ( late_transitions @ ( res @ X2 @ ( output @ X2 @ B2 @ P ) ) @ Rs ) ).
% 0.32/0.49
% 0.32/0.49 % resTrans(1)
% 0.32/0.49 thf(fact_228_outputBoundTrans,axiom,
% 0.32/0.49 ! [A2: name,B2: name,P: pi,C3: late_subject,X2: name,P2: pi] :
% 0.32/0.49 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_BoundR @ C3 @ X2 @ P2 ) ) ).
% 0.32/0.49
% 0.32/0.49 % outputBoundTrans
% 0.32/0.49 thf(fact_229_nilSim_I3_J,axiom,
% 0.32/0.49 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.32/0.49 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B2 @ P ) ) ).
% 0.32/0.49
% 0.32/0.49 % nilSim(3)
% 0.32/0.49 thf(fact_230_freeRes_Orecs_I2_J,axiom,
% 0.32/0.49 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 0.32/0.49 ( ! [X13: name,X23: name] : ( P @ ( F1 @ X13 @ X23 ) )
% 0.32/0.49 => ( ( P @ F22 )
% 0.32/0.49 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 0.32/0.49 = F22 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % freeRes.recs(2)
% 0.32/0.49 thf(fact_231_Late__Semantics_OComm2,axiom,
% 0.32/0.49 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.32/0.49 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.32/0.49 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.32/0.49 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Late_Semantics.Comm2
% 0.32/0.49 thf(fact_232_Late__Semantics_OComm1,axiom,
% 0.32/0.49 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.32/0.49 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.32/0.49 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.32/0.49 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Late_Semantics.Comm1
% 0.32/0.49 thf(fact_233_Output,axiom,
% 0.32/0.49 ! [A2: name,B2: name,P: pi] : ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P ) ) ).
% 0.32/0.49
% 0.32/0.49 % Output
% 0.32/0.49 thf(fact_234_outputIneqTrans,axiom,
% 0.32/0.49 ! [A2: name,B2: name,P: pi,C3: name,D3: name,P2: pi] :
% 0.32/0.49 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ C3 @ D3 ) @ P2 ) )
% 0.32/0.49 => ~ ( ( A2 != C3 )
% 0.32/0.49 | ( B2 != D3 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % outputIneqTrans
% 0.32/0.49 thf(fact_235_outputCases_H,axiom,
% 0.32/0.49 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 0.32/0.49 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ Rs )
% 0.32/0.49 => ~ ! [A4: name,B4: name,P4: pi] :
% 0.32/0.49 ( ( ( A2 = A4 )
% 0.32/0.49 & ( B2 = B4 )
% 0.32/0.49 & ( P = P4 ) )
% 0.32/0.49 => ( Rs
% 0.32/0.49 != ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P4 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % outputCases'
% 0.32/0.49 thf(fact_236_outputCases,axiom,
% 0.32/0.49 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.32/0.49 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.32/0.49 => ( ( ( Alpha
% 0.32/0.49 = ( late_OutputR @ A2 @ B2 ) )
% 0.32/0.49 => ( ( P = P2 )
% 0.32/0.49 => ( Prop @ ( late_OutputR @ A2 @ B2 ) @ P ) ) )
% 0.32/0.49 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % outputCases
% 0.32/0.49 thf(fact_237_outputFreshTrans,axiom,
% 0.32/0.49 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.32/0.49 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.32/0.49 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 0.32/0.49 | ( fresh @ name @ late_freeRes @ B2 @ Alpha ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % outputFreshTrans
% 0.32/0.49 thf(fact_238_transitions_OComm2,axiom,
% 0.32/0.49 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.32/0.49 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 0.32/0.49 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.32/0.49 => ( ( X2 != A2 )
% 0.32/0.49 => ( ( X2 != B2 )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 0.32/0.49 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % transitions.Comm2
% 0.32/0.49 thf(fact_239_transitions_OComm1,axiom,
% 0.32/0.49 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 0.32/0.49 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.32/0.49 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.32/0.49 => ( ( X2 != A2 )
% 0.32/0.49 => ( ( X2 != B2 )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.32/0.49 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % transitions.Comm1
% 0.32/0.49 thf(fact_240_Tau,axiom,
% 0.32/0.49 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.32/0.49
% 0.32/0.49 % Tau
% 0.32/0.49 thf(fact_241_tauCases_H,axiom,
% 0.32/0.49 ! [P: pi,Rs: late_residual] :
% 0.32/0.49 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.32/0.49 => ~ ! [P4: pi] :
% 0.32/0.49 ( ( ( tau @ P )
% 0.32/0.49 = ( tau @ P4 ) )
% 0.32/0.49 => ( Rs
% 0.32/0.49 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % tauCases'
% 0.32/0.49 thf(fact_242_tauCases,axiom,
% 0.32/0.49 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.32/0.49 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.32/0.49 => ( ( ( Alpha = late_TauR )
% 0.32/0.49 => ( ( P = P2 )
% 0.32/0.49 => ( Prop @ late_TauR @ P ) ) )
% 0.32/0.49 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % tauCases
% 0.32/0.49 thf(fact_243_transitions_OClose2,axiom,
% 0.32/0.49 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.32/0.49 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.32/0.49 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.32/0.49 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/0.49 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.32/0.49 => ( ( X2 != A2 )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 0.32/0.49 => ( ( Y != A2 )
% 0.32/0.49 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 0.32/0.49 => ( ( X2 != Y )
% 0.32/0.49 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % transitions.Close2
% 0.32/0.49 thf(fact_244_transitions_OClose1,axiom,
% 0.32/0.49 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.32/0.49 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 0.32/0.49 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ P )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ Q )
% 0.32/0.49 => ( ( fresh @ name @ pi @ Y @ P )
% 0.32/0.49 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.32/0.49 => ( ( X2 != A2 )
% 0.32/0.49 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 0.32/0.49 => ( ( Y != A2 )
% 0.32/0.49 => ( ( fresh @ name @ pi @ Y @ P2 )
% 0.32/0.49 => ( ( X2 != Y )
% 0.32/0.49 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % transitions.Close1
% 0.32/0.49 thf(fact_245_Late__Semantics_OClose2,axiom,
% 0.32/0.49 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 0.32/0.49 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 0.32/0.49 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 0.32/0.49 => ( ( fresh @ name @ pi @ Y @ Q )
% 0.32/0.49 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % Late_Semantics.Close2
% 0.32/0.49 thf(fact_246_mismatchIdRight,axiom,
% 0.32/0.49 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.32/0.49 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.32/0.49 => ( ( A2 != B2 )
% 0.32/0.49 => ( strong743114133lation @ P @ Rel @ ( mismatch @ A2 @ B2 @ P ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % mismatchIdRight
% 0.32/0.49 thf(fact_247_mismatchIdLeft,axiom,
% 0.32/0.49 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 0.32/0.49 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 0.32/0.49 => ( ( A2 != B2 )
% 0.32/0.49 => ( strong743114133lation @ ( mismatch @ A2 @ B2 @ P ) @ Rel @ P ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % mismatchIdLeft
% 0.32/0.49 thf(fact_248_pi_Ofresh_I6_J,axiom,
% 0.32/0.49 ! [A2: name,X32: name,X22: name,X1: pi] :
% 0.32/0.49 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X22 @ X1 ) )
% 0.32/0.49 = ( ( fresh @ name @ name @ A2 @ X32 )
% 0.32/0.49 & ( fresh @ name @ name @ A2 @ X22 )
% 0.32/0.49 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % pi.fresh(6)
% 0.32/0.49 thf(fact_249_pi_Odistinct_I25_J,axiom,
% 0.32/0.49 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 0.32/0.49 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.32/0.49 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 0.32/0.49
% 0.32/0.49 % pi.distinct(25)
% 0.32/0.49 thf(fact_250_pi_Odistinct_I9_J,axiom,
% 0.32/0.49 ! [Name1: name,Name22: name,Pi: pi] :
% 0.32/0.49 ( piNil
% 0.32/0.49 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 0.32/0.49
% 0.32/0.49 % pi.distinct(9)
% 0.32/0.49 thf(fact_251_pi_Odistinct_I71_J,axiom,
% 0.32/0.49 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.32/0.49 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 0.32/0.49 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.32/0.49
% 0.32/0.49 % pi.distinct(71)
% 0.32/0.49 thf(fact_252_pi_Odistinct_I51_J,axiom,
% 0.32/0.49 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 0.32/0.49 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.32/0.49 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 0.32/0.49
% 0.32/0.49 % pi.distinct(51)
% 0.32/0.49 thf(fact_253_pi_Odistinct_I39_J,axiom,
% 0.32/0.49 ! [Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 0.32/0.49 ( ( tau @ Pi4 )
% 0.32/0.49 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 0.32/0.49
% 0.32/0.49 % pi.distinct(39)
% 0.32/0.49 thf(fact_254_pi_Oinject_I5_J,axiom,
% 0.32/0.49 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.32/0.49 ( ( ( mismatch @ X32 @ X22 @ X1 )
% 0.32/0.49 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 0.32/0.49 = ( ( X32 = Y32 )
% 0.32/0.49 & ( X22 = Y2 )
% 0.32/0.49 & ( X1 = Y1 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 % pi.inject(5)
% 0.32/0.49 thf(fact_255_pi_Odistinct_I73_J,axiom,
% 0.32/0.49 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.32/0.49 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 0.32/0.49 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.32/0.49
% 0.32/0.49 % pi.distinct(73)
% 0.32/0.49
% 0.32/0.49 % Type constructors (17)
% 0.32/0.49 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.32/0.49 ! [A8: $tType,A9: $tType] :
% 0.32/0.49 ( ( preorder @ A9 )
% 0.32/0.49 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.32/0.49 ! [A8: $tType,A9: $tType] :
% 0.32/0.49 ( ( order @ A9 )
% 0.32/0.49 => ( order @ ( A8 > A9 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_fun___Orderings_Oord,axiom,
% 0.32/0.49 ! [A8: $tType,A9: $tType] :
% 0.32/0.49 ( ( ord @ A9 )
% 0.32/0.49 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 0.32/0.49 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 0.32/0.49 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 0.32/0.49 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 0.32/0.49 fs_name @ pi ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 0.32/0.49 preorder @ $o ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.32/0.49 linorder @ $o ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_HOL_Obool___Orderings_Oorder_5,axiom,
% 0.32/0.49 order @ $o ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 0.32/0.49 ord @ $o ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_HOL_Obool___Agent_Ofs__name_7,axiom,
% 0.32/0.49 fs_name @ $o ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_Agent_Oname___Agent_Ofs__name_8,axiom,
% 0.32/0.49 fs_name @ name ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_9,axiom,
% 0.32/0.49 ! [A8: $tType,A9: $tType] :
% 0.32/0.49 ( ( ( fs_name @ A8 )
% 0.32/0.49 & ( fs_name @ A9 ) )
% 0.32/0.49 => ( fs_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_10,axiom,
% 0.32/0.49 fs_name @ late_freeRes ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11,axiom,
% 0.32/0.49 fs_name @ late_subject ).
% 0.32/0.49
% 0.32/0.49 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_12,axiom,
% 0.32/0.49 fs_name @ late_residual ).
% 0.32/0.49
% 0.32/0.49 % Conjectures (1)
% 0.32/0.49 thf(conj_0,conjecture,
% 0.32/0.49 y != x ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 2.83/1.51 ---- Embedded in THF ---
% 2.83/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.83/1.52 %%% Generated on Tue Feb 24 08:28:57 EST 2026
% 2.83/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.83/1.52 %%% Logic specification used:
% 2.83/1.52 %%% thf(spec, logic, $$dhol).
% 2.83/1.52
% 2.83/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xvru83IF3W/DTF2DTF31617.p
% 2.83/1.52 thf(ty_t_Late__Semantics_Oresidual, type, late_residual: $tType).
% 2.83/1.52 thf(ty_t_Late__Semantics_Osubject, type, late_subject: $tType).
% 2.83/1.52 thf(ty_t_Late__Semantics_OfreeRes, type, late_freeRes: $tType).
% 2.83/1.52 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.83/1.52 thf(ty_t_Nominal_Onoption, type, noption: ($tType > $tType)).
% 2.83/1.52 thf(ty_t_Agent_Oname, type, name: $tType).
% 2.83/1.52 thf(ty_t_Agent_Opi, type, pi: $tType).
% 2.83/1.52 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.83/1.52 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.83/1.52 thf(sy_cl_Agent_Ofs__name, type, fs_name: (!> [A:$tType]: ($o))).
% 2.83/1.52 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.83/1.52 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.83/1.52 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.83/1.52 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.83/1.52 thf(sy_c_Agent_Opi_OInput, type, input: (name > (name > (pi > pi)))).
% 2.83/1.52 thf(sy_c_Agent_Opi_OMismatch, type, mismatch: (name > (name > (pi > pi)))).
% 2.83/1.52 thf(sy_c_Agent_Opi_OOutput, type, output: (name > (name > (pi > pi)))).
% 2.83/1.52 thf(sy_c_Agent_Opi_OPar, type, par: (pi > (pi > pi))).
% 2.83/1.52 thf(sy_c_Agent_Opi_OPiNil, type, piNil: pi).
% 2.83/1.52 thf(sy_c_Agent_Opi_ORes, type, res: (name > (pi > pi))).
% 2.83/1.52 thf(sy_c_Agent_Opi_OSum, type, sum: (pi > (pi > pi))).
% 2.83/1.52 thf(sy_c_Agent_Opi_OTau, type, tau: (pi > pi)).
% 2.83/1.52 thf(sy_c_Agent_Osubs, type, subs: (pi > (name > (name > pi)))).
% 2.83/1.52 thf(sy_c_Late__Semantics_OfreeRes_OOutputR, type, late_OutputR: (name > (name > late_freeRes))).
% 2.83/1.52 thf(sy_c_Late__Semantics_OfreeRes_OTauR, type, late_TauR: late_freeRes).
% 2.83/1.52 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec, type, late_freeRes_rec: (!> [T:$tType]: (((name > (name > T)) > (T > (late_freeRes > T)))))).
% 2.83/1.52 thf(sy_c_Late__Semantics_Oresidual_OBoundR, type, late_BoundR: (late_subject > (name > (pi > late_residual)))).
% 2.83/1.52 thf(sy_c_Late__Semantics_Oresidual_OFreeR, type, late_FreeR: (late_freeRes > (pi > late_residual))).
% 2.83/1.52 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS, type, late_BoundOutputS: (name > late_subject)).
% 2.83/1.52 thf(sy_c_Late__Semantics_Osubject_OInputS, type, late_InputS: (name > late_subject)).
% 2.83/1.52 thf(sy_c_Late__Semantics_Osubject_Osubject__rec, type, late_subject_rec: (!> [T:$tType]: (((name > T) > ((name > T) > (late_subject > T)))))).
% 2.83/1.52 thf(sy_c_Late__Semantics_Otransitions, type, late_transitions: (pi > (late_residual > $o))).
% 2.83/1.52 thf(sy_c_Nominal_Oabs__fun, type, abs_fun: (!> [X:$tType,A:$tType]: ((X > (A > (X > (noption @ A))))))).
% 2.83/1.52 thf(sy_c_Nominal_Ofresh, type, fresh: (!> [X:$tType,A:$tType]: ((X > (A > $o))))).
% 2.83/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.83/1.52 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.83/1.52 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.83/1.52 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.83/1.52 thf(sy_c_Rel_Oeqvt, type, eqvt: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 2.83/1.52 thf(sy_c_Relation_OId, type, id: (!> [A:$tType]: ((set @ ((product_prod @ A) @ A))))).
% 2.83/1.52 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.83/1.52 thf(sy_c_Strong__Late__Sim_Oderivative, type, strong2129052853vative: (pi > (pi > (late_subject > (name > ((set @ ((product_prod @ pi) @ pi)) > $o)))))).
% 2.83/1.52 thf(sy_c_Strong__Late__Sim_Osimulation, type, strong743114133lation: (pi > ((set @ ((product_prod @ pi) @ pi)) > (pi > $o)))).
% 2.83/1.52 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.83/1.52 thf(sy_v_P, type, p: pi).
% 2.83/1.52 thf(sy_v_PQ____, type, pq: pi).
% 2.83/1.52 thf(sy_v_Q, type, q: pi).
% 2.83/1.52 thf(sy_v_Rel, type, rel: (set @ ((product_prod @ pi) @ pi))).
% 2.83/1.52 thf(sy_v_a____, type, a: late_subject).
% 2.83/1.52 thf(sy_v_x, type, x: name).
% 2.83/1.52 thf(sy_v_y____, type, y: name).
% 2.83/1.52 thf(fact_0_Eqvt, axiom, ((eqvt @ pi) @ rel)).
% 2.83/1.52 thf(fact_1_Bound_Ohyps_I5_J, axiom, ((((fresh @ name) @ ((product_prod @ name) @ ((product_prod @ pi) @ pi))) @ y) @ ((((product_Pair @ name) @ ((product_prod @ pi) @ pi)) @ x) @ ((((product_Pair @ pi) @ pi) @ p) @ q)))).
% 2.83/1.52 thf(fact_2_Bound_Ohyps_I4_J, axiom, ((((fresh @ name) @ late_subject) @ y) @ a)).
% 2.83/1.52 thf(fact_3_Bound_Ohyps_I3_J, axiom, ((((fresh @ name) @ pi) @ y) @ ((res @ x) @ ((sum @ p) @ q)))).
% 2.83/1.52 thf(fact_4_Bound_Ohyps_I2_J, axiom, ((((fresh @ name) @ pi) @ y) @ ((sum @ ((res @ x) @ p)) @ ((res @ x) @ q)))).
% 2.83/1.52 thf(fact_5_Bound_Ohyps_I1_J, axiom, ((late_transitions @ ((res @ x) @ ((sum @ p) @ q))) @ (((late_BoundR @ a) @ y) @ pq))).
% 2.83/1.52 thf(fact_6_fresh__prod, axiom, (! [A:$tType,X:$tType,B:$tType,A2:X,X2:A,Y:B]: ((((((fresh @ X) @ ((product_prod @ A) @ B)) @ A2) @ ((((product_Pair @ A) @ B) @ X2) @ Y)) = (((((fresh @ X) @ A) @ A2) @ X2) & ((((fresh @ X) @ B) @ A2) @ Y)))))).
% 2.83/1.52 thf(fact_7_pi_Ofresh_I7_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((sum @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.83/1.52 thf(fact_8_transitions_OResB, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X2) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X2) @ ((res @ Y) @ P2))))))))))).
% 2.83/1.52 thf(fact_9_freshBoundDerivative_I1_J, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((((fresh @ name) @ late_subject) @ Y) @ A2)))))).
% 2.83/1.52 thf(fact_10_Late__Semantics_OResB, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ late_subject) @ Y) @ A2) => ((Y != X2) => ((late_transitions @ ((res @ Y) @ P)) @ (((late_BoundR @ A2) @ X2) @ ((res @ Y) @ P2))))))))).
% 2.83/1.52 thf(fact_11_fresh__prodD_I2_J, axiom, (! [B:$tType,A:$tType,C:$tType,A2:A,X2:B,Y:C]: ((((((fresh @ A) @ ((product_prod @ B) @ C)) @ A2) @ ((((product_Pair @ B) @ C) @ X2) @ Y)) => ((((fresh @ A) @ C) @ A2) @ Y))))).
% 2.83/1.52 thf(fact_12_fresh__prodD_I1_J, axiom, (! [C:$tType,A:$tType,B:$tType,A2:A,X2:B,Y:C]: ((((((fresh @ A) @ ((product_prod @ B) @ C)) @ A2) @ ((((product_Pair @ B) @ C) @ X2) @ Y)) => ((((fresh @ A) @ B) @ A2) @ X2))))).
% 2.83/1.52 thf(fact_13_freshBoundDerivative_I2_J, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Y:name]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ Y) @ P) => ((Y != X2) => ((((fresh @ name) @ pi) @ Y) @ P2))))))).
% 2.83/1.52 thf(fact_14_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X22:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X22) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X22 = Y2)))))).
% 2.83/1.52 thf(fact_15_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) = ((A2 = A3) & (B2 = B3)))))).
% 2.83/1.52 thf(fact_16_pi_Odistinct_I81_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((sum @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 2.83/1.52 thf(fact_17_freshResidual, axiom, (! [P:pi,Rs:late_residual,X2:name]: ((((late_transitions @ P) @ Rs) => (((((fresh @ name) @ pi) @ X2) @ P) => ((((fresh @ name) @ late_residual) @ X2) @ Rs)))))).
% 2.83/1.52 thf(fact_18_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P @ Prod))))).
% 2.83/1.52 thf(fact_19_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A4:A,B4:B]: ((Y != ((((product_Pair @ A) @ B) @ A4) @ B4))))))))).
% 2.83/1.52 thf(fact_20_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) => (~ (((A2 = A3) => (B2 != B3)))))))).
% 2.83/1.52 thf(fact_21_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P3:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P @ P3))))).
% 2.83/1.52 thf(fact_22_surj__pair, axiom, (! [A:$tType,B:$tType,P3:((product_prod @ A) @ B)]: ((? [X3:A,Y3:B]: ((P3 = ((((product_Pair @ A) @ B) @ X3) @ Y3))))))).
% 2.83/1.52 thf(fact_23_name__exists__fresh, axiom, (! [A:$tType]: (((fs_name @ A) => (! [X2:A]: ((~ ((! [C2:name]: ((~ (((((fresh @ name) @ A) @ C2) @ X2))))))))))))).
% 2.83/1.52 thf(fact_24_pi_Oinject_I6_J, axiom, (! [X22:pi,X1:pi,Y2:pi,Y1:pi]: (((((sum @ X22) @ X1) = ((sum @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.83/1.52 thf(fact_25_prod__induct7, axiom, (! [G:$tType,F:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))))]: (((! [A4:A,B4:B,C2:C,D2:D,E2:E,F2:F,G2:G]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F) @ G)) @ E2) @ ((((product_Pair @ F) @ G) @ F2) @ G2))))))))) => (P @ X2))))).
% 2.83/1.52 thf(fact_26_prod__induct6, axiom, (! [F:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))))]: (((! [A4:A,B4:B,C2:C,D2:D,E2:E,F2:F]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F)) @ D2) @ ((((product_Pair @ E) @ F) @ E2) @ F2)))))))) => (P @ X2))))).
% 2.83/1.52 thf(fact_27_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A4:A,B4:B,C2:C,D2:D,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P @ X2))))).
% 2.83/1.52 thf(fact_28_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A4:A,B4:B,C2:C,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2)))))) => (P @ X2))))).
% 2.83/1.52 thf(fact_29_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X2:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A4:A,B4:B,C2:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C2))))) => (P @ X2))))).
% 2.83/1.52 thf(fact_30_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F:$tType,G:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E2:E,F2:F,G2:G]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F) @ G))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F) @ G)) @ E2) @ ((((product_Pair @ F) @ G) @ F2) @ G2)))))))))))))).
% 2.83/1.52 thf(fact_31_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E2:E,F2:F]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F)) @ D2) @ ((((product_Pair @ E) @ F) @ E2) @ F2))))))))))))).
% 2.83/1.52 thf(fact_32_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 2.83/1.52 thf(fact_33_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A4:A,B4:B,C2:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2))))))))))).
% 2.83/1.52 thf(fact_34_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A4:A,B4:B,C2:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C2)))))))))).
% 2.83/1.52 thf(fact_35_freshRes, axiom, (! [A2:name,P:pi]: (((((fresh @ name) @ pi) @ A2) @ ((res @ A2) @ P))))).
% 2.83/1.52 thf(fact_36_Sum2, axiom, (! [Q:pi,Rs:late_residual,P:pi]: ((((late_transitions @ Q) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 2.83/1.52 thf(fact_37_Sum1, axiom, (! [P:pi,Rs:late_residual,Q:pi]: ((((late_transitions @ P) @ Rs) => ((late_transitions @ ((sum @ P) @ Q)) @ Rs))))).
% 2.83/1.52 thf(fact_38_sumCases_H, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 2.83/1.52 thf(fact_39_sumCases, axiom, (! [P:pi,Q:pi,Rs:late_residual]: ((((late_transitions @ ((sum @ P) @ Q)) @ Rs) => ((~ (((late_transitions @ P) @ Rs))) => ((late_transitions @ Q) @ Rs)))))).
% 2.83/1.52 thf(fact_40_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.83/1.52 thf(fact_41_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C3 @ A2) @ B2))))).
% 2.83/1.52 thf(fact_42_Id, axiom, (((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ rel)).
% 2.83/1.52 thf(fact_43_transitions_OPar2B, axiom, (! [Q:pi,A2:late_subject,X2:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P) @ Q2)))))))))).
% 2.83/1.52 thf(fact_44_transitions_OPar1B, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ late_subject) @ X2) @ A2) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P2) @ Q)))))))))).
% 2.83/1.52 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.83/1.52 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A5)))) = A5)))).
% 2.83/1.52 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.83/1.52 thf(fact_48_parCasesB_H, axiom, (! [P:pi,Q:pi,B2:late_subject,Y:name,P2:pi]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ B2) @ Y) @ P2)) => ((! [P4:pi,A4:late_subject,X3:name,P5:pi,Q3:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q3)) => (((((late_BoundR @ B2) @ Y) @ P2) = (((late_BoundR @ A4) @ X3) @ ((par @ P5) @ Q3))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X3) @ P5)) => (((((fresh @ name) @ pi) @ X3) @ P4) => (((((fresh @ name) @ pi) @ X3) @ Q3) => (~ (((((fresh @ name) @ late_subject) @ X3) @ A4)))))))))) => (~ ((! [Q3:pi,A4:late_subject,X3:name,Q4:pi,P4:pi]: (((((par @ P) @ Q) = ((par @ P4) @ Q3)) => (((((late_BoundR @ B2) @ Y) @ P2) = (((late_BoundR @ A4) @ X3) @ ((par @ P4) @ Q4))) => (((late_transitions @ Q3) @ (((late_BoundR @ A4) @ X3) @ Q4)) => (((((fresh @ name) @ pi) @ X3) @ P4) => (((((fresh @ name) @ pi) @ X3) @ Q3) => (~ (((((fresh @ name) @ late_subject) @ X3) @ A4))))))))))))))))).
% 2.83/1.52 thf(fact_49_inputIneqTrans, axiom, (! [A2:name,X2:name,P:pi,B2:late_subject,Y:name,P2:pi]: ((((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ B2) @ Y) @ P2)) => (~ (((((fresh @ name) @ late_subject) @ A2) @ B2))))))).
% 2.83/1.52 thf(fact_50_resTauBoundTrans, axiom, (! [X2:name,P:pi,A2:late_subject,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (tau @ P))) @ (((late_BoundR @ A2) @ Y) @ P2))))))).
% 2.83/1.52 thf(fact_51_residual_Ostrong__inducts, axiom, (! [A:$tType]: (((fs_name @ A) => (! [P:(A > (late_residual > $o)),Z:A,Residual:late_residual]: (((! [Subject:late_subject,Name2:name,Pi3:pi,Z2:A]: ((((((fresh @ name) @ A) @ Name2) @ Z2) => (((((fresh @ name) @ late_subject) @ Name2) @ Subject) => ((P @ Z2) @ (((late_BoundR @ Subject) @ Name2) @ Pi3)))))) => ((! [FreeRes:late_freeRes,Pi3:pi,Z2:A]: (((P @ Z2) @ ((late_FreeR @ FreeRes) @ Pi3)))) => ((P @ Z) @ Residual))))))))).
% 2.83/1.52 thf(fact_52_residual_Ostrong__induct, axiom, (! [N:$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))))))))).
% 2.83/1.52 thf(fact_53_pi_Ofresh_I8_J, axiom, (! [A2:name,X22:pi,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((par @ X22) @ X1)) = (((((fresh @ name) @ pi) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.83/1.52 thf(fact_54_pi_Ofresh_I3_J, axiom, (! [A2:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (tau @ X1)) = ((((fresh @ name) @ pi) @ A2) @ X1))))).
% 2.83/1.52 thf(fact_55_residual_Ofresh_I2_J, axiom, (! [A2:name,X22:late_freeRes,X1:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ ((late_FreeR @ X22) @ X1)) = (((((fresh @ name) @ late_freeRes) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1)))))).
% 2.83/1.52 thf(fact_56_residual_Oinject_I2_J, axiom, (! [X22:late_freeRes,X1:pi,Y2:late_freeRes,Y1:pi]: (((((late_FreeR @ X22) @ X1) = ((late_FreeR @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.83/1.52 thf(fact_57_pi_Odistinct_I35_J, axiom, (! [Pi4:pi,Name1:name,Name22:name,Pi:pi]: (((tau @ Pi4) != (((input @ Name1) @ Name22) @ Pi))))).
% 2.83/1.52 thf(fact_58_pi_Odistinct_I43_J, axiom, (! [Pi4:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 2.83/1.52 thf(fact_59_pi_Odistinct_I55_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((input @ Name12) @ Name23) @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 2.83/1.52 thf(fact_60_pi_Oinject_I2_J, axiom, (! [X1:pi,Y1:pi]: ((((tau @ X1) = (tau @ Y1)) = (X1 = Y1))))).
% 2.83/1.52 thf(fact_61_pi_Oinject_I7_J, axiom, (! [X22:pi,X1:pi,Y2:pi,Y1:pi]: (((((par @ X22) @ X1) = ((par @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.83/1.52 thf(fact_62_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))))))).
% 2.83/1.52 thf(fact_63_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))))))).
% 2.83/1.52 thf(fact_64_inputFreeTrans, axiom, (! [A2:name,X2:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ ((late_FreeR @ Alpha) @ P2))))))).
% 2.83/1.52 thf(fact_65_resInputFreeTrans, axiom, (! [X2:name,A2:name,Y:name,P:pi,Alpha:late_freeRes,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ A2) @ Y) @ P))) @ ((late_FreeR @ Alpha) @ P2))))))).
% 2.83/1.52 thf(fact_66_pi_Odistinct_I85_J, axiom, (! [Pi1:pi,Pi2:pi,Name:name,Pi:pi]: ((((par @ Pi1) @ Pi2) != ((res @ Name) @ Pi))))).
% 2.83/1.52 thf(fact_67_pi_Odistinct_I79_J, axiom, (! [Pi1:pi,Pi2:pi,Pi12:pi,Pi22:pi]: ((((sum @ Pi1) @ Pi2) != ((par @ Pi12) @ Pi22))))).
% 2.83/1.52 thf(fact_68_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))))).
% 2.83/1.52 thf(fact_69_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)))))).
% 2.83/1.52 thf(fact_70_pi_Odistinct_I57_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name:name,Pi:pi]: (((((input @ Name12) @ Name23) @ Pi4) != ((res @ Name) @ Pi))))).
% 2.83/1.52 thf(fact_71_pi_Odistinct_I45_J, axiom, (! [Pi4:pi,Name:name,Pi:pi]: (((tau @ Pi4) != ((res @ Name) @ Pi))))).
% 2.83/1.52 thf(fact_72_pi_Odistinct_I53_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((input @ Name12) @ Name23) @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 2.83/1.52 thf(fact_73_pi_Odistinct_I41_J, axiom, (! [Pi4:pi,Pi12:pi,Pi22:pi]: (((tau @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 2.83/1.52 thf(fact_74_resCasesF, axiom, (! [X2:name,P:pi,Alpha:late_freeRes,XP:pi,F3:(pi > $o)]: ((((late_transitions @ ((res @ X2) @ P)) @ ((late_FreeR @ Alpha) @ XP)) => ((! [P5:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P5)) => (((((fresh @ name) @ late_freeRes) @ X2) @ Alpha) => (F3 @ ((res @ X2) @ P5)))))) => (F3 @ XP)))))).
% 2.83/1.52 thf(fact_75_resCasesF_H, axiom, (! [X2:name,P:pi,Alpha:late_freeRes,P2:pi]: ((((late_transitions @ ((res @ X2) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (~ ((! [P4:pi,Alpha2:late_freeRes,P5:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P4)) => ((((late_FreeR @ Alpha) @ P2) = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P5))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P5)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))).
% 2.83/1.52 thf(fact_76_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)))))))).
% 2.83/1.52 thf(fact_77_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)))))).
% 2.83/1.52 thf(fact_78_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)))))).
% 2.83/1.52 thf(fact_79_resTrans_I2_J, axiom, (! [X2:name,Y:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ X2) @ Y) @ P))) @ Rs)))))).
% 2.83/1.52 thf(fact_80_tauBoundTrans, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ (((late_BoundR @ A2) @ X2) @ P2))))))).
% 2.83/1.52 thf(fact_81_Late__Semantics_OPar1B, axiom, (! [P:pi,A2:late_subject,X2:name,P2:pi,Q:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P2)) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P2) @ Q)))))))).
% 2.83/1.52 thf(fact_82_Late__Semantics_OPar2B, axiom, (! [Q:pi,A2:late_subject,X2:name,Q2:pi,P:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => ((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ ((par @ P) @ Q2)))))))).
% 2.83/1.52 thf(fact_83_parCasesB, axiom, (! [P:pi,Q:pi,A2:late_subject,X2:name,PQ:pi,Prop:(pi > $o)]: ((((late_transitions @ ((par @ P) @ Q)) @ (((late_BoundR @ A2) @ X2) @ PQ)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((! [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P5)) => (Prop @ ((par @ P5) @ Q))))) => ((! [Q4:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q4)) => (Prop @ ((par @ P) @ Q4))))) => (Prop @ PQ))))))))).
% 2.83/1.52 thf(fact_84_IdI, axiom, (! [A:$tType,A2:A]: ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ A2)) @ (id @ A))))).
% 2.83/1.52 thf(fact_85_pair__in__Id__conv, axiom, (! [A:$tType,A2:A,B2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ (id @ A)) = (A2 = B2))))).
% 2.83/1.52 thf(fact_86_subsetI, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A5) => (((member @ A) @ X3) @ B5)))) => (((ord_less_eq @ (set @ A)) @ A5) @ B5))))).
% 2.83/1.52 thf(fact_87_subset__antisym, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ A5) => (A5 = B5)))))).
% 2.83/1.52 thf(fact_88_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ X2) @ X2))))))).
% 2.83/1.52 thf(fact_89_IdE, axiom, (! [A:$tType,P3:((product_prod @ A) @ A)]: (((((member @ ((product_prod @ A) @ A)) @ P3) @ (id @ A)) => (~ ((! [X3:A]: ((P3 != ((((product_Pair @ A) @ A) @ X3) @ X3)))))))))).
% 2.83/1.52 thf(fact_90_IdD, axiom, (! [A:$tType,A2:A,B2:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ A2) @ B2)) @ (id @ A)) => (A2 = B2))))).
% 2.83/1.52 thf(fact_91_subrelI, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((! [X3:A,Y3:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ R) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y3)) @ S)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R) @ S))))).
% 2.83/1.52 thf(fact_92_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 2.83/1.52 thf(fact_93_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [A6:A,B6:A]: (((((ord_less_eq @ A) @ B6) @ A6) & (((ord_less_eq @ A) @ A6) @ B6))))))))).
% 2.83/1.52 thf(fact_94_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C3) @ B2) => (((ord_less_eq @ A) @ C3) @ A2))))))))).
% 2.83/1.52 thf(fact_95_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((P @ A4) @ B4)))) => ((! [A4:A,B4:A]: ((((P @ B4) @ A4) => ((P @ A4) @ B4)))) => ((P @ A2) @ B2))))))))).
% 2.83/1.52 thf(fact_96_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.83/1.52 thf(fact_97_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X2) @ Z))))))))).
% 2.83/1.52 thf(fact_98_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 2.83/1.52 thf(fact_99_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.83/1.52 thf(fact_100_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C3:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.83/1.52 thf(fact_101_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [A6:A,B6:A]: (((((ord_less_eq @ A) @ A6) @ B6) & (((ord_less_eq @ A) @ B6) @ A6))))))))).
% 2.83/1.52 thf(fact_102_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X2:A]: (((((ord_less_eq @ A) @ Y) @ X2) => ((((ord_less_eq @ A) @ X2) @ Y) = (X2 = Y))))))))).
% 2.83/1.52 thf(fact_103_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A,Z:A]: ((((((ord_less_eq @ A) @ X2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z)))) => (((((ord_less_eq @ A) @ Y) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Z)))) => (((((ord_less_eq @ A) @ X2) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y)))) => (((((ord_less_eq @ A) @ Z) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X2)))) => (((((ord_less_eq @ A) @ Y) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X2)))) => (~ (((((ord_less_eq @ A) @ Z) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Y))))))))))))))))).
% 2.83/1.52 thf(fact_104_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 2.83/1.52 thf(fact_105_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y))) => (((ord_less_eq @ A) @ Y) @ X2)))))))).
% 2.83/1.52 thf(fact_106_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A]: (((X2 = Y) => (((ord_less_eq @ A) @ X2) @ Y)))))))).
% 2.83/1.52 thf(fact_107_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) | (((ord_less_eq @ A) @ Y) @ X2)))))))).
% 2.83/1.52 thf(fact_108_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((((ord_less_eq @ A) @ Y) @ X2) => (X2 = Y))))))))).
% 2.83/1.52 thf(fact_109_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X4))))))))).
% 2.83/1.52 thf(fact_110_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F4:(A > B),C3:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F4 @ B2) = C3) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ B) @ (F4 @ X3)) @ (F4 @ Y3))))) => (((ord_less_eq @ B) @ (F4 @ A2)) @ C3)))))))))).
% 2.83/1.52 thf(fact_111_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F4:(B > A),B2:B,C3:B]: (((A2 = (F4 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F4 @ X3)) @ (F4 @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F4 @ C3))))))))))).
% 2.83/1.52 thf(fact_112_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A2:A,B2:A,F4:(A > C),C3:C]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C) @ (F4 @ B2)) @ C3) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ C) @ (F4 @ X3)) @ (F4 @ Y3))))) => (((ord_less_eq @ C) @ (F4 @ A2)) @ C3)))))))))).
% 2.83/1.52 thf(fact_113_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F4:(B > A),B2:B,C3:B]: (((((ord_less_eq @ A) @ A2) @ (F4 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C3) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F4 @ X3)) @ (F4 @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F4 @ C3))))))))))).
% 2.83/1.52 thf(fact_114_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F5:(A > B),G3:(A > B)]: ((! [X4:A]: ((((ord_less_eq @ B) @ (F5 @ X4)) @ (G3 @ X4))))))))))).
% 2.83/1.52 thf(fact_115_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F4:(A > B),G4:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F4 @ X3)) @ (G4 @ X3)))) => (((ord_less_eq @ (A > B)) @ F4) @ G4)))))))).
% 2.83/1.52 thf(fact_116_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F4:(A > B),G4:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F4) @ G4) => (((ord_less_eq @ B) @ (F4 @ X2)) @ (G4 @ X2))))))))).
% 2.83/1.52 thf(fact_117_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F4:(A > B),G4:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F4) @ G4) => (((ord_less_eq @ B) @ (F4 @ X2)) @ (G4 @ X2))))))))).
% 2.83/1.52 thf(fact_118_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X4:A]: (((P @ X4) => (Q @ X4)))))))).
% 2.83/1.52 thf(fact_119_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y4:(set @ A),Z3:(set @ A)]: ((Y4 = Z3))) = (^ [A7:(set @ A),B7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ B7) & (((ord_less_eq @ (set @ A)) @ B7) @ A7)))))))).
% 2.83/1.52 thf(fact_120_subset__trans, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ C4) => (((ord_less_eq @ (set @ A)) @ A5) @ C4)))))).
% 2.83/1.52 thf(fact_121_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.83/1.52 thf(fact_122_subset__refl, axiom, (! [A:$tType,A5:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A5) @ A5)))).
% 2.83/1.52 thf(fact_123_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A7) => (((member @ A) @ T2) @ B7)))))))))).
% 2.83/1.52 thf(fact_124_equalityD2, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (((ord_less_eq @ (set @ A)) @ B5) @ A5))))).
% 2.83/1.52 thf(fact_125_equalityD1, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (((ord_less_eq @ (set @ A)) @ A5) @ B5))))).
% 2.83/1.52 thf(fact_126_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: ((! [X4:A]: (((((member @ A) @ X4) @ A7) => (((member @ A) @ X4) @ B7)))))))))).
% 2.83/1.52 thf(fact_127_equalityE, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A)]: (((A5 = B5) => (~ (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => (~ ((((ord_less_eq @ (set @ A)) @ B5) @ A5)))))))))).
% 2.83/1.52 thf(fact_128_subsetD, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((member @ A) @ C3) @ A5) => (((member @ A) @ C3) @ B5)))))).
% 2.83/1.52 thf(fact_129_in__mono, axiom, (! [A:$tType,A5:(set @ A),B5:(set @ A),X2:A]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) => ((((member @ A) @ X2) @ A5) => (((member @ A) @ X2) @ B5)))))).
% 2.83/1.52 thf(fact_130_resInputBoundOutputTrans, axiom, (! [X2:name,A2:name,Y:name,P:pi,B2:name,Z:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((input @ A2) @ Y) @ P))) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Z) @ P2))))))).
% 2.83/1.52 thf(fact_131_resTauOutputTrans, axiom, (! [X2:name,P:pi,A2:name,B2:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (tau @ P))) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2))))))).
% 2.83/1.52 thf(fact_132_simCasesCont, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,P:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [A4:late_subject,X3:name,Q4:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ X3) @ Q4)) => (((((fresh @ name) @ pi) @ X3) @ P) => (((((fresh @ name) @ pi) @ X3) @ Q) => (((((fresh @ name) @ late_subject) @ X3) @ A4) => (((((fresh @ name) @ A) @ X3) @ C4) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ X3) @ P6)) & (((((strong2129052853vative @ P6) @ Q4) @ A4) @ X3) @ Rel))))))))))) => ((! [Alpha2:late_freeRes,Q4:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q4)) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q4)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))))))).
% 2.83/1.52 thf(fact_133_residual_Ofresh_I1_J, axiom, (! [A2:name,X32:late_subject,X1:name,X22:pi]: ((((((fresh @ name) @ late_residual) @ A2) @ (((late_BoundR @ X32) @ X1) @ X22)) = (((((fresh @ name) @ late_subject) @ A2) @ X32) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22))))))).
% 2.83/1.52 thf(fact_134_resCases_H, axiom, (! [X2:name,P:pi,Rs:late_residual]: ((((late_transitions @ ((res @ X2) @ P)) @ Rs) => ((! [P4:pi,A4:name,B4:name]: (((((res @ X2) @ P) = ((res @ B4) @ P4)) => (! [P5:pi]: (((Rs = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B4) @ P5)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A4) @ B4)) @ P5)) => (A4 = B4)))))))) => ((! [P4:pi,A4:late_subject,X3:name,P5:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P4)) => ((Rs = (((late_BoundR @ A4) @ X3) @ ((res @ Y3) @ P5))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X3) @ P5)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X3) => (((((fresh @ name) @ pi) @ X3) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X3) @ A4))))))))))) => (~ ((! [P4:pi,Alpha2:late_freeRes,P5:pi,Y3:name]: (((((res @ X2) @ P) = ((res @ Y3) @ P4)) => ((Rs = ((late_FreeR @ Alpha2) @ ((res @ Y3) @ P5))) => (((late_transitions @ P4) @ ((late_FreeR @ Alpha2) @ P5)) => (~ (((((fresh @ name) @ late_freeRes) @ Y3) @ Alpha2)))))))))))))))).
% 2.83/1.52 thf(fact_135_Late__Semantics_OfreeRes_Oinject, axiom, (! [X22:name,X1:name,Y2:name,Y1:name]: (((((late_OutputR @ X22) @ X1) = ((late_OutputR @ Y2) @ Y1)) = ((X22 = Y2) & (X1 = Y1)))))).
% 2.83/1.52 thf(fact_136_Late__Semantics_Osubject_Oinject_I2_J, axiom, (! [X1:name,Y1:name]: ((((late_BoundOutputS @ X1) = (late_BoundOutputS @ Y1)) = (X1 = Y1))))).
% 2.83/1.52 thf(fact_137_subject_Ofresh_I2_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_BoundOutputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 2.83/1.52 thf(fact_138_freeRes_Ofresh_I1_J, axiom, (! [A2:name,X22:name,X1:name]: ((((((fresh @ name) @ late_freeRes) @ A2) @ ((late_OutputR @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ name) @ A2) @ X1)))))).
% 2.83/1.52 thf(fact_139_pi_Ofresh_I9_J, axiom, (! [A2:name,X1:name,X22:pi]: ((((((fresh @ name) @ pi) @ A2) @ ((res @ X1) @ X22)) = ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22)))))).
% 2.83/1.52 thf(fact_140_pi_Ofresh_I4_J, axiom, (! [A2:name,X32:name,X1:name,X22:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((input @ X32) @ X1) @ X22)) = (((((fresh @ name) @ name) @ A2) @ X32) & ((((fresh @ name) @ (name > (noption @ pi))) @ A2) @ ((((abs_fun @ name) @ pi) @ X1) @ X22))))))).
% 2.83/1.52 thf(fact_141_monotonic, axiom, (! [P:pi,A5:(set @ ((product_prod @ pi) @ pi)),P2:pi,B5:(set @ ((product_prod @ pi) @ pi))]: (((((strong743114133lation @ P) @ A5) @ P2) => ((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ A5) @ B5) => (((strong743114133lation @ P) @ B5) @ P2)))))).
% 2.83/1.52 thf(fact_142_abs__fun__eq1, axiom, (! [X:$tType,A:$tType,A2:X,X2:A,Y:A]: (((((((abs_fun @ X) @ A) @ A2) @ X2) = ((((abs_fun @ X) @ A) @ A2) @ Y)) = (X2 = Y))))).
% 2.83/1.52 thf(fact_143_derivativeMonotonic, axiom, (! [P:pi,Q:pi,A2:late_subject,X2:name,A5:(set @ ((product_prod @ pi) @ pi)),B5:(set @ ((product_prod @ pi) @ pi))]: (((((((strong2129052853vative @ P) @ Q) @ A2) @ X2) @ A5) => ((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ A5) @ B5) => (((((strong2129052853vative @ P) @ Q) @ A2) @ X2) @ B5)))))).
% 2.83/1.52 thf(fact_144_pi_Oinject_I8_J, axiom, (! [X1:name,X22:pi,Y1:name,Y2:pi]: (((((res @ X1) @ X22) = ((res @ Y1) @ Y2)) = (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2)))))).
% 2.83/1.52 thf(fact_145_residual_Oinject_I1_J, axiom, (! [X32:late_subject,X1:name,X22:pi,Y32:late_subject,Y1:name,Y2:pi]: ((((((late_BoundR @ X32) @ X1) @ X22) = (((late_BoundR @ Y32) @ Y1) @ Y2)) = ((X32 = Y32) & (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2))))))).
% 2.83/1.52 thf(fact_146_abs__fresh_I1_J, axiom, (! [X5:$tType]: (((fs_name @ X5) => (! [B2:name,A2:name,X2:X5]: ((((((fresh @ name) @ (name > (noption @ X5))) @ B2) @ ((((abs_fun @ name) @ X5) @ A2) @ X2)) = ((B2 = A2) | ((((fresh @ name) @ X5) @ B2) @ X2))))))))).
% 2.83/1.52 thf(fact_147_name__fresh__abs, axiom, (! [A:$tType]: (((fs_name @ A) => (! [B2:name,A2:name,X2:A]: ((((((fresh @ name) @ (name > (noption @ A))) @ B2) @ ((((abs_fun @ name) @ A) @ A2) @ X2)) = ((B2 = A2) | ((((fresh @ name) @ A) @ B2) @ X2))))))))).
% 2.83/1.52 thf(fact_148_pi_Oinject_I3_J, axiom, (! [X32:name,X1:name,X22:pi,Y32:name,Y1:name,Y2:pi]: ((((((input @ X32) @ X1) @ X22) = (((input @ Y32) @ Y1) @ Y2)) = ((X32 = Y32) & (((((abs_fun @ name) @ pi) @ X1) @ X22) = ((((abs_fun @ name) @ pi) @ Y1) @ Y2))))))).
% 2.83/1.52 thf(fact_149_simE_I1_J, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,A2:late_subject,X2:name,Q2:pi]: (((((strong743114133lation @ P) @ Rel) @ Q) => (((late_transitions @ Q) @ (((late_BoundR @ A2) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (? [P5:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A2) @ X2) @ P5)) & (((((strong2129052853vative @ P5) @ Q2) @ A2) @ X2) @ Rel)))))))))).
% 2.83/1.52 thf(fact_150_Strong__Late__Sim_Oreflexive, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ P) @ Rel) @ P))))).
% 2.83/1.52 thf(fact_151_Open, axiom, (! [P:pi,A2:name,B2:name,P2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => ((A2 != B2) => ((late_transitions @ ((res @ B2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ B2) @ P2))))))).
% 2.83/1.52 thf(fact_152_derivativeReflexive, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,A2:late_subject,X2:name]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((((strong2129052853vative @ P) @ P) @ A2) @ X2) @ Rel))))).
% 2.83/1.52 thf(fact_153_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)) => (? [P5:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha) @ P5)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P5) @ Q2)) @ Rel))))))))).
% 2.83/1.52 thf(fact_154_resSimCases, axiom, (! [A:$tType]: (((fs_name @ A) => (! [Rel:(set @ ((product_prod @ pi) @ pi)),Q:pi,X2:name,P:pi,C4:A]: ((((eqvt @ pi) @ Rel) => ((! [Q4:pi,A4:name]: ((((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A4) @ X2)) @ Q4)) => ((A4 != X2) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A4)) @ X2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q4)) @ Rel)))))))) => ((! [Q4:pi,A4:late_subject,Y3:name]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y3) @ Q4)) => (((((fresh @ name) @ late_subject) @ X2) @ A4) => ((X2 != Y3) => (((((fresh @ name) @ A) @ Y3) @ C4) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ Y3) @ P6)) & (((((strong2129052853vative @ P6) @ ((res @ X2) @ Q4)) @ A4) @ Y3) @ Rel)))))))))) => ((! [Q4:pi,Alpha2:late_freeRes]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q4)) => (((((fresh @ name) @ late_freeRes) @ X2) @ Alpha2) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ ((res @ X2) @ Q4))) @ Rel)))))))) => (((strong743114133lation @ P) @ Rel) @ ((res @ X2) @ Q)))))))))))).
% 2.83/1.52 thf(fact_155_simCases, axiom, (! [Q:pi,P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: (((! [A4:late_subject,Y3:name,Q4:pi]: ((((late_transitions @ Q) @ (((late_BoundR @ A4) @ Y3) @ Q4)) => (((((fresh @ name) @ pi) @ Y3) @ P) => (? [P6:pi]: ((((late_transitions @ P) @ (((late_BoundR @ A4) @ Y3) @ P6)) & (((((strong2129052853vative @ P6) @ Q4) @ A4) @ Y3) @ Rel)))))))) => ((! [Alpha2:late_freeRes,Q4:pi]: ((((late_transitions @ Q) @ ((late_FreeR @ Alpha2) @ Q4)) => (? [P6:pi]: ((((late_transitions @ P) @ ((late_FreeR @ Alpha2) @ P6)) & (((member @ ((product_prod @ pi) @ pi)) @ ((((product_Pair @ pi) @ pi) @ P6) @ Q4)) @ Rel))))))) => (((strong743114133lation @ P) @ Rel) @ Q)))))).
% 2.83/1.52 thf(fact_156_simulation__def, axiom, (strong743114133lation = (^ [P7:pi,Rel2:(set @ ((product_prod @ pi) @ pi)),Q5:pi]: (((! [A6:late_subject,X4:name,Q6:pi]: (((((late_transitions @ Q5) @ (((late_BoundR @ A6) @ X4) @ Q6)) & ((((fresh @ name) @ pi) @ X4) @ P7)) => (? [P8:pi]: ((((late_transitions @ P7) @ (((late_BoundR @ A6) @ X4) @ P8)) & (((((strong2129052853vative @ P8) @ Q6) @ A6) @ 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)))))))))))).
% 2.83/1.52 thf(fact_157_resCasesB_H, axiom, (! [X6:name,P:pi,A2:late_subject,Y6:name,P2:pi]: ((((late_transitions @ ((res @ X6) @ P)) @ (((late_BoundR @ A2) @ Y6) @ P2)) => ((! [P4:pi,A4:name,B4:name]: (((((res @ X6) @ P) = ((res @ B4) @ P4)) => (! [P5:pi]: ((((((late_BoundR @ A2) @ Y6) @ P2) = (((late_BoundR @ (late_BoundOutputS @ A4)) @ B4) @ P5)) => (((late_transitions @ P4) @ ((late_FreeR @ ((late_OutputR @ A4) @ B4)) @ P5)) => (A4 = B4)))))))) => (~ ((! [P4:pi,A4:late_subject,X3:name,P5:pi,Y3:name]: (((((res @ X6) @ P) = ((res @ Y3) @ P4)) => (((((late_BoundR @ A2) @ Y6) @ P2) = (((late_BoundR @ A4) @ X3) @ ((res @ Y3) @ P5))) => (((late_transitions @ P4) @ (((late_BoundR @ A4) @ X3) @ P5)) => (((((fresh @ name) @ late_subject) @ Y3) @ A4) => ((Y3 != X3) => (((((fresh @ name) @ pi) @ X3) @ P4) => (~ (((((fresh @ name) @ late_subject) @ X3) @ A4)))))))))))))))))).
% 2.83/1.52 thf(fact_158_tauOutputTrans, axiom, (! [P:pi,A2:name,B2:name,P2:pi]: ((~ (((late_transitions @ (tau @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2))))))).
% 2.83/1.52 thf(fact_159_inputBoundOutputTrans, axiom, (! [A2:name,X2:name,P:pi,B2:name,Y:name,P2:pi]: ((~ (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_BoundOutputS @ B2)) @ Y) @ P2))))))).
% 2.83/1.52 thf(fact_160_sumIdempRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ P)) @ Rel) @ P))))).
% 2.83/1.52 thf(fact_161_sumAssocRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi,R2:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ ((sum @ Q) @ R2))) @ Rel) @ ((sum @ ((sum @ P) @ Q)) @ R2)))))).
% 2.83/1.52 thf(fact_162_sumIdempLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ P) @ Rel) @ ((sum @ P) @ P)))))).
% 2.83/1.52 thf(fact_163_sumAssocLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi,R2:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ ((sum @ P) @ Q)) @ R2)) @ Rel) @ ((sum @ P) @ ((sum @ Q) @ R2))))))).
% 2.83/1.52 thf(fact_164_sumSym, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi,Q:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ Q)) @ Rel) @ ((sum @ Q) @ P)))))).
% 2.83/1.52 thf(fact_165_Late__Semantics1_Osubject_Oinject_I2_J, axiom, (! [X22:name,Y2:name]: ((((late_BoundOutputS @ X22) = (late_BoundOutputS @ Y2)) = (X22 = Y2))))).
% 2.83/1.52 thf(fact_166_Late__Semantics1_OfreeRes_Oinject, axiom, (! [X11:name,X12:name,Y11:name,Y12:name]: (((((late_OutputR @ X11) @ X12) = ((late_OutputR @ Y11) @ Y12)) = ((X11 = Y11) & (X12 = Y12)))))).
% 2.83/1.52 thf(fact_167_sumZeroRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ P) @ Rel) @ ((sum @ P) @ piNil)))))).
% 2.83/1.52 thf(fact_168_sumZeroLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => (((strong743114133lation @ ((sum @ P) @ piNil)) @ Rel) @ P))))).
% 2.83/1.52 thf(fact_169_name__fresh, axiom, (((fresh @ name) @ name) = (^ [A6:name,B6:name]: ((A6 != B6))))).
% 2.83/1.52 thf(fact_170_pi_Ofresh_I1_J, axiom, (! [A2:name]: (((((fresh @ name) @ pi) @ A2) @ piNil)))).
% 2.83/1.52 thf(fact_171_zeroTrans, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 2.83/1.52 thf(fact_172_nilCases_H, axiom, (! [Rs:late_residual]: ((~ (((late_transitions @ piNil) @ Rs)))))).
% 2.83/1.52 thf(fact_173_pi_Odistinct_I15_J, axiom, (! [Name:name,Pi:pi]: ((piNil != ((res @ Name) @ Pi))))).
% 2.83/1.52 thf(fact_174_pi_Odistinct_I13_J, axiom, (! [Pi12:pi,Pi22:pi]: ((piNil != ((par @ Pi12) @ Pi22))))).
% 2.83/1.52 thf(fact_175_pi_Odistinct_I11_J, axiom, (! [Pi12:pi,Pi22:pi]: ((piNil != ((sum @ Pi12) @ Pi22))))).
% 2.83/1.52 thf(fact_176_pi_Odistinct_I5_J, axiom, (! [Name1:name,Name22:name,Pi:pi]: ((piNil != (((input @ Name1) @ Name22) @ Pi))))).
% 2.83/1.52 thf(fact_177_pi_Odistinct_I3_J, axiom, (! [Pi:pi]: ((piNil != (tau @ Pi))))).
% 2.83/1.52 thf(fact_178_nilSimRight, axiom, (! [P:pi,Rel:(set @ ((product_prod @ pi) @ pi))]: ((((strong743114133lation @ P) @ Rel) @ piNil)))).
% 2.83/1.52 thf(fact_179_resZeroTrans, axiom, (! [X2:name,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ piNil)) @ Rs)))))).
% 2.83/1.52 thf(fact_180_nilSim_I2_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,X2:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((input @ A2) @ X2) @ P))))))).
% 2.83/1.52 thf(fact_181_nilSim_I1_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (tau @ P))))))).
% 2.83/1.52 thf(fact_182_inputCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((input @ A2) @ B2) @ P)) @ Rs) => (~ ((! [X3:name,A4:name,P4:pi]: ((((A2 = A4) & (((((abs_fun @ name) @ pi) @ B2) @ P) = ((((abs_fun @ name) @ pi) @ X3) @ P4))) => ((Rs = (((late_BoundR @ (late_InputS @ A4)) @ X3) @ P4)) => (X3 = A4))))))))))).
% 2.83/1.52 thf(fact_183_subject_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F22:(name > T),Name3:name]: (((! [X13:name]: ((P @ (F1 @ X13)))) => ((! [X13:name]: ((P @ (F22 @ X13)))) => (((((late_subject_rec @ T) @ F1) @ F22) @ (late_BoundOutputS @ Name3)) = (F22 @ Name3))))))).
% 2.83/1.52 thf(fact_184_freeRes_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F22:T,Name12:name,Name23:name]: (((! [X13:name,X23:name]: ((P @ ((F1 @ X13) @ X23)))) => ((P @ F22) => (((((late_freeRes_rec @ T) @ F1) @ F22) @ ((late_OutputR @ Name12) @ Name23)) = ((F1 @ Name12) @ Name23))))))).
% 2.83/1.52 thf(fact_185_subject_Ofresh_I1_J, axiom, (! [A2:name,X1:name]: ((((((fresh @ name) @ late_subject) @ A2) @ (late_InputS @ X1)) = ((((fresh @ name) @ name) @ A2) @ X1))))).
% 2.83/1.52 thf(fact_186_Late__Semantics1_Osubject_Odistinct_I1_J, axiom, (! [X1:name,X22:name]: (((late_InputS @ X1) != (late_BoundOutputS @ X22))))).
% 2.83/1.52 thf(fact_187_subject_Oexhaust, axiom, (! [Y:late_subject]: (((! [X13:name]: ((Y != (late_InputS @ X13)))) => (~ ((! [X23:name]: ((Y != (late_BoundOutputS @ X23)))))))))).
% 2.83/1.52 thf(fact_188_Late__Semantics_Osubject_Odistinct_I1_J, axiom, (! [Name3:name,Name:name]: (((late_InputS @ Name3) != (late_BoundOutputS @ Name))))).
% 2.83/1.52 thf(fact_189_subject_Oinducts, axiom, (! [P:(late_subject > $o),Subject2:late_subject]: (((! [Name2:name]: ((P @ (late_InputS @ Name2)))) => ((! [Name2:name]: ((P @ (late_BoundOutputS @ Name2)))) => (P @ Subject2)))))).
% 2.83/1.52 thf(fact_190_subject_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_subject > $o)),Z:N,Subject2:late_subject]: (((! [Name2:name,Z2:N]: (((P @ Z2) @ (late_InputS @ Name2)))) => ((! [Name2:name,Z2:N]: (((P @ Z2) @ (late_BoundOutputS @ Name2)))) => ((P @ Z) @ Subject2)))))).
% 2.83/1.52 thf(fact_191_subject_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_subject > $o)),Z:A,Subject2:late_subject]: (((! [Name2:name,Z2:A]: (((P @ Z2) @ (late_InputS @ Name2)))) => ((! [Name2:name,Z2:A]: (((P @ Z2) @ (late_BoundOutputS @ Name2)))) => ((P @ Z) @ Subject2)))))).
% 2.83/1.52 thf(fact_192_subject_Orecs_I1_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > T),F22:(name > T),Name3:name]: (((! [X13:name]: ((P @ (F1 @ X13)))) => ((! [X13:name]: ((P @ (F22 @ X13)))) => (((((late_subject_rec @ T) @ F1) @ F22) @ (late_InputS @ Name3)) = (F1 @ Name3))))))).
% 2.83/1.52 thf(fact_193_Late__Semantics_OInput, axiom, (! [A2:name,X2:name,P:pi]: (((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P))))).
% 2.83/1.52 thf(fact_194_transitions_OInput, axiom, (! [X2:name,A2:name,P:pi]: (((X2 != A2) => ((late_transitions @ (((input @ A2) @ X2) @ P)) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P)))))).
% 2.83/1.52 thf(fact_195_resOutputInputTrans, axiom, (! [X2:name,A2:name,B2:name,P:pi,C3:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ B2) @ P))) @ (((late_BoundR @ (late_InputS @ C3)) @ Y) @ P2))))))).
% 2.83/1.52 thf(fact_196_resOutputOutputTrans, axiom, (! [X2:name,A2:name,P:pi,B2:name,Y:name,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ X2) @ P))) @ ((late_FreeR @ ((late_OutputR @ B2) @ Y)) @ P2))))))).
% 2.83/1.52 thf(fact_197_Late__Semantics_OClose1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ 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) @ X2) @ Y)) @ Q2)))))))))).
% 2.83/1.52 thf(fact_198_subst__identity, axiom, (! [P:pi,A2:name]: (((((subs @ P) @ A2) @ A2) = P)))).
% 2.83/1.52 thf(fact_199_simps_I9_J, axiom, (! [X2:name,C3:name,D3:name,P:pi]: (((X2 != C3) => ((X2 != D3) => ((((subs @ ((res @ X2) @ P)) @ C3) @ D3) = ((res @ X2) @ (((subs @ P) @ C3) @ D3)))))))).
% 2.83/1.52 thf(fact_200_simps_I8_J, axiom, (! [P:pi,Q:pi,C3:name,D3:name]: (((((subs @ ((par @ P) @ Q)) @ C3) @ D3) = ((par @ (((subs @ P) @ C3) @ D3)) @ (((subs @ Q) @ C3) @ D3)))))).
% 2.83/1.52 thf(fact_201_substTrans, axiom, (! [B2:name,P:pi,A2:name,C3:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ (((subs @ P) @ A2) @ B2)) @ B2) @ C3) = (((subs @ P) @ A2) @ C3)))))).
% 2.83/1.52 thf(fact_202_simps_I7_J, axiom, (! [P:pi,Q:pi,C3:name,D3:name]: (((((subs @ ((sum @ P) @ Q)) @ C3) @ D3) = ((sum @ (((subs @ P) @ C3) @ D3)) @ (((subs @ Q) @ C3) @ D3)))))).
% 2.83/1.52 thf(fact_203_simps_I2_J, axiom, (! [P:pi,C3:name,D3:name]: (((((subs @ (tau @ P)) @ C3) @ D3) = (tau @ (((subs @ P) @ C3) @ D3)))))).
% 2.83/1.52 thf(fact_204_simps_I1_J, axiom, (! [C3:name,D3:name]: (((((subs @ piNil) @ C3) @ D3) = piNil)))).
% 2.83/1.52 thf(fact_205_freeRes_Ofresh_I2_J, axiom, (! [A2:name]: (((((fresh @ name) @ late_freeRes) @ A2) @ late_TauR)))).
% 2.83/1.52 thf(fact_206_pi_Ofresh_I2_J, axiom, (! [A2:name,X32:name,X22:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((output @ X32) @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X32) & (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 2.83/1.52 thf(fact_207_resOutputTauTrans, axiom, (! [X2:name,A2:name,B2:name,P:pi,P2:pi]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ A2) @ B2) @ P))) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 2.83/1.52 thf(fact_208_outputTauTrans, axiom, (! [A2:name,B2:name,P:pi,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ late_TauR) @ P2))))))).
% 2.83/1.52 thf(fact_209_pi_Odistinct_I31_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name:name,Pi:pi]: (((((output @ Name12) @ Name23) @ Pi4) != ((res @ Name) @ Pi))))).
% 2.83/1.52 thf(fact_210_pi_Odistinct_I29_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((output @ Name12) @ Name23) @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 2.83/1.52 thf(fact_211_pi_Odistinct_I27_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((output @ Name12) @ Name23) @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 2.83/1.52 thf(fact_212_pi_Oinject_I1_J, axiom, (! [X32:name,X22:name,X1:pi,Y32:name,Y2:name,Y1:pi]: ((((((output @ X32) @ X22) @ X1) = (((output @ Y32) @ Y2) @ Y1)) = ((X32 = Y32) & ((X22 = Y2) & (X1 = Y1))))))).
% 2.83/1.52 thf(fact_213_freeRes_Ostrong__inducts, axiom, (! [A:$tType,P:(A > (late_freeRes > $o)),Z:A,FreeRes3:late_freeRes]: (((! [Name13:name,Name24:name,Z2:A]: (((P @ Z2) @ ((late_OutputR @ Name13) @ Name24)))) => ((! [Z2:A]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 2.83/1.52 thf(fact_214_freeRes_Ostrong__induct_H, axiom, (! [N:$tType,P:(N > (late_freeRes > $o)),Z:N,FreeRes3:late_freeRes]: (((! [Name13:name,Name24:name,Z2:N]: (((P @ Z2) @ ((late_OutputR @ Name13) @ Name24)))) => ((! [Z2:N]: (((P @ Z2) @ late_TauR))) => ((P @ Z) @ FreeRes3)))))).
% 2.83/1.52 thf(fact_215_freeRes_Oinducts, axiom, (! [P:(late_freeRes > $o),FreeRes3:late_freeRes]: (((! [Name13:name,Name24:name]: ((P @ ((late_OutputR @ Name13) @ Name24)))) => ((P @ late_TauR) => (P @ FreeRes3)))))).
% 2.83/1.52 thf(fact_216_Late__Semantics_OfreeRes_Odistinct_I1_J, axiom, (! [Name12:name,Name23:name]: ((((late_OutputR @ Name12) @ Name23) != late_TauR)))).
% 2.83/1.52 thf(fact_217_pi_Odistinct_I19_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi:pi]: (((((output @ Name12) @ Name23) @ Pi4) != (tau @ Pi))))).
% 2.83/1.52 thf(fact_218_pi_Odistinct_I21_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name1:name,Name22:name,Pi:pi]: (((((output @ Name12) @ Name23) @ Pi4) != (((input @ Name1) @ Name22) @ Pi))))).
% 2.83/1.52 thf(fact_219_pi_Odistinct_I1_J, axiom, (! [Name1:name,Name22:name,Pi:pi]: ((piNil != (((output @ Name1) @ Name22) @ Pi))))).
% 2.83/1.52 thf(fact_220_fresh__fact2, axiom, (! [A2:name,B2:name,P:pi]: (((A2 != B2) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ A2) @ B2)))))).
% 2.83/1.52 thf(fact_221_fresh__fact1, axiom, (! [A2:name,P:pi,C3:name,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((A2 != C3) => ((((fresh @ name) @ pi) @ A2) @ (((subs @ P) @ B2) @ C3))))))).
% 2.83/1.52 thf(fact_222_forget, axiom, (! [A2:name,P:pi,B2:name]: ((((((fresh @ name) @ pi) @ A2) @ P) => ((((subs @ P) @ A2) @ B2) = P))))).
% 2.83/1.52 thf(fact_223_freeRes_Oexhaust, axiom, (! [Y:late_freeRes]: (((! [X112:name,X122:name]: ((Y != ((late_OutputR @ X112) @ X122)))) => (Y = late_TauR))))).
% 2.83/1.52 thf(fact_224_Late__Semantics1_OfreeRes_Odistinct_I1_J, axiom, (! [X11:name,X12:name]: ((((late_OutputR @ X11) @ X12) != late_TauR)))).
% 2.83/1.52 thf(fact_225_substRes3, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => ((((subs @ ((res @ A2) @ P)) @ A2) @ B2) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 2.83/1.52 thf(fact_226_substRes2, axiom, (! [B2:name,P:pi,A2:name]: ((((((fresh @ name) @ pi) @ B2) @ P) => (((res @ A2) @ P) = ((res @ B2) @ (((subs @ P) @ A2) @ B2))))))).
% 2.83/1.52 thf(fact_227_resTrans_I1_J, axiom, (! [X2:name,B2:name,P:pi,Rs:late_residual]: ((~ (((late_transitions @ ((res @ X2) @ (((output @ X2) @ B2) @ P))) @ Rs)))))).
% 2.83/1.52 thf(fact_228_outputBoundTrans, axiom, (! [A2:name,B2:name,P:pi,C3:late_subject,X2:name,P2:pi]: ((~ (((late_transitions @ (((output @ A2) @ B2) @ P)) @ (((late_BoundR @ C3) @ X2) @ P2))))))).
% 2.83/1.52 thf(fact_229_nilSim_I3_J, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,B2:name,P:pi]: ((~ ((((strong743114133lation @ piNil) @ Rel) @ (((output @ A2) @ B2) @ P))))))).
% 2.83/1.52 thf(fact_230_freeRes_Orecs_I2_J, axiom, (! [T:$tType,P:(T > $o),F1:(name > (name > T)),F22:T]: (((! [X13:name,X23:name]: ((P @ ((F1 @ X13) @ X23)))) => ((P @ F22) => (((((late_freeRes_rec @ T) @ F1) @ F22) @ late_TauR) = F22)))))).
% 2.83/1.52 thf(fact_231_Late__Semantics_OComm2, axiom, (! [P:pi,A2:name,B2:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ B2))))))))).
% 2.83/1.52 thf(fact_232_Late__Semantics_OComm1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X2) @ B2)) @ Q2)))))))).
% 2.83/1.52 thf(fact_233_Output, axiom, (! [A2:name,B2:name,P:pi]: (((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P))))).
% 2.83/1.52 thf(fact_234_outputIneqTrans, axiom, (! [A2:name,B2:name,P:pi,C3:name,D3:name,P2:pi]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ ((late_OutputR @ C3) @ D3)) @ P2)) => (~ (((A2 != C3) | (B2 != D3)))))))).
% 2.83/1.52 thf(fact_235_outputCases_H, axiom, (! [A2:name,B2:name,P:pi,Rs:late_residual]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ Rs) => (~ ((! [A4:name,B4:name,P4:pi]: ((((A2 = A4) & ((B2 = B4) & (P = P4))) => (Rs != ((late_FreeR @ ((late_OutputR @ A4) @ B4)) @ P4))))))))))).
% 2.83/1.52 thf(fact_236_outputCases, axiom, (! [A2:name,B2:name,P:pi,Alpha:late_freeRes,P2:pi,Prop:(late_freeRes > (pi > $o))]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (((Alpha = ((late_OutputR @ A2) @ B2)) => ((P = P2) => ((Prop @ ((late_OutputR @ A2) @ B2)) @ P))) => ((Prop @ Alpha) @ P2)))))).
% 2.83/1.52 thf(fact_237_outputFreshTrans, axiom, (! [A2:name,B2:name,P:pi,Alpha:late_freeRes,P2:pi]: ((((late_transitions @ (((output @ A2) @ B2) @ P)) @ ((late_FreeR @ Alpha) @ P2)) => (~ ((((((fresh @ name) @ late_freeRes) @ A2) @ Alpha) | ((((fresh @ name) @ late_freeRes) @ B2) @ Alpha)))))))).
% 2.83/1.52 thf(fact_238_transitions_OComm2, axiom, (! [P:pi,A2:name,B2:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B2) => (((((fresh @ name) @ pi) @ X2) @ P2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ B2)))))))))))))).
% 2.83/1.52 thf(fact_239_transitions_OComm1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,B2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ ((late_FreeR @ ((late_OutputR @ A2) @ B2)) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => ((X2 != A2) => ((X2 != B2) => (((((fresh @ name) @ pi) @ X2) @ Q2) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((par @ (((subs @ P2) @ X2) @ B2)) @ Q2))))))))))))).
% 2.83/1.52 thf(fact_240_Tau, axiom, (! [P:pi]: (((late_transitions @ (tau @ P)) @ ((late_FreeR @ late_TauR) @ P))))).
% 2.83/1.52 thf(fact_241_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))))))))))).
% 2.83/1.52 thf(fact_242_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)))))).
% 2.83/1.52 thf(fact_243_transitions_OClose2, axiom, (! [P:pi,A2:name,Y:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X2 != A2) => (((((fresh @ name) @ pi) @ X2) @ P2) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ Q2) => ((X2 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ Y))))))))))))))))))).
% 2.83/1.52 thf(fact_244_transitions_OClose1, axiom, (! [P:pi,A2:name,X2:name,P2:pi,Q:pi,Y:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ Q2)) => (((((fresh @ name) @ pi) @ X2) @ P) => (((((fresh @ name) @ pi) @ X2) @ Q) => (((((fresh @ name) @ pi) @ Y) @ P) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((X2 != A2) => (((((fresh @ name) @ pi) @ X2) @ Q2) => ((Y != A2) => (((((fresh @ name) @ pi) @ Y) @ P2) => ((X2 != Y) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ (((subs @ P2) @ X2) @ Y)) @ Q2)))))))))))))))))).
% 2.83/1.52 thf(fact_245_Late__Semantics_OClose2, axiom, (! [P:pi,A2:name,Y:name,P2:pi,Q:pi,X2:name,Q2:pi]: ((((late_transitions @ P) @ (((late_BoundR @ (late_BoundOutputS @ A2)) @ Y) @ P2)) => (((late_transitions @ Q) @ (((late_BoundR @ (late_InputS @ A2)) @ X2) @ Q2)) => (((((fresh @ name) @ pi) @ Y) @ Q) => ((late_transitions @ ((par @ P) @ Q)) @ ((late_FreeR @ late_TauR) @ ((res @ Y) @ ((par @ P2) @ (((subs @ Q2) @ X2) @ Y))))))))))).
% 2.83/1.52 thf(fact_246_mismatchIdRight, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,B2:name,P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => ((A2 != B2) => (((strong743114133lation @ P) @ Rel) @ (((mismatch @ A2) @ B2) @ P))))))).
% 2.83/1.52 thf(fact_247_mismatchIdLeft, axiom, (! [Rel:(set @ ((product_prod @ pi) @ pi)),A2:name,B2:name,P:pi]: (((((ord_less_eq @ (set @ ((product_prod @ pi) @ pi))) @ (id @ pi)) @ Rel) => ((A2 != B2) => (((strong743114133lation @ (((mismatch @ A2) @ B2) @ P)) @ Rel) @ P)))))).
% 2.83/1.52 thf(fact_248_pi_Ofresh_I6_J, axiom, (! [A2:name,X32:name,X22:name,X1:pi]: ((((((fresh @ name) @ pi) @ A2) @ (((mismatch @ X32) @ X22) @ X1)) = (((((fresh @ name) @ name) @ A2) @ X32) & (((((fresh @ name) @ name) @ A2) @ X22) & ((((fresh @ name) @ pi) @ A2) @ X1))))))).
% 2.83/1.52 thf(fact_249_pi_Odistinct_I25_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name1:name,Name22:name,Pi:pi]: (((((output @ Name12) @ Name23) @ Pi4) != (((mismatch @ Name1) @ Name22) @ Pi))))).
% 2.83/1.52 thf(fact_250_pi_Odistinct_I9_J, axiom, (! [Name1:name,Name22:name,Pi:pi]: ((piNil != (((mismatch @ Name1) @ Name22) @ Pi))))).
% 2.83/1.52 thf(fact_251_pi_Odistinct_I71_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((mismatch @ Name12) @ Name23) @ Pi4) != ((sum @ Pi12) @ Pi22))))).
% 2.83/1.52 thf(fact_252_pi_Odistinct_I51_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Name1:name,Name22:name,Pi:pi]: (((((input @ Name12) @ Name23) @ Pi4) != (((mismatch @ Name1) @ Name22) @ Pi))))).
% 2.83/1.52 thf(fact_253_pi_Odistinct_I39_J, axiom, (! [Pi4:pi,Name1:name,Name22:name,Pi:pi]: (((tau @ Pi4) != (((mismatch @ Name1) @ Name22) @ Pi))))).
% 2.83/1.52 thf(fact_254_pi_Oinject_I5_J, axiom, (! [X32:name,X22:name,X1:pi,Y32:name,Y2:name,Y1:pi]: ((((((mismatch @ X32) @ X22) @ X1) = (((mismatch @ Y32) @ Y2) @ Y1)) = ((X32 = Y32) & ((X22 = Y2) & (X1 = Y1))))))).
% 2.83/1.52 thf(fact_255_pi_Odistinct_I73_J, axiom, (! [Name12:name,Name23:name,Pi4:pi,Pi12:pi,Pi22:pi]: (((((mismatch @ Name12) @ Name23) @ Pi4) != ((par @ Pi12) @ Pi22))))).
% 2.83/1.52 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 2.83/1.52 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 2.83/1.52 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 2.83/1.52 thf(tcon_Set_Oset___Orderings_Opreorder_1, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 2.83/1.52 thf(tcon_Set_Oset___Orderings_Oorder_2, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 2.83/1.52 thf(tcon_Set_Oset___Orderings_Oord_3, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 2.83/1.52 thf(tcon_Agent_Opi___Agent_Ofs__name, axiom, (fs_name @ pi)).
% 2.83/1.52 thf(tcon_HOL_Obool___Orderings_Opreorder_4, axiom, (preorder @ $o)).
% 2.83/1.52 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.83/1.52 thf(tcon_HOL_Obool___Orderings_Oorder_5, axiom, (order @ $o)).
% 2.83/1.52 thf(tcon_HOL_Obool___Orderings_Oord_6, axiom, (ord @ $o)).
% 2.83/1.52 thf(tcon_HOL_Obool___Agent_Ofs__name_7, axiom, (fs_name @ $o)).
% 2.83/1.52 thf(tcon_Agent_Oname___Agent_Ofs__name_8, axiom, (fs_name @ name)).
% 2.83/1.52 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_9, axiom, (! [A8:$tType,A9:$tType]: ((((fs_name @ A8) & (fs_name @ A9)) => (fs_name @ ((product_prod @ A8) @ A9)))))).
% 2.83/1.52 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_10, axiom, (fs_name @ late_freeRes)).
% 2.83/1.52 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11, axiom, (fs_name @ late_subject)).
% 2.83/1.52 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_12, axiom, (fs_name @ late_residual)).
% 2.83/1.52 thf(conj_0, conjecture, (y != x)).
% 2.83/1.52 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.xvru83IF3W/DTF2DTF31617.p
% 2.83/1.52 ------------------------
% 2.83/1.55 ---- Cleaned THF ---
% 2.83/1.55 thf(ty_t_Late__Semantics_Oresidual,type,
% 2.83/1.55 late_residual: $tType ).
% 2.83/1.55
% 2.83/1.55 thf(ty_t_Late__Semantics_Osubject,type,
% 2.83/1.55 late_subject: $tType ).
% 2.83/1.55
% 2.83/1.55 thf(ty_t_Late__Semantics_OfreeRes,type,
% 2.83/1.55 late_freeRes: $tType ).
% 2.83/1.55
% 2.83/1.55 thf(ty_t_Product__Type_Oprod,type,
% 2.83/1.55 product_prod: $tType > $tType > $tType ).
% 2.83/1.55
% 2.83/1.55 thf(ty_t_Nominal_Onoption,type,
% 2.83/1.55 noption: $tType > $tType ).
% 2.83/1.55
% 2.83/1.55 thf(ty_t_Agent_Oname,type,
% 2.83/1.55 name: $tType ).
% 2.83/1.55
% 2.83/1.55 thf(ty_t_Agent_Opi,type,
% 2.83/1.55 pi: $tType ).
% 2.83/1.55
% 2.83/1.55 thf(ty_t_Set_Oset,type,
% 2.83/1.55 set: $tType > $tType ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_HOL_Otype,type,
% 2.83/1.55 type:
% 2.83/1.55 !>[A: $tType] : $o ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Agent_Ofs__name,type,
% 2.83/1.55 fs_name:
% 2.83/1.55 !>[A: $tType] : $o ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Oord,type,
% 2.83/1.55 ord:
% 2.83/1.55 !>[A: $tType] : $o ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Oorder,type,
% 2.83/1.55 order:
% 2.83/1.55 !>[A: $tType] : $o ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Olinorder,type,
% 2.83/1.55 linorder:
% 2.83/1.55 !>[A: $tType] : $o ).
% 2.83/1.55
% 2.83/1.55 thf(sy_cl_Orderings_Opreorder,type,
% 2.83/1.55 preorder:
% 2.83/1.55 !>[A: $tType] : $o ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Agent_Opi_OInput,type,
% 2.83/1.55 input: name > name > pi > pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Agent_Opi_OMismatch,type,
% 2.83/1.55 mismatch: name > name > pi > pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Agent_Opi_OOutput,type,
% 2.83/1.55 output: name > name > pi > pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Agent_Opi_OPar,type,
% 2.83/1.55 par: pi > pi > pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Agent_Opi_OPiNil,type,
% 2.83/1.55 piNil: pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Agent_Opi_ORes,type,
% 2.83/1.55 res: name > pi > pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Agent_Opi_OSum,type,
% 2.83/1.55 sum: pi > pi > pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Agent_Opi_OTau,type,
% 2.83/1.55 tau: pi > pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Agent_Osubs,type,
% 2.83/1.55 subs: pi > name > name > pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 2.83/1.55 late_OutputR: name > name > late_freeRes ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 2.83/1.55 late_TauR: late_freeRes ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Late__Semantics_OfreeRes_OfreeRes__rec,type,
% 2.83/1.55 late_freeRes_rec:
% 2.83/1.55 !>[T: $tType] : ( ( name > name > T ) > T > late_freeRes > T ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 2.83/1.55 late_BoundR: late_subject > name > pi > late_residual ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 2.83/1.55 late_FreeR: late_freeRes > pi > late_residual ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 2.83/1.55 late_BoundOutputS: name > late_subject ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 2.83/1.55 late_InputS: name > late_subject ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Late__Semantics_Osubject_Osubject__rec,type,
% 2.83/1.55 late_subject_rec:
% 2.83/1.55 !>[T: $tType] : ( ( name > T ) > ( name > T ) > late_subject > T ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Late__Semantics_Otransitions,type,
% 2.83/1.55 late_transitions: pi > late_residual > $o ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Nominal_Oabs__fun,type,
% 2.83/1.55 abs_fun:
% 2.83/1.55 !>[X: $tType,A: $tType] : ( X > A > X > ( noption @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Nominal_Ofresh,type,
% 2.83/1.55 fresh:
% 2.83/1.55 !>[X: $tType,A: $tType] : ( X > A > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.83/1.55 ord_less_eq:
% 2.83/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Product__Type_OPair,type,
% 2.83/1.55 product_Pair:
% 2.83/1.55 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.83/1.55 produc2004651681e_prod:
% 2.83/1.55 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.83/1.55 product_rec_prod:
% 2.83/1.55 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Rel_Oeqvt,type,
% 2.83/1.55 eqvt:
% 2.83/1.55 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Relation_OId,type,
% 2.83/1.55 id:
% 2.83/1.55 !>[A: $tType] : ( set @ ( product_prod @ A @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Set_OCollect,type,
% 2.83/1.55 collect:
% 2.83/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 2.83/1.55 strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 2.83/1.55 strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
% 2.83/1.55
% 2.83/1.55 thf(sy_c_member,type,
% 2.83/1.55 member:
% 2.83/1.55 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_v_P,type,
% 2.83/1.55 p: pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_v_PQ____,type,
% 2.83/1.55 pq: pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_v_Q,type,
% 2.83/1.55 q: pi ).
% 2.83/1.55
% 2.83/1.55 thf(sy_v_Rel,type,
% 2.83/1.55 rel: set @ ( product_prod @ pi @ pi ) ).
% 2.83/1.55
% 2.83/1.55 thf(sy_v_a____,type,
% 2.83/1.55 a: late_subject ).
% 2.83/1.55
% 2.83/1.55 thf(sy_v_x,type,
% 2.83/1.55 x: name ).
% 2.83/1.55
% 2.83/1.55 thf(sy_v_y____,type,
% 2.83/1.55 y: name ).
% 2.83/1.55
% 2.83/1.55 thf(fact_0_Eqvt,axiom,
% 2.83/1.55 eqvt @ pi @ rel ).
% 2.83/1.55
% 2.83/1.55 thf(fact_1_Bound_Ohyps_I5_J,axiom,
% 2.83/1.55 fresh @ name @ ( product_prod @ name @ ( product_prod @ pi @ pi ) ) @ y @ ( product_Pair @ name @ ( product_prod @ pi @ pi ) @ x @ ( product_Pair @ pi @ pi @ p @ q ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_2_Bound_Ohyps_I4_J,axiom,
% 2.83/1.55 fresh @ name @ late_subject @ y @ a ).
% 2.83/1.55
% 2.83/1.55 thf(fact_3_Bound_Ohyps_I3_J,axiom,
% 2.83/1.55 fresh @ name @ pi @ y @ ( res @ x @ ( sum @ p @ q ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_4_Bound_Ohyps_I2_J,axiom,
% 2.83/1.55 fresh @ name @ pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_5_Bound_Ohyps_I1_J,axiom,
% 2.83/1.55 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ a @ y @ pq ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_6_fresh__prod,axiom,
% 2.83/1.55 ! [A: $tType,X: $tType,B: $tType,A2: X,X2: A,Y: B] :
% 2.83/1.55 ( ( fresh @ X @ ( product_prod @ A @ B ) @ A2 @ ( product_Pair @ A @ B @ X2 @ Y ) )
% 2.83/1.55 = ( ( fresh @ X @ A @ A2 @ X2 )
% 2.83/1.55 & ( fresh @ X @ B @ A2 @ Y ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_7_pi_Ofresh_I7_J,axiom,
% 2.83/1.55 ! [A2: name,X22: pi,X1: pi] :
% 2.83/1.55 ( ( fresh @ name @ pi @ A2 @ ( sum @ X22 @ X1 ) )
% 2.83/1.55 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 2.83/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_8_transitions_OResB,axiom,
% 2.83/1.55 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.83/1.55 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 2.83/1.55 => ( ( Y != X2 )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.83/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.83/1.55 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_9_freshBoundDerivative_I1_J,axiom,
% 2.83/1.55 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.83/1.55 => ( fresh @ name @ late_subject @ Y @ A2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_10_Late__Semantics_OResB,axiom,
% 2.83/1.55 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.83/1.55 => ( ( fresh @ name @ late_subject @ Y @ A2 )
% 2.83/1.55 => ( ( Y != X2 )
% 2.83/1.55 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A2 @ X2 @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_11_fresh__prodD_I2_J,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType,C: $tType,A2: A,X2: B,Y: C] :
% 2.83/1.55 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X2 @ Y ) )
% 2.83/1.55 => ( fresh @ A @ C @ A2 @ Y ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_12_fresh__prodD_I1_J,axiom,
% 2.83/1.55 ! [C: $tType,A: $tType,B: $tType,A2: A,X2: B,Y: C] :
% 2.83/1.55 ( ( fresh @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ X2 @ Y ) )
% 2.83/1.55 => ( fresh @ A @ B @ A2 @ X2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_13_freshBoundDerivative_I2_J,axiom,
% 2.83/1.55 ! [P: pi,A2: late_subject,X2: name,P2: pi,Y: name] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.83/1.55 => ( ( Y != X2 )
% 2.83/1.55 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_14_prod_Oinject,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType,X1: A,X22: B,Y1: A,Y2: B] :
% 2.83/1.55 ( ( ( product_Pair @ A @ B @ X1 @ X22 )
% 2.83/1.55 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 2.83/1.55 = ( ( X1 = Y1 )
% 2.83/1.55 & ( X22 = Y2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_15_old_Oprod_Oinject,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 2.83/1.55 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.83/1.55 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.83/1.55 = ( ( A2 = A3 )
% 2.83/1.55 & ( B2 = B3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_16_pi_Odistinct_I81_J,axiom,
% 2.83/1.55 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 2.83/1.55 ( ( sum @ Pi1 @ Pi2 )
% 2.83/1.55 != ( res @ Name @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_17_freshResidual,axiom,
% 2.83/1.55 ! [P: pi,Rs: late_residual,X2: name] :
% 2.83/1.55 ( ( late_transitions @ P @ Rs )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.83/1.55 => ( fresh @ name @ late_residual @ X2 @ Rs ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_18_old_Oprod_Oinducts,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.83/1.55 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.83/1.55 => ( P @ Prod ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_19_old_Oprod_Oexhaust,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.83/1.55 ~ ! [A4: A,B4: B] :
% 2.83/1.55 ( Y
% 2.83/1.55 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_20_Pair__inject,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 2.83/1.55 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.83/1.55 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.83/1.55 => ~ ( ( A2 = A3 )
% 2.83/1.55 => ( B2 != B3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_21_prod__cases,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 2.83/1.55 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.83/1.55 => ( P @ P3 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_22_surj__pair,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 2.83/1.55 ? [X3: A,Y3: B] :
% 2.83/1.55 ( P3
% 2.83/1.55 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_23_name__exists__fresh,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( fs_name @ A )
% 2.83/1.55 => ! [X2: A] :
% 2.83/1.55 ~ ! [C2: name] :
% 2.83/1.55 ~ ( fresh @ name @ A @ C2 @ X2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_24_pi_Oinject_I6_J,axiom,
% 2.83/1.55 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.83/1.55 ( ( ( sum @ X22 @ X1 )
% 2.83/1.55 = ( sum @ Y2 @ Y1 ) )
% 2.83/1.55 = ( ( X22 = Y2 )
% 2.83/1.55 & ( X1 = Y1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_25_prod__induct7,axiom,
% 2.83/1.55 ! [G: $tType,F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 2.83/1.55 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F,G2: G] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) )
% 2.83/1.55 => ( P @ X2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_26_prod__induct6,axiom,
% 2.83/1.55 ! [F: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 2.83/1.55 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) )
% 2.83/1.55 => ( P @ X2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_27_prod__induct5,axiom,
% 2.83/1.55 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.83/1.55 ( ! [A4: A,B4: B,C2: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 2.83/1.55 => ( P @ X2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_28_prod__induct4,axiom,
% 2.83/1.55 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.83/1.55 ( ! [A4: A,B4: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 2.83/1.55 => ( P @ X2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_29_prod__induct3,axiom,
% 2.83/1.55 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X2: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.83/1.55 ( ! [A4: A,B4: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 2.83/1.55 => ( P @ X2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_30_prod__cases7,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 2.83/1.55 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F,G2: G] :
% 2.83/1.55 ( Y
% 2.83/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_31_prod__cases6,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) )] :
% 2.83/1.55 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E,F2: F] :
% 2.83/1.55 ( Y
% 2.83/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F ) @ D2 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_32_prod__cases5,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.83/1.55 ~ ! [A4: A,B4: B,C2: C,D2: D,E2: E] :
% 2.83/1.55 ( Y
% 2.83/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_33_prod__cases4,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.83/1.55 ~ ! [A4: A,B4: B,C2: C,D2: D] :
% 2.83/1.55 ( Y
% 2.83/1.55 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_34_prod__cases3,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.83/1.55 ~ ! [A4: A,B4: B,C2: C] :
% 2.83/1.55 ( Y
% 2.83/1.55 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_35_freshRes,axiom,
% 2.83/1.55 ! [A2: name,P: pi] : ( fresh @ name @ pi @ A2 @ ( res @ A2 @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_36_Sum2,axiom,
% 2.83/1.55 ! [Q: pi,Rs: late_residual,P: pi] :
% 2.83/1.55 ( ( late_transitions @ Q @ Rs )
% 2.83/1.55 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_37_Sum1,axiom,
% 2.83/1.55 ! [P: pi,Rs: late_residual,Q: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ Rs )
% 2.83/1.55 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_38_sumCases_H,axiom,
% 2.83/1.55 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.83/1.55 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.83/1.55 => ( ~ ( late_transitions @ P @ Rs )
% 2.83/1.55 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_39_sumCases,axiom,
% 2.83/1.55 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.83/1.55 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.83/1.55 => ( ~ ( late_transitions @ P @ Rs )
% 2.83/1.55 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_40_old_Oprod_Orec,axiom,
% 2.83/1.55 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.83/1.55 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.83/1.55 = ( F1 @ A2 @ B2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_41_internal__case__prod__conv,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 2.83/1.55 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 2.83/1.55 = ( C3 @ A2 @ B2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_42_Id,axiom,
% 2.83/1.55 ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ rel ).
% 2.83/1.55
% 2.83/1.55 thf(fact_43_transitions_OPar2B,axiom,
% 2.83/1.55 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 2.83/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.83/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_44_transitions_OPar1B,axiom,
% 2.83/1.55 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.83/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A2 )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_45_mem__Collect__eq,axiom,
% 2.83/1.55 ! [A: $tType,A2: A,P: A > $o] :
% 2.83/1.55 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.83/1.55 = ( P @ A2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_46_Collect__mem__eq,axiom,
% 2.83/1.55 ! [A: $tType,A5: set @ A] :
% 2.83/1.55 ( ( collect @ A
% 2.83/1.55 @ ^ [X4: A] : ( member @ A @ X4 @ A5 ) )
% 2.83/1.55 = A5 ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_47_Collect__cong,axiom,
% 2.83/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.83/1.55 ( ! [X3: A] :
% 2.83/1.55 ( ( P @ X3 )
% 2.83/1.55 = ( Q @ X3 ) )
% 2.83/1.55 => ( ( collect @ A @ P )
% 2.83/1.55 = ( collect @ A @ Q ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_48_parCasesB_H,axiom,
% 2.83/1.55 ! [P: pi,Q: pi,B2: late_subject,Y: name,P2: pi] :
% 2.83/1.55 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 2.83/1.55 => ( ! [P4: pi,A4: late_subject,X3: name,P5: pi,Q3: pi] :
% 2.83/1.55 ( ( ( par @ P @ Q )
% 2.83/1.55 = ( par @ P4 @ Q3 ) )
% 2.83/1.55 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 2.83/1.55 = ( late_BoundR @ A4 @ X3 @ ( par @ P5 @ Q3 ) ) )
% 2.83/1.55 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X3 @ P5 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X3 @ P4 )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X3 @ Q3 )
% 2.83/1.55 => ~ ( fresh @ name @ late_subject @ X3 @ A4 ) ) ) ) ) )
% 2.83/1.55 => ~ ! [Q3: pi,A4: late_subject,X3: name,Q4: pi,P4: pi] :
% 2.83/1.55 ( ( ( par @ P @ Q )
% 2.83/1.55 = ( par @ P4 @ Q3 ) )
% 2.83/1.55 => ( ( ( late_BoundR @ B2 @ Y @ P2 )
% 2.83/1.55 = ( late_BoundR @ A4 @ X3 @ ( par @ P4 @ Q4 ) ) )
% 2.83/1.55 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A4 @ X3 @ Q4 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X3 @ P4 )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X3 @ Q3 )
% 2.83/1.55 => ~ ( fresh @ name @ late_subject @ X3 @ A4 ) ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_49_inputIneqTrans,axiom,
% 2.83/1.55 ! [A2: name,X2: name,P: pi,B2: late_subject,Y: name,P2: pi] :
% 2.83/1.55 ( ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
% 2.83/1.55 => ~ ( fresh @ name @ late_subject @ A2 @ B2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_50_resTauBoundTrans,axiom,
% 2.83/1.55 ! [X2: name,P: pi,A2: late_subject,Y: name,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_BoundR @ A2 @ Y @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_51_residual_Ostrong__inducts,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( fs_name @ A )
% 2.83/1.55 => ! [P: A > late_residual > $o,Z: A,Residual: late_residual] :
% 2.83/1.55 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: A] :
% 2.83/1.55 ( ( fresh @ name @ A @ Name2 @ Z2 )
% 2.83/1.55 => ( ( fresh @ name @ late_subject @ Name2 @ Subject )
% 2.83/1.55 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 2.83/1.55 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: A] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.83/1.55 => ( P @ Z @ Residual ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_52_residual_Ostrong__induct,axiom,
% 2.83/1.55 ! [N: $tType] :
% 2.83/1.55 ( ( fs_name @ N )
% 2.83/1.55 => ! [P: N > late_residual > $o,Z: N,Residual: late_residual] :
% 2.83/1.55 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: N] :
% 2.83/1.55 ( ( fresh @ name @ N @ Name2 @ Z2 )
% 2.83/1.55 => ( ( fresh @ name @ late_subject @ Name2 @ Subject )
% 2.83/1.55 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 2.83/1.55 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: N] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.83/1.55 => ( P @ Z @ Residual ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_53_pi_Ofresh_I8_J,axiom,
% 2.83/1.55 ! [A2: name,X22: pi,X1: pi] :
% 2.83/1.55 ( ( fresh @ name @ pi @ A2 @ ( par @ X22 @ X1 ) )
% 2.83/1.55 = ( ( fresh @ name @ pi @ A2 @ X22 )
% 2.83/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_54_pi_Ofresh_I3_J,axiom,
% 2.83/1.55 ! [A2: name,X1: pi] :
% 2.83/1.55 ( ( fresh @ name @ pi @ A2 @ ( tau @ X1 ) )
% 2.83/1.55 = ( fresh @ name @ pi @ A2 @ X1 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_55_residual_Ofresh_I2_J,axiom,
% 2.83/1.55 ! [A2: name,X22: late_freeRes,X1: pi] :
% 2.83/1.55 ( ( fresh @ name @ late_residual @ A2 @ ( late_FreeR @ X22 @ X1 ) )
% 2.83/1.55 = ( ( fresh @ name @ late_freeRes @ A2 @ X22 )
% 2.83/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_56_residual_Oinject_I2_J,axiom,
% 2.83/1.55 ! [X22: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 2.83/1.55 ( ( ( late_FreeR @ X22 @ X1 )
% 2.83/1.55 = ( late_FreeR @ Y2 @ Y1 ) )
% 2.83/1.55 = ( ( X22 = Y2 )
% 2.83/1.55 & ( X1 = Y1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_57_pi_Odistinct_I35_J,axiom,
% 2.83/1.55 ! [Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 2.83/1.55 ( ( tau @ Pi4 )
% 2.83/1.55 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_58_pi_Odistinct_I43_J,axiom,
% 2.83/1.55 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.83/1.55 ( ( tau @ Pi4 )
% 2.83/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_59_pi_Odistinct_I55_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.83/1.55 ( ( input @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_60_pi_Oinject_I2_J,axiom,
% 2.83/1.55 ! [X1: pi,Y1: pi] :
% 2.83/1.55 ( ( ( tau @ X1 )
% 2.83/1.55 = ( tau @ Y1 ) )
% 2.83/1.55 = ( X1 = Y1 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_61_pi_Oinject_I7_J,axiom,
% 2.83/1.55 ! [X22: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.83/1.55 ( ( ( par @ X22 @ X1 )
% 2.83/1.55 = ( par @ Y2 @ Y1 ) )
% 2.83/1.55 = ( ( X22 = Y2 )
% 2.83/1.55 & ( X1 = Y1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_62_Par2F,axiom,
% 2.83/1.55 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 2.83/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_63_Par1F,axiom,
% 2.83/1.55 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_64_inputFreeTrans,axiom,
% 2.83/1.55 ! [A2: name,X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_65_resInputFreeTrans,axiom,
% 2.83/1.55 ! [X2: name,A2: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_66_pi_Odistinct_I85_J,axiom,
% 2.83/1.55 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 2.83/1.55 ( ( par @ Pi1 @ Pi2 )
% 2.83/1.55 != ( res @ Name @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_67_pi_Odistinct_I79_J,axiom,
% 2.83/1.55 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 2.83/1.55 ( ( sum @ Pi1 @ Pi2 )
% 2.83/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_68_residual_Odistinct_I1_J,axiom,
% 2.83/1.55 ! [Subject2: late_subject,Name3: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
% 2.83/1.55 ( ( late_BoundR @ Subject2 @ Name3 @ Pi4 )
% 2.83/1.55 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_69_residual_Oinducts,axiom,
% 2.83/1.55 ! [P: late_residual > $o,Residual: late_residual] :
% 2.83/1.55 ( ! [Subject: late_subject,Name2: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) )
% 2.83/1.55 => ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.83/1.55 => ( P @ Residual ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_70_pi_Odistinct_I57_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 2.83/1.55 ( ( input @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( res @ Name @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_71_pi_Odistinct_I45_J,axiom,
% 2.83/1.55 ! [Pi4: pi,Name: name,Pi: pi] :
% 2.83/1.55 ( ( tau @ Pi4 )
% 2.83/1.55 != ( res @ Name @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_72_pi_Odistinct_I53_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.83/1.55 ( ( input @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_73_pi_Odistinct_I41_J,axiom,
% 2.83/1.55 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.83/1.55 ( ( tau @ Pi4 )
% 2.83/1.55 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_74_resCasesF,axiom,
% 2.83/1.55 ! [X2: name,P: pi,Alpha: late_freeRes,XP: pi,F3: pi > $o] :
% 2.83/1.55 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 2.83/1.55 => ( ! [P5: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 2.83/1.55 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha )
% 2.83/1.55 => ( F3 @ ( res @ X2 @ P5 ) ) ) )
% 2.83/1.55 => ( F3 @ XP ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_75_resCasesF_H,axiom,
% 2.83/1.55 ! [X2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.83/1.55 ( ( late_transitions @ ( res @ X2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.83/1.55 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 2.83/1.55 ( ( ( res @ X2 @ P )
% 2.83/1.55 = ( res @ Y3 @ P4 ) )
% 2.83/1.55 => ( ( ( late_FreeR @ Alpha @ P2 )
% 2.83/1.55 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 2.83/1.55 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 2.83/1.55 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_76_ResF,axiom,
% 2.83/1.55 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.83/1.55 => ( ( fresh @ name @ late_freeRes @ Y @ Alpha )
% 2.83/1.55 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_77_freshFreeDerivative_I2_J,axiom,
% 2.83/1.55 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.83/1.55 => ( fresh @ name @ pi @ Y @ P2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_78_freshFreeDerivative_I1_J,axiom,
% 2.83/1.55 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.83/1.55 => ( fresh @ name @ late_freeRes @ Y @ Alpha ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_79_resTrans_I2_J,axiom,
% 2.83/1.55 ! [X2: name,Y: name,P: pi,Rs: late_residual] :
% 2.83/1.55 ~ ( late_transitions @ ( res @ X2 @ ( input @ X2 @ Y @ P ) ) @ Rs ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_80_tauBoundTrans,axiom,
% 2.83/1.55 ! [P: pi,A2: late_subject,X2: name,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A2 @ X2 @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_81_Late__Semantics_OPar1B,axiom,
% 2.83/1.55 ! [P: pi,A2: late_subject,X2: name,P2: pi,Q: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P2 @ Q ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_82_Late__Semantics_OPar2B,axiom,
% 2.83/1.55 ! [Q: pi,A2: late_subject,X2: name,Q2: pi,P: pi] :
% 2.83/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ ( par @ P @ Q2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_83_parCasesB,axiom,
% 2.83/1.55 ! [P: pi,Q: pi,A2: late_subject,X2: name,PQ: pi,Prop: pi > $o] :
% 2.83/1.55 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A2 @ X2 @ PQ ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.83/1.55 => ( ! [P5: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P5 ) )
% 2.83/1.55 => ( Prop @ ( par @ P5 @ Q ) ) )
% 2.83/1.55 => ( ! [Q4: pi] :
% 2.83/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q4 ) )
% 2.83/1.55 => ( Prop @ ( par @ P @ Q4 ) ) )
% 2.83/1.55 => ( Prop @ PQ ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_84_IdI,axiom,
% 2.83/1.55 ! [A: $tType,A2: A] : ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ A2 ) @ ( id @ A ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_85_pair__in__Id__conv,axiom,
% 2.83/1.55 ! [A: $tType,A2: A,B2: A] :
% 2.83/1.55 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 2.83/1.55 = ( A2 = B2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_86_subsetI,axiom,
% 2.83/1.55 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.83/1.55 ( ! [X3: A] :
% 2.83/1.55 ( ( member @ A @ X3 @ A5 )
% 2.83/1.55 => ( member @ A @ X3 @ B5 ) )
% 2.83/1.55 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_87_subset__antisym,axiom,
% 2.83/1.55 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.83/1.55 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A5 )
% 2.83/1.55 => ( A5 = B5 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_88_order__refl,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( preorder @ A )
% 2.83/1.55 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_89_IdE,axiom,
% 2.83/1.55 ! [A: $tType,P3: product_prod @ A @ A] :
% 2.83/1.55 ( ( member @ ( product_prod @ A @ A ) @ P3 @ ( id @ A ) )
% 2.83/1.55 => ~ ! [X3: A] :
% 2.83/1.55 ( P3
% 2.83/1.55 != ( product_Pair @ A @ A @ X3 @ X3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_90_IdD,axiom,
% 2.83/1.55 ! [A: $tType,A2: A,B2: A] :
% 2.83/1.55 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ A2 @ B2 ) @ ( id @ A ) )
% 2.83/1.55 => ( A2 = B2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_91_subrelI,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 2.83/1.55 ( ! [X3: A,Y3: B] :
% 2.83/1.55 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ R )
% 2.83/1.55 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y3 ) @ S ) )
% 2.83/1.55 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_92_dual__order_Oantisym,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A )
% 2.83/1.55 => ! [B2: A,A2: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.55 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.55 => ( A2 = B2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_93_dual__order_Oeq__iff,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A )
% 2.83/1.55 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 2.83/1.55 = ( ^ [A6: A,B6: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ B6 @ A6 )
% 2.83/1.55 & ( ord_less_eq @ A @ A6 @ B6 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_94_dual__order_Otrans,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A )
% 2.83/1.55 => ! [B2: A,A2: A,C3: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.55 => ( ( ord_less_eq @ A @ C3 @ B2 )
% 2.83/1.55 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_95_linorder__wlog,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( linorder @ A )
% 2.83/1.55 => ! [P: A > A > $o,A2: A,B2: A] :
% 2.83/1.55 ( ! [A4: A,B4: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ A4 @ B4 )
% 2.83/1.55 => ( P @ A4 @ B4 ) )
% 2.83/1.55 => ( ! [A4: A,B4: A] :
% 2.83/1.55 ( ( P @ B4 @ A4 )
% 2.83/1.55 => ( P @ A4 @ B4 ) )
% 2.83/1.55 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_96_dual__order_Orefl,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A )
% 2.83/1.55 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_97_order__trans,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( preorder @ A )
% 2.83/1.55 => ! [X2: A,Y: A,Z: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.83/1.55 => ( ( ord_less_eq @ A @ Y @ Z )
% 2.83/1.55 => ( ord_less_eq @ A @ X2 @ Z ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_98_order__class_Oorder_Oantisym,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A )
% 2.83/1.55 => ! [A2: A,B2: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.55 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.55 => ( A2 = B2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_99_ord__le__eq__trans,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( ord @ A )
% 2.83/1.55 => ! [A2: A,B2: A,C3: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.55 => ( ( B2 = C3 )
% 2.83/1.55 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_100_ord__eq__le__trans,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( ord @ A )
% 2.83/1.55 => ! [A2: A,B2: A,C3: A] :
% 2.83/1.55 ( ( A2 = B2 )
% 2.83/1.55 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 2.83/1.55 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_101_order__class_Oorder_Oeq__iff,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A )
% 2.83/1.55 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 2.83/1.55 = ( ^ [A6: A,B6: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ A6 @ B6 )
% 2.83/1.55 & ( ord_less_eq @ A @ B6 @ A6 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_102_antisym__conv,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A )
% 2.83/1.55 => ! [Y: A,X2: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ Y @ X2 )
% 2.83/1.55 => ( ( ord_less_eq @ A @ X2 @ Y )
% 2.83/1.55 = ( X2 = Y ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_103_le__cases3,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( linorder @ A )
% 2.83/1.55 => ! [X2: A,Y: A,Z: A] :
% 2.83/1.55 ( ( ( ord_less_eq @ A @ X2 @ Y )
% 2.83/1.55 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 2.83/1.55 => ( ( ( ord_less_eq @ A @ Y @ X2 )
% 2.83/1.55 => ~ ( ord_less_eq @ A @ X2 @ Z ) )
% 2.83/1.55 => ( ( ( ord_less_eq @ A @ X2 @ Z )
% 2.83/1.55 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 2.83/1.55 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 2.83/1.55 => ~ ( ord_less_eq @ A @ Y @ X2 ) )
% 2.83/1.55 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 2.83/1.55 => ~ ( ord_less_eq @ A @ Z @ X2 ) )
% 2.83/1.55 => ~ ( ( ord_less_eq @ A @ Z @ X2 )
% 2.83/1.55 => ~ ( ord_less_eq @ A @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_104_order_Otrans,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A )
% 2.83/1.55 => ! [A2: A,B2: A,C3: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.55 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 2.83/1.55 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_105_le__cases,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( linorder @ A )
% 2.83/1.55 => ! [X2: A,Y: A] :
% 2.83/1.55 ( ~ ( ord_less_eq @ A @ X2 @ Y )
% 2.83/1.55 => ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_106_eq__refl,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( preorder @ A )
% 2.83/1.55 => ! [X2: A,Y: A] :
% 2.83/1.55 ( ( X2 = Y )
% 2.83/1.55 => ( ord_less_eq @ A @ X2 @ Y ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_107_linear,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( linorder @ A )
% 2.83/1.55 => ! [X2: A,Y: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.83/1.55 | ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_108_antisym,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A )
% 2.83/1.55 => ! [X2: A,Y: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ X2 @ Y )
% 2.83/1.55 => ( ( ord_less_eq @ A @ Y @ X2 )
% 2.83/1.55 => ( X2 = Y ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_109_eq__iff,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( order @ A )
% 2.83/1.55 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 2.83/1.55 = ( ^ [X4: A,Y5: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 2.83/1.55 & ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_110_ord__le__eq__subst,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType] :
% 2.83/1.55 ( ( ( ord @ B )
% 2.83/1.55 & ( ord @ A ) )
% 2.83/1.55 => ! [A2: A,B2: A,F4: A > B,C3: B] :
% 2.83/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.55 => ( ( ( F4 @ B2 )
% 2.83/1.55 = C3 )
% 2.83/1.55 => ( ! [X3: A,Y3: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.83/1.55 => ( ord_less_eq @ B @ ( F4 @ X3 ) @ ( F4 @ Y3 ) ) )
% 2.83/1.55 => ( ord_less_eq @ B @ ( F4 @ A2 ) @ C3 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_111_ord__eq__le__subst,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType] :
% 2.83/1.55 ( ( ( ord @ B )
% 2.83/1.55 & ( ord @ A ) )
% 2.83/1.55 => ! [A2: A,F4: B > A,B2: B,C3: B] :
% 2.83/1.55 ( ( A2
% 2.83/1.55 = ( F4 @ B2 ) )
% 2.83/1.55 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 2.83/1.55 => ( ! [X3: B,Y3: B] :
% 2.83/1.55 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 2.83/1.55 => ( ord_less_eq @ A @ ( F4 @ X3 ) @ ( F4 @ Y3 ) ) )
% 2.83/1.55 => ( ord_less_eq @ A @ A2 @ ( F4 @ C3 ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_112_order__subst2,axiom,
% 2.83/1.55 ! [A: $tType,C: $tType] :
% 2.83/1.55 ( ( ( order @ C )
% 2.83/1.55 & ( order @ A ) )
% 2.83/1.55 => ! [A2: A,B2: A,F4: A > C,C3: C] :
% 2.83/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.55 => ( ( ord_less_eq @ C @ ( F4 @ B2 ) @ C3 )
% 2.83/1.55 => ( ! [X3: A,Y3: A] :
% 2.83/1.55 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.83/1.55 => ( ord_less_eq @ C @ ( F4 @ X3 ) @ ( F4 @ Y3 ) ) )
% 2.83/1.55 => ( ord_less_eq @ C @ ( F4 @ A2 ) @ C3 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_113_order__subst1,axiom,
% 2.83/1.55 ! [A: $tType,B: $tType] :
% 2.83/1.55 ( ( ( order @ B )
% 2.83/1.55 & ( order @ A ) )
% 2.83/1.55 => ! [A2: A,F4: B > A,B2: B,C3: B] :
% 2.83/1.55 ( ( ord_less_eq @ A @ A2 @ ( F4 @ B2 ) )
% 2.83/1.55 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 2.83/1.55 => ( ! [X3: B,Y3: B] :
% 2.83/1.55 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 2.83/1.55 => ( ord_less_eq @ A @ ( F4 @ X3 ) @ ( F4 @ Y3 ) ) )
% 2.83/1.55 => ( ord_less_eq @ A @ A2 @ ( F4 @ C3 ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_114_le__fun__def,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType] :
% 2.83/1.55 ( ( ord @ B )
% 2.83/1.55 => ( ( ord_less_eq @ ( A > B ) )
% 2.83/1.55 = ( ^ [F5: A > B,G3: A > B] :
% 2.83/1.55 ! [X4: A] : ( ord_less_eq @ B @ ( F5 @ X4 ) @ ( G3 @ X4 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_115_le__funI,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType] :
% 2.83/1.55 ( ( ord @ B )
% 2.83/1.55 => ! [F4: A > B,G4: A > B] :
% 2.83/1.55 ( ! [X3: A] : ( ord_less_eq @ B @ ( F4 @ X3 ) @ ( G4 @ X3 ) )
% 2.83/1.55 => ( ord_less_eq @ ( A > B ) @ F4 @ G4 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_116_le__funE,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType] :
% 2.83/1.55 ( ( ord @ B )
% 2.83/1.55 => ! [F4: A > B,G4: A > B,X2: A] :
% 2.83/1.55 ( ( ord_less_eq @ ( A > B ) @ F4 @ G4 )
% 2.83/1.55 => ( ord_less_eq @ B @ ( F4 @ X2 ) @ ( G4 @ X2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_117_le__funD,axiom,
% 2.83/1.55 ! [B: $tType,A: $tType] :
% 2.83/1.55 ( ( ord @ B )
% 2.83/1.55 => ! [F4: A > B,G4: A > B,X2: A] :
% 2.83/1.55 ( ( ord_less_eq @ ( A > B ) @ F4 @ G4 )
% 2.83/1.55 => ( ord_less_eq @ B @ ( F4 @ X2 ) @ ( G4 @ X2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_118_Collect__mono__iff,axiom,
% 2.83/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.83/1.55 = ( ! [X4: A] :
% 2.83/1.55 ( ( P @ X4 )
% 2.83/1.55 => ( Q @ X4 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_119_set__eq__subset,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( ^ [Y4: set @ A,Z3: set @ A] : ( Y4 = Z3 ) )
% 2.83/1.55 = ( ^ [A7: set @ A,B7: set @ A] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 2.83/1.55 & ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_120_subset__trans,axiom,
% 2.83/1.55 ! [A: $tType,A5: set @ A,B5: set @ A,C4: set @ A] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.83/1.55 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 2.83/1.55 => ( ord_less_eq @ ( set @ A ) @ A5 @ C4 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_121_Collect__mono,axiom,
% 2.83/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.83/1.55 ( ! [X3: A] :
% 2.83/1.55 ( ( P @ X3 )
% 2.83/1.55 => ( Q @ X3 ) )
% 2.83/1.55 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_122_subset__refl,axiom,
% 2.83/1.55 ! [A: $tType,A5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A5 @ A5 ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_123_subset__iff,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ A ) )
% 2.83/1.55 = ( ^ [A7: set @ A,B7: set @ A] :
% 2.83/1.55 ! [T2: A] :
% 2.83/1.55 ( ( member @ A @ T2 @ A7 )
% 2.83/1.55 => ( member @ A @ T2 @ B7 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_124_equalityD2,axiom,
% 2.83/1.55 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.83/1.55 ( ( A5 = B5 )
% 2.83/1.55 => ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_125_equalityD1,axiom,
% 2.83/1.55 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.83/1.55 ( ( A5 = B5 )
% 2.83/1.55 => ( ord_less_eq @ ( set @ A ) @ A5 @ B5 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_126_subset__eq,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ A ) )
% 2.83/1.55 = ( ^ [A7: set @ A,B7: set @ A] :
% 2.83/1.55 ! [X4: A] :
% 2.83/1.55 ( ( member @ A @ X4 @ A7 )
% 2.83/1.55 => ( member @ A @ X4 @ B7 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_127_equalityE,axiom,
% 2.83/1.55 ! [A: $tType,A5: set @ A,B5: set @ A] :
% 2.83/1.55 ( ( A5 = B5 )
% 2.83/1.55 => ~ ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.83/1.55 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_128_subsetD,axiom,
% 2.83/1.55 ! [A: $tType,A5: set @ A,B5: set @ A,C3: A] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.83/1.55 => ( ( member @ A @ C3 @ A5 )
% 2.83/1.55 => ( member @ A @ C3 @ B5 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_129_in__mono,axiom,
% 2.83/1.55 ! [A: $tType,A5: set @ A,B5: set @ A,X2: A] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.83/1.55 => ( ( member @ A @ X2 @ A5 )
% 2.83/1.55 => ( member @ A @ X2 @ B5 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_130_resInputBoundOutputTrans,axiom,
% 2.83/1.55 ! [X2: name,A2: name,Y: name,P: pi,B2: name,Z: name,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( res @ X2 @ ( input @ A2 @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_131_resTauOutputTrans,axiom,
% 2.83/1.55 ! [X2: name,P: pi,A2: name,B2: name,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( res @ X2 @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_132_simCasesCont,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( fs_name @ A )
% 2.83/1.55 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,P: pi,C4: A] :
% 2.83/1.55 ( ( eqvt @ pi @ Rel )
% 2.83/1.55 => ( ! [A4: late_subject,X3: name,Q4: pi] :
% 2.83/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X3 @ Q4 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X3 @ P )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X3 @ Q )
% 2.83/1.55 => ( ( fresh @ name @ late_subject @ X3 @ A4 )
% 2.83/1.55 => ( ( fresh @ name @ A @ X3 @ C4 )
% 2.83/1.55 => ? [P6: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X3 @ P6 ) )
% 2.83/1.55 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ X3 @ Rel ) ) ) ) ) ) )
% 2.83/1.55 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.83/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.83/1.55 => ? [P6: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.83/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.83/1.55 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_133_residual_Ofresh_I1_J,axiom,
% 2.83/1.55 ! [A2: name,X32: late_subject,X1: name,X22: pi] :
% 2.83/1.55 ( ( fresh @ name @ late_residual @ A2 @ ( late_BoundR @ X32 @ X1 @ X22 ) )
% 2.83/1.55 = ( ( fresh @ name @ late_subject @ A2 @ X32 )
% 2.83/1.55 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_134_resCases_H,axiom,
% 2.83/1.55 ! [X2: name,P: pi,Rs: late_residual] :
% 2.83/1.55 ( ( late_transitions @ ( res @ X2 @ P ) @ Rs )
% 2.83/1.55 => ( ! [P4: pi,A4: name,B4: name] :
% 2.83/1.55 ( ( ( res @ X2 @ P )
% 2.83/1.55 = ( res @ B4 @ P4 ) )
% 2.83/1.55 => ! [P5: pi] :
% 2.83/1.55 ( ( Rs
% 2.83/1.55 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 2.83/1.55 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 2.83/1.55 => ( A4 = B4 ) ) ) )
% 2.83/1.55 => ( ! [P4: pi,A4: late_subject,X3: name,P5: pi,Y3: name] :
% 2.83/1.55 ( ( ( res @ X2 @ P )
% 2.83/1.55 = ( res @ Y3 @ P4 ) )
% 2.83/1.55 => ( ( Rs
% 2.83/1.55 = ( late_BoundR @ A4 @ X3 @ ( res @ Y3 @ P5 ) ) )
% 2.83/1.55 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X3 @ P5 ) )
% 2.83/1.55 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 2.83/1.55 => ( ( Y3 != X3 )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X3 @ P4 )
% 2.83/1.55 => ~ ( fresh @ name @ late_subject @ X3 @ A4 ) ) ) ) ) ) )
% 2.83/1.55 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 2.83/1.55 ( ( ( res @ X2 @ P )
% 2.83/1.55 = ( res @ Y3 @ P4 ) )
% 2.83/1.55 => ( ( Rs
% 2.83/1.55 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 2.83/1.55 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 2.83/1.55 => ~ ( fresh @ name @ late_freeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_135_Late__Semantics_OfreeRes_Oinject,axiom,
% 2.83/1.55 ! [X22: name,X1: name,Y2: name,Y1: name] :
% 2.83/1.55 ( ( ( late_OutputR @ X22 @ X1 )
% 2.83/1.55 = ( late_OutputR @ Y2 @ Y1 ) )
% 2.83/1.55 = ( ( X22 = Y2 )
% 2.83/1.55 & ( X1 = Y1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_136_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 2.83/1.55 ! [X1: name,Y1: name] :
% 2.83/1.55 ( ( ( late_BoundOutputS @ X1 )
% 2.83/1.55 = ( late_BoundOutputS @ Y1 ) )
% 2.83/1.55 = ( X1 = Y1 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_137_subject_Ofresh_I2_J,axiom,
% 2.83/1.55 ! [A2: name,X1: name] :
% 2.83/1.55 ( ( fresh @ name @ late_subject @ A2 @ ( late_BoundOutputS @ X1 ) )
% 2.83/1.55 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_138_freeRes_Ofresh_I1_J,axiom,
% 2.83/1.55 ! [A2: name,X22: name,X1: name] :
% 2.83/1.55 ( ( fresh @ name @ late_freeRes @ A2 @ ( late_OutputR @ X22 @ X1 ) )
% 2.83/1.55 = ( ( fresh @ name @ name @ A2 @ X22 )
% 2.83/1.55 & ( fresh @ name @ name @ A2 @ X1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_139_pi_Ofresh_I9_J,axiom,
% 2.83/1.55 ! [A2: name,X1: name,X22: pi] :
% 2.83/1.55 ( ( fresh @ name @ pi @ A2 @ ( res @ X1 @ X22 ) )
% 2.83/1.55 = ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_140_pi_Ofresh_I4_J,axiom,
% 2.83/1.55 ! [A2: name,X32: name,X1: name,X22: pi] :
% 2.83/1.55 ( ( fresh @ name @ pi @ A2 @ ( input @ X32 @ X1 @ X22 ) )
% 2.83/1.55 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.83/1.55 & ( fresh @ name @ ( name > ( noption @ pi ) ) @ A2 @ ( abs_fun @ name @ pi @ X1 @ X22 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_141_monotonic,axiom,
% 2.83/1.55 ! [P: pi,A5: set @ ( product_prod @ pi @ pi ),P2: pi,B5: set @ ( product_prod @ pi @ pi )] :
% 2.83/1.55 ( ( strong743114133lation @ P @ A5 @ P2 )
% 2.83/1.55 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A5 @ B5 )
% 2.83/1.55 => ( strong743114133lation @ P @ B5 @ P2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_142_abs__fun__eq1,axiom,
% 2.83/1.55 ! [X: $tType,A: $tType,A2: X,X2: A,Y: A] :
% 2.83/1.55 ( ( ( abs_fun @ X @ A @ A2 @ X2 )
% 2.83/1.55 = ( abs_fun @ X @ A @ A2 @ Y ) )
% 2.83/1.55 = ( X2 = Y ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_143_derivativeMonotonic,axiom,
% 2.83/1.55 ! [P: pi,Q: pi,A2: late_subject,X2: name,A5: set @ ( product_prod @ pi @ pi ),B5: set @ ( product_prod @ pi @ pi )] :
% 2.83/1.55 ( ( strong2129052853vative @ P @ Q @ A2 @ X2 @ A5 )
% 2.83/1.55 => ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ A5 @ B5 )
% 2.83/1.55 => ( strong2129052853vative @ P @ Q @ A2 @ X2 @ B5 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_144_pi_Oinject_I8_J,axiom,
% 2.83/1.55 ! [X1: name,X22: pi,Y1: name,Y2: pi] :
% 2.83/1.55 ( ( ( res @ X1 @ X22 )
% 2.83/1.55 = ( res @ Y1 @ Y2 ) )
% 2.83/1.55 = ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 2.83/1.55 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_145_residual_Oinject_I1_J,axiom,
% 2.83/1.55 ! [X32: late_subject,X1: name,X22: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 2.83/1.55 ( ( ( late_BoundR @ X32 @ X1 @ X22 )
% 2.83/1.55 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 2.83/1.55 = ( ( X32 = Y32 )
% 2.83/1.55 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 2.83/1.55 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_146_abs__fresh_I1_J,axiom,
% 2.83/1.55 ! [X5: $tType] :
% 2.83/1.55 ( ( fs_name @ X5 )
% 2.83/1.55 => ! [B2: name,A2: name,X2: X5] :
% 2.83/1.55 ( ( fresh @ name @ ( name > ( noption @ X5 ) ) @ B2 @ ( abs_fun @ name @ X5 @ A2 @ X2 ) )
% 2.83/1.55 = ( ( B2 = A2 )
% 2.83/1.55 | ( fresh @ name @ X5 @ B2 @ X2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_147_name__fresh__abs,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( fs_name @ A )
% 2.83/1.55 => ! [B2: name,A2: name,X2: A] :
% 2.83/1.55 ( ( fresh @ name @ ( name > ( noption @ A ) ) @ B2 @ ( abs_fun @ name @ A @ A2 @ X2 ) )
% 2.83/1.55 = ( ( B2 = A2 )
% 2.83/1.55 | ( fresh @ name @ A @ B2 @ X2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_148_pi_Oinject_I3_J,axiom,
% 2.83/1.55 ! [X32: name,X1: name,X22: pi,Y32: name,Y1: name,Y2: pi] :
% 2.83/1.55 ( ( ( input @ X32 @ X1 @ X22 )
% 2.83/1.55 = ( input @ Y32 @ Y1 @ Y2 ) )
% 2.83/1.55 = ( ( X32 = Y32 )
% 2.83/1.55 & ( ( abs_fun @ name @ pi @ X1 @ X22 )
% 2.83/1.55 = ( abs_fun @ name @ pi @ Y1 @ Y2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_149_simE_I1_J,axiom,
% 2.83/1.55 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,A2: late_subject,X2: name,Q2: pi] :
% 2.83/1.55 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.83/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ A2 @ X2 @ Q2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.83/1.55 => ? [P5: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A2 @ X2 @ P5 ) )
% 2.83/1.55 & ( strong2129052853vative @ P5 @ Q2 @ A2 @ X2 @ Rel ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_150_Strong__Late__Sim_Oreflexive,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 2.83/1.55 => ( strong743114133lation @ P @ Rel @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_151_Open,axiom,
% 2.83/1.55 ! [P: pi,A2: name,B2: name,P2: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 2.83/1.55 => ( ( A2 != B2 )
% 2.83/1.55 => ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ B2 @ P2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_152_derivativeReflexive,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,A2: late_subject,X2: name] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 2.83/1.55 => ( strong2129052853vative @ P @ P @ A2 @ X2 @ Rel ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_153_simE_I2_J,axiom,
% 2.83/1.55 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi ),Q: pi,Alpha: late_freeRes,Q2: pi] :
% 2.83/1.55 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.83/1.55 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.83/1.55 => ? [P5: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 2.83/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_154_resSimCases,axiom,
% 2.83/1.55 ! [A: $tType] :
% 2.83/1.55 ( ( fs_name @ A )
% 2.83/1.55 => ! [Rel: set @ ( product_prod @ pi @ pi ),Q: pi,X2: name,P: pi,C4: A] :
% 2.83/1.55 ( ( eqvt @ pi @ Rel )
% 2.83/1.55 => ( ! [Q4: pi,A4: name] :
% 2.83/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X2 ) @ Q4 ) )
% 2.83/1.55 => ( ( A4 != X2 )
% 2.83/1.55 => ? [P6: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X2 @ P6 ) )
% 2.83/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 2.83/1.55 => ( ! [Q4: pi,A4: late_subject,Y3: name] :
% 2.83/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 2.83/1.55 => ( ( fresh @ name @ late_subject @ X2 @ A4 )
% 2.83/1.55 => ( ( X2 != Y3 )
% 2.83/1.55 => ( ( fresh @ name @ A @ Y3 @ C4 )
% 2.83/1.55 => ? [P6: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 2.83/1.55 & ( strong2129052853vative @ P6 @ ( res @ X2 @ Q4 ) @ A4 @ Y3 @ Rel ) ) ) ) ) )
% 2.83/1.55 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 2.83/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.83/1.55 => ( ( fresh @ name @ late_freeRes @ X2 @ Alpha2 )
% 2.83/1.55 => ? [P6: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.83/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ ( res @ X2 @ Q4 ) ) @ Rel ) ) ) )
% 2.83/1.55 => ( strong743114133lation @ P @ Rel @ ( res @ X2 @ Q ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_155_simCases,axiom,
% 2.83/1.55 ! [Q: pi,P: pi,Rel: set @ ( product_prod @ pi @ pi )] :
% 2.83/1.55 ( ! [A4: late_subject,Y3: name,Q4: pi] :
% 2.83/1.55 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y3 @ Q4 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y3 @ P )
% 2.83/1.55 => ? [P6: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y3 @ P6 ) )
% 2.83/1.55 & ( strong2129052853vative @ P6 @ Q4 @ A4 @ Y3 @ Rel ) ) ) )
% 2.83/1.55 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.83/1.55 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.83/1.55 => ? [P6: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.83/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.83/1.55 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_156_simulation__def,axiom,
% 2.83/1.55 ( strong743114133lation
% 2.83/1.55 = ( ^ [P7: pi,Rel2: set @ ( product_prod @ pi @ pi ),Q5: pi] :
% 2.83/1.55 ( ! [A6: late_subject,X4: name,Q6: pi] :
% 2.83/1.55 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A6 @ X4 @ Q6 ) )
% 2.83/1.55 & ( fresh @ name @ pi @ X4 @ P7 ) )
% 2.83/1.55 => ? [P8: pi] :
% 2.83/1.55 ( ( late_transitions @ P7 @ ( late_BoundR @ A6 @ X4 @ P8 ) )
% 2.83/1.55 & ( strong2129052853vative @ P8 @ Q6 @ A6 @ X4 @ Rel2 ) ) )
% 2.83/1.55 & ! [Alpha3: late_freeRes,Q6: pi] :
% 2.83/1.55 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 2.83/1.55 => ? [P8: pi] :
% 2.83/1.55 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 2.83/1.55 & ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_157_resCasesB_H,axiom,
% 2.83/1.55 ! [X6: name,P: pi,A2: late_subject,Y6: name,P2: pi] :
% 2.83/1.55 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A2 @ Y6 @ P2 ) )
% 2.83/1.55 => ( ! [P4: pi,A4: name,B4: name] :
% 2.83/1.55 ( ( ( res @ X6 @ P )
% 2.83/1.55 = ( res @ B4 @ P4 ) )
% 2.83/1.55 => ! [P5: pi] :
% 2.83/1.55 ( ( ( late_BoundR @ A2 @ Y6 @ P2 )
% 2.83/1.55 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B4 @ P5 ) )
% 2.83/1.55 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P5 ) )
% 2.83/1.55 => ( A4 = B4 ) ) ) )
% 2.83/1.55 => ~ ! [P4: pi,A4: late_subject,X3: name,P5: pi,Y3: name] :
% 2.83/1.55 ( ( ( res @ X6 @ P )
% 2.83/1.55 = ( res @ Y3 @ P4 ) )
% 2.83/1.55 => ( ( ( late_BoundR @ A2 @ Y6 @ P2 )
% 2.83/1.55 = ( late_BoundR @ A4 @ X3 @ ( res @ Y3 @ P5 ) ) )
% 2.83/1.55 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X3 @ P5 ) )
% 2.83/1.55 => ( ( fresh @ name @ late_subject @ Y3 @ A4 )
% 2.83/1.55 => ( ( Y3 != X3 )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X3 @ P4 )
% 2.83/1.55 => ~ ( fresh @ name @ late_subject @ X3 @ A4 ) ) ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_158_tauOutputTrans,axiom,
% 2.83/1.55 ! [P: pi,A2: name,B2: name,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_159_inputBoundOutputTrans,axiom,
% 2.83/1.55 ! [A2: name,X2: name,P: pi,B2: name,Y: name,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_160_sumIdempRight,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 2.83/1.55 => ( strong743114133lation @ ( sum @ P @ P ) @ Rel @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_161_sumAssocRight,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R2: pi] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 2.83/1.55 => ( strong743114133lation @ ( sum @ P @ ( sum @ Q @ R2 ) ) @ Rel @ ( sum @ ( sum @ P @ Q ) @ R2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_162_sumIdempLeft,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 2.83/1.55 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ P ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_163_sumAssocLeft,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi,R2: pi] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 2.83/1.55 => ( strong743114133lation @ ( sum @ ( sum @ P @ Q ) @ R2 ) @ Rel @ ( sum @ P @ ( sum @ Q @ R2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_164_sumSym,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi,Q: pi] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 2.83/1.55 => ( strong743114133lation @ ( sum @ P @ Q ) @ Rel @ ( sum @ Q @ P ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_165_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 2.83/1.55 ! [X22: name,Y2: name] :
% 2.83/1.55 ( ( ( late_BoundOutputS @ X22 )
% 2.83/1.55 = ( late_BoundOutputS @ Y2 ) )
% 2.83/1.55 = ( X22 = Y2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_166_Late__Semantics1_OfreeRes_Oinject,axiom,
% 2.83/1.55 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 2.83/1.55 ( ( ( late_OutputR @ X11 @ X12 )
% 2.83/1.55 = ( late_OutputR @ Y11 @ Y12 ) )
% 2.83/1.55 = ( ( X11 = Y11 )
% 2.83/1.55 & ( X12 = Y12 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_167_sumZeroRight,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 2.83/1.55 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ piNil ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_168_sumZeroLeft,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 2.83/1.55 => ( strong743114133lation @ ( sum @ P @ piNil ) @ Rel @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_169_name__fresh,axiom,
% 2.83/1.55 ( ( fresh @ name @ name )
% 2.83/1.55 = ( ^ [A6: name,B6: name] : ( A6 != B6 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_170_pi_Ofresh_I1_J,axiom,
% 2.83/1.55 ! [A2: name] : ( fresh @ name @ pi @ A2 @ piNil ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_171_zeroTrans,axiom,
% 2.83/1.55 ! [Rs: late_residual] :
% 2.83/1.55 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_172_nilCases_H,axiom,
% 2.83/1.55 ! [Rs: late_residual] :
% 2.83/1.55 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_173_pi_Odistinct_I15_J,axiom,
% 2.83/1.55 ! [Name: name,Pi: pi] :
% 2.83/1.55 ( piNil
% 2.83/1.55 != ( res @ Name @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_174_pi_Odistinct_I13_J,axiom,
% 2.83/1.55 ! [Pi12: pi,Pi22: pi] :
% 2.83/1.55 ( piNil
% 2.83/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_175_pi_Odistinct_I11_J,axiom,
% 2.83/1.55 ! [Pi12: pi,Pi22: pi] :
% 2.83/1.55 ( piNil
% 2.83/1.55 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_176_pi_Odistinct_I5_J,axiom,
% 2.83/1.55 ! [Name1: name,Name22: name,Pi: pi] :
% 2.83/1.55 ( piNil
% 2.83/1.55 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_177_pi_Odistinct_I3_J,axiom,
% 2.83/1.55 ! [Pi: pi] :
% 2.83/1.55 ( piNil
% 2.83/1.55 != ( tau @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_178_nilSimRight,axiom,
% 2.83/1.55 ! [P: pi,Rel: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_179_resZeroTrans,axiom,
% 2.83/1.55 ! [X2: name,Rs: late_residual] :
% 2.83/1.55 ~ ( late_transitions @ ( res @ X2 @ piNil ) @ Rs ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_180_nilSim_I2_J,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,X2: name,P: pi] :
% 2.83/1.55 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A2 @ X2 @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_181_nilSim_I1_J,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),P: pi] :
% 2.83/1.55 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_182_inputCases_H,axiom,
% 2.83/1.55 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 2.83/1.55 ( ( late_transitions @ ( input @ A2 @ B2 @ P ) @ Rs )
% 2.83/1.55 => ~ ! [X3: name,A4: name,P4: pi] :
% 2.83/1.55 ( ( ( A2 = A4 )
% 2.83/1.55 & ( ( abs_fun @ name @ pi @ B2 @ P )
% 2.83/1.55 = ( abs_fun @ name @ pi @ X3 @ P4 ) ) )
% 2.83/1.55 => ( ( Rs
% 2.83/1.55 = ( late_BoundR @ ( late_InputS @ A4 ) @ X3 @ P4 ) )
% 2.83/1.55 => ( X3 = A4 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_183_subject_Orecs_I2_J,axiom,
% 2.83/1.55 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 2.83/1.55 ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 2.83/1.55 => ( ! [X13: name] : ( P @ ( F22 @ X13 ) )
% 2.83/1.55 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_BoundOutputS @ Name3 ) )
% 2.83/1.55 = ( F22 @ Name3 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_184_freeRes_Orecs_I1_J,axiom,
% 2.83/1.55 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T,Name12: name,Name23: name] :
% 2.83/1.55 ( ! [X13: name,X23: name] : ( P @ ( F1 @ X13 @ X23 ) )
% 2.83/1.55 => ( ( P @ F22 )
% 2.83/1.55 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ ( late_OutputR @ Name12 @ Name23 ) )
% 2.83/1.55 = ( F1 @ Name12 @ Name23 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_185_subject_Ofresh_I1_J,axiom,
% 2.83/1.55 ! [A2: name,X1: name] :
% 2.83/1.55 ( ( fresh @ name @ late_subject @ A2 @ ( late_InputS @ X1 ) )
% 2.83/1.55 = ( fresh @ name @ name @ A2 @ X1 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_186_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 2.83/1.55 ! [X1: name,X22: name] :
% 2.83/1.55 ( ( late_InputS @ X1 )
% 2.83/1.55 != ( late_BoundOutputS @ X22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_187_subject_Oexhaust,axiom,
% 2.83/1.55 ! [Y: late_subject] :
% 2.83/1.55 ( ! [X13: name] :
% 2.83/1.55 ( Y
% 2.83/1.55 != ( late_InputS @ X13 ) )
% 2.83/1.55 => ~ ! [X23: name] :
% 2.83/1.55 ( Y
% 2.83/1.55 != ( late_BoundOutputS @ X23 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_188_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 2.83/1.55 ! [Name3: name,Name: name] :
% 2.83/1.55 ( ( late_InputS @ Name3 )
% 2.83/1.55 != ( late_BoundOutputS @ Name ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_189_subject_Oinducts,axiom,
% 2.83/1.55 ! [P: late_subject > $o,Subject2: late_subject] :
% 2.83/1.55 ( ! [Name2: name] : ( P @ ( late_InputS @ Name2 ) )
% 2.83/1.55 => ( ! [Name2: name] : ( P @ ( late_BoundOutputS @ Name2 ) )
% 2.83/1.55 => ( P @ Subject2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_190_subject_Ostrong__induct_H,axiom,
% 2.83/1.55 ! [N: $tType,P: N > late_subject > $o,Z: N,Subject2: late_subject] :
% 2.83/1.55 ( ! [Name2: name,Z2: N] : ( P @ Z2 @ ( late_InputS @ Name2 ) )
% 2.83/1.55 => ( ! [Name2: name,Z2: N] : ( P @ Z2 @ ( late_BoundOutputS @ Name2 ) )
% 2.83/1.55 => ( P @ Z @ Subject2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_191_subject_Ostrong__inducts,axiom,
% 2.83/1.55 ! [A: $tType,P: A > late_subject > $o,Z: A,Subject2: late_subject] :
% 2.83/1.55 ( ! [Name2: name,Z2: A] : ( P @ Z2 @ ( late_InputS @ Name2 ) )
% 2.83/1.55 => ( ! [Name2: name,Z2: A] : ( P @ Z2 @ ( late_BoundOutputS @ Name2 ) )
% 2.83/1.55 => ( P @ Z @ Subject2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_192_subject_Orecs_I1_J,axiom,
% 2.83/1.55 ! [T: $tType,P: T > $o,F1: name > T,F22: name > T,Name3: name] :
% 2.83/1.55 ( ! [X13: name] : ( P @ ( F1 @ X13 ) )
% 2.83/1.55 => ( ! [X13: name] : ( P @ ( F22 @ X13 ) )
% 2.83/1.55 => ( ( late_subject_rec @ T @ F1 @ F22 @ ( late_InputS @ Name3 ) )
% 2.83/1.55 = ( F1 @ Name3 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_193_Late__Semantics_OInput,axiom,
% 2.83/1.55 ! [A2: name,X2: name,P: pi] : ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_194_transitions_OInput,axiom,
% 2.83/1.55 ! [X2: name,A2: name,P: pi] :
% 2.83/1.55 ( ( X2 != A2 )
% 2.83/1.55 => ( late_transitions @ ( input @ A2 @ X2 @ P ) @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_195_resOutputInputTrans,axiom,
% 2.83/1.55 ! [X2: name,A2: name,B2: name,P: pi,C3: name,Y: name,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C3 ) @ Y @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_196_resOutputOutputTrans,axiom,
% 2.83/1.55 ! [X2: name,A2: name,P: pi,B2: name,Y: name,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ X2 @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B2 @ Y ) @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_197_Late__Semantics_OClose1,axiom,
% 2.83/1.55 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.83/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_198_subst__identity,axiom,
% 2.83/1.55 ! [P: pi,A2: name] :
% 2.83/1.55 ( ( subs @ P @ A2 @ A2 )
% 2.83/1.55 = P ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_199_simps_I9_J,axiom,
% 2.83/1.55 ! [X2: name,C3: name,D3: name,P: pi] :
% 2.83/1.55 ( ( X2 != C3 )
% 2.83/1.55 => ( ( X2 != D3 )
% 2.83/1.55 => ( ( subs @ ( res @ X2 @ P ) @ C3 @ D3 )
% 2.83/1.55 = ( res @ X2 @ ( subs @ P @ C3 @ D3 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_200_simps_I8_J,axiom,
% 2.83/1.55 ! [P: pi,Q: pi,C3: name,D3: name] :
% 2.83/1.55 ( ( subs @ ( par @ P @ Q ) @ C3 @ D3 )
% 2.83/1.55 = ( par @ ( subs @ P @ C3 @ D3 ) @ ( subs @ Q @ C3 @ D3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_201_substTrans,axiom,
% 2.83/1.55 ! [B2: name,P: pi,A2: name,C3: name] :
% 2.83/1.55 ( ( fresh @ name @ pi @ B2 @ P )
% 2.83/1.55 => ( ( subs @ ( subs @ P @ A2 @ B2 ) @ B2 @ C3 )
% 2.83/1.55 = ( subs @ P @ A2 @ C3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_202_simps_I7_J,axiom,
% 2.83/1.55 ! [P: pi,Q: pi,C3: name,D3: name] :
% 2.83/1.55 ( ( subs @ ( sum @ P @ Q ) @ C3 @ D3 )
% 2.83/1.55 = ( sum @ ( subs @ P @ C3 @ D3 ) @ ( subs @ Q @ C3 @ D3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_203_simps_I2_J,axiom,
% 2.83/1.55 ! [P: pi,C3: name,D3: name] :
% 2.83/1.55 ( ( subs @ ( tau @ P ) @ C3 @ D3 )
% 2.83/1.55 = ( tau @ ( subs @ P @ C3 @ D3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_204_simps_I1_J,axiom,
% 2.83/1.55 ! [C3: name,D3: name] :
% 2.83/1.55 ( ( subs @ piNil @ C3 @ D3 )
% 2.83/1.55 = piNil ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_205_freeRes_Ofresh_I2_J,axiom,
% 2.83/1.55 ! [A2: name] : ( fresh @ name @ late_freeRes @ A2 @ late_TauR ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_206_pi_Ofresh_I2_J,axiom,
% 2.83/1.55 ! [A2: name,X32: name,X22: name,X1: pi] :
% 2.83/1.55 ( ( fresh @ name @ pi @ A2 @ ( output @ X32 @ X22 @ X1 ) )
% 2.83/1.55 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.83/1.55 & ( fresh @ name @ name @ A2 @ X22 )
% 2.83/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_207_resOutputTauTrans,axiom,
% 2.83/1.55 ! [X2: name,A2: name,B2: name,P: pi,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( res @ X2 @ ( output @ A2 @ B2 @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_208_outputTauTrans,axiom,
% 2.83/1.55 ! [A2: name,B2: name,P: pi,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_209_pi_Odistinct_I31_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 2.83/1.55 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( res @ Name @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_210_pi_Odistinct_I29_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.83/1.55 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_211_pi_Odistinct_I27_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.83/1.55 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_212_pi_Oinject_I1_J,axiom,
% 2.83/1.55 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.83/1.55 ( ( ( output @ X32 @ X22 @ X1 )
% 2.83/1.55 = ( output @ Y32 @ Y2 @ Y1 ) )
% 2.83/1.55 = ( ( X32 = Y32 )
% 2.83/1.55 & ( X22 = Y2 )
% 2.83/1.55 & ( X1 = Y1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_213_freeRes_Ostrong__inducts,axiom,
% 2.83/1.55 ! [A: $tType,P: A > late_freeRes > $o,Z: A,FreeRes3: late_freeRes] :
% 2.83/1.55 ( ! [Name13: name,Name24: name,Z2: A] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name24 ) )
% 2.83/1.55 => ( ! [Z2: A] : ( P @ Z2 @ late_TauR )
% 2.83/1.55 => ( P @ Z @ FreeRes3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_214_freeRes_Ostrong__induct_H,axiom,
% 2.83/1.55 ! [N: $tType,P: N > late_freeRes > $o,Z: N,FreeRes3: late_freeRes] :
% 2.83/1.55 ( ! [Name13: name,Name24: name,Z2: N] : ( P @ Z2 @ ( late_OutputR @ Name13 @ Name24 ) )
% 2.83/1.55 => ( ! [Z2: N] : ( P @ Z2 @ late_TauR )
% 2.83/1.55 => ( P @ Z @ FreeRes3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_215_freeRes_Oinducts,axiom,
% 2.83/1.55 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 2.83/1.55 ( ! [Name13: name,Name24: name] : ( P @ ( late_OutputR @ Name13 @ Name24 ) )
% 2.83/1.55 => ( ( P @ late_TauR )
% 2.83/1.55 => ( P @ FreeRes3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_216_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name] :
% 2.83/1.55 ( ( late_OutputR @ Name12 @ Name23 )
% 2.83/1.55 != late_TauR ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_217_pi_Odistinct_I19_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 2.83/1.55 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( tau @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_218_pi_Odistinct_I21_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 2.83/1.55 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_219_pi_Odistinct_I1_J,axiom,
% 2.83/1.55 ! [Name1: name,Name22: name,Pi: pi] :
% 2.83/1.55 ( piNil
% 2.83/1.55 != ( output @ Name1 @ Name22 @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_220_fresh__fact2,axiom,
% 2.83/1.55 ! [A2: name,B2: name,P: pi] :
% 2.83/1.55 ( ( A2 != B2 )
% 2.83/1.55 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ A2 @ B2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_221_fresh__fact1,axiom,
% 2.83/1.55 ! [A2: name,P: pi,C3: name,B2: name] :
% 2.83/1.55 ( ( fresh @ name @ pi @ A2 @ P )
% 2.83/1.55 => ( ( A2 != C3 )
% 2.83/1.55 => ( fresh @ name @ pi @ A2 @ ( subs @ P @ B2 @ C3 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_222_forget,axiom,
% 2.83/1.55 ! [A2: name,P: pi,B2: name] :
% 2.83/1.55 ( ( fresh @ name @ pi @ A2 @ P )
% 2.83/1.55 => ( ( subs @ P @ A2 @ B2 )
% 2.83/1.55 = P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_223_freeRes_Oexhaust,axiom,
% 2.83/1.55 ! [Y: late_freeRes] :
% 2.83/1.55 ( ! [X112: name,X122: name] :
% 2.83/1.55 ( Y
% 2.83/1.55 != ( late_OutputR @ X112 @ X122 ) )
% 2.83/1.55 => ( Y = late_TauR ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_224_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 2.83/1.55 ! [X11: name,X12: name] :
% 2.83/1.55 ( ( late_OutputR @ X11 @ X12 )
% 2.83/1.55 != late_TauR ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_225_substRes3,axiom,
% 2.83/1.55 ! [B2: name,P: pi,A2: name] :
% 2.83/1.55 ( ( fresh @ name @ pi @ B2 @ P )
% 2.83/1.55 => ( ( subs @ ( res @ A2 @ P ) @ A2 @ B2 )
% 2.83/1.55 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_226_substRes2,axiom,
% 2.83/1.55 ! [B2: name,P: pi,A2: name] :
% 2.83/1.55 ( ( fresh @ name @ pi @ B2 @ P )
% 2.83/1.55 => ( ( res @ A2 @ P )
% 2.83/1.55 = ( res @ B2 @ ( subs @ P @ A2 @ B2 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_227_resTrans_I1_J,axiom,
% 2.83/1.55 ! [X2: name,B2: name,P: pi,Rs: late_residual] :
% 2.83/1.55 ~ ( late_transitions @ ( res @ X2 @ ( output @ X2 @ B2 @ P ) ) @ Rs ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_228_outputBoundTrans,axiom,
% 2.83/1.55 ! [A2: name,B2: name,P: pi,C3: late_subject,X2: name,P2: pi] :
% 2.83/1.55 ~ ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_BoundR @ C3 @ X2 @ P2 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_229_nilSim_I3_J,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 2.83/1.55 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A2 @ B2 @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_230_freeRes_Orecs_I2_J,axiom,
% 2.83/1.55 ! [T: $tType,P: T > $o,F1: name > name > T,F22: T] :
% 2.83/1.55 ( ! [X13: name,X23: name] : ( P @ ( F1 @ X13 @ X23 ) )
% 2.83/1.55 => ( ( P @ F22 )
% 2.83/1.55 => ( ( late_freeRes_rec @ T @ F1 @ F22 @ late_TauR )
% 2.83/1.55 = F22 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_231_Late__Semantics_OComm2,axiom,
% 2.83/1.55 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 2.83/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_232_Late__Semantics_OComm1,axiom,
% 2.83/1.55 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.83/1.55 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_233_Output,axiom,
% 2.83/1.55 ! [A2: name,B2: name,P: pi] : ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_234_outputIneqTrans,axiom,
% 2.83/1.55 ! [A2: name,B2: name,P: pi,C3: name,D3: name,P2: pi] :
% 2.83/1.55 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ C3 @ D3 ) @ P2 ) )
% 2.83/1.55 => ~ ( ( A2 != C3 )
% 2.83/1.55 | ( B2 != D3 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_235_outputCases_H,axiom,
% 2.83/1.55 ! [A2: name,B2: name,P: pi,Rs: late_residual] :
% 2.83/1.55 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ Rs )
% 2.83/1.55 => ~ ! [A4: name,B4: name,P4: pi] :
% 2.83/1.55 ( ( ( A2 = A4 )
% 2.83/1.55 & ( B2 = B4 )
% 2.83/1.55 & ( P = P4 ) )
% 2.83/1.55 => ( Rs
% 2.83/1.55 != ( late_FreeR @ ( late_OutputR @ A4 @ B4 ) @ P4 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_236_outputCases,axiom,
% 2.83/1.55 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.83/1.55 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.83/1.55 => ( ( ( Alpha
% 2.83/1.55 = ( late_OutputR @ A2 @ B2 ) )
% 2.83/1.55 => ( ( P = P2 )
% 2.83/1.55 => ( Prop @ ( late_OutputR @ A2 @ B2 ) @ P ) ) )
% 2.83/1.55 => ( Prop @ Alpha @ P2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_237_outputFreshTrans,axiom,
% 2.83/1.55 ! [A2: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.83/1.55 ( ( late_transitions @ ( output @ A2 @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.83/1.55 => ~ ( ( fresh @ name @ late_freeRes @ A2 @ Alpha )
% 2.83/1.55 | ( fresh @ name @ late_freeRes @ B2 @ Alpha ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_238_transitions_OComm2,axiom,
% 2.83/1.55 ! [P: pi,A2: name,B2: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ P2 ) )
% 2.83/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.83/1.55 => ( ( X2 != A2 )
% 2.83/1.55 => ( ( X2 != B2 )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X2 @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_239_transitions_OComm1,axiom,
% 2.83/1.55 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,B2: name,Q2: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.83/1.55 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A2 @ B2 ) @ Q2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.83/1.55 => ( ( X2 != A2 )
% 2.83/1.55 => ( ( X2 != B2 )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X2 @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_240_Tau,axiom,
% 2.83/1.55 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_241_tauCases_H,axiom,
% 2.83/1.55 ! [P: pi,Rs: late_residual] :
% 2.83/1.55 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 2.83/1.55 => ~ ! [P4: pi] :
% 2.83/1.55 ( ( ( tau @ P )
% 2.83/1.55 = ( tau @ P4 ) )
% 2.83/1.55 => ( Rs
% 2.83/1.55 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_242_tauCases,axiom,
% 2.83/1.55 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.83/1.55 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.83/1.55 => ( ( ( Alpha = late_TauR )
% 2.83/1.55 => ( ( P = P2 )
% 2.83/1.55 => ( Prop @ late_TauR @ P ) ) )
% 2.83/1.55 => ( Prop @ Alpha @ P2 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_243_transitions_OClose2,axiom,
% 2.83/1.55 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 2.83/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.83/1.55 => ( ( X2 != A2 )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P2 )
% 2.83/1.55 => ( ( Y != A2 )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ Q2 )
% 2.83/1.55 => ( ( X2 != Y )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_244_transitions_OClose1,axiom,
% 2.83/1.55 ! [P: pi,A2: name,X2: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ P2 ) )
% 2.83/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ Q2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ P )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ Q )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ P )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.83/1.55 => ( ( X2 != A2 )
% 2.83/1.55 => ( ( fresh @ name @ pi @ X2 @ Q2 )
% 2.83/1.55 => ( ( Y != A2 )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ P2 )
% 2.83/1.55 => ( ( X2 != Y )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X2 @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_245_Late__Semantics_OClose2,axiom,
% 2.83/1.55 ! [P: pi,A2: name,Y: name,P2: pi,Q: pi,X2: name,Q2: pi] :
% 2.83/1.55 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A2 ) @ Y @ P2 ) )
% 2.83/1.55 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A2 ) @ X2 @ Q2 ) )
% 2.83/1.55 => ( ( fresh @ name @ pi @ Y @ Q )
% 2.83/1.55 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_246_mismatchIdRight,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 2.83/1.55 => ( ( A2 != B2 )
% 2.83/1.55 => ( strong743114133lation @ P @ Rel @ ( mismatch @ A2 @ B2 @ P ) ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_247_mismatchIdLeft,axiom,
% 2.83/1.55 ! [Rel: set @ ( product_prod @ pi @ pi ),A2: name,B2: name,P: pi] :
% 2.83/1.55 ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ Rel )
% 2.83/1.55 => ( ( A2 != B2 )
% 2.83/1.55 => ( strong743114133lation @ ( mismatch @ A2 @ B2 @ P ) @ Rel @ P ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_248_pi_Ofresh_I6_J,axiom,
% 2.83/1.55 ! [A2: name,X32: name,X22: name,X1: pi] :
% 2.83/1.55 ( ( fresh @ name @ pi @ A2 @ ( mismatch @ X32 @ X22 @ X1 ) )
% 2.83/1.55 = ( ( fresh @ name @ name @ A2 @ X32 )
% 2.83/1.55 & ( fresh @ name @ name @ A2 @ X22 )
% 2.83/1.55 & ( fresh @ name @ pi @ A2 @ X1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_249_pi_Odistinct_I25_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 2.83/1.55 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_250_pi_Odistinct_I9_J,axiom,
% 2.83/1.55 ! [Name1: name,Name22: name,Pi: pi] :
% 2.83/1.55 ( piNil
% 2.83/1.55 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_251_pi_Odistinct_I71_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.83/1.55 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_252_pi_Odistinct_I51_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 2.83/1.55 ( ( input @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_253_pi_Odistinct_I39_J,axiom,
% 2.83/1.55 ! [Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 2.83/1.55 ( ( tau @ Pi4 )
% 2.83/1.55 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_254_pi_Oinject_I5_J,axiom,
% 2.83/1.55 ! [X32: name,X22: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.83/1.55 ( ( ( mismatch @ X32 @ X22 @ X1 )
% 2.83/1.55 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 2.83/1.55 = ( ( X32 = Y32 )
% 2.83/1.55 & ( X22 = Y2 )
% 2.83/1.55 & ( X1 = Y1 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(fact_255_pi_Odistinct_I73_J,axiom,
% 2.83/1.55 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.83/1.55 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 2.83/1.55 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( preorder @ A9 )
% 2.83/1.55 => ( preorder @ ( A8 > A9 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( order @ A9 )
% 2.83/1.55 => ( order @ ( A8 > A9 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_fun___Orderings_Oord,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( ord @ A9 )
% 2.83/1.55 => ( ord @ ( A8 > A9 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 2.83/1.55 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 2.83/1.55 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 2.83/1.55 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Agent_Opi___Agent_Ofs__name,axiom,
% 2.83/1.55 fs_name @ pi ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 2.83/1.55 preorder @ $o ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.83/1.55 linorder @ $o ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Orderings_Oorder_5,axiom,
% 2.83/1.55 order @ $o ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 2.83/1.55 ord @ $o ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_HOL_Obool___Agent_Ofs__name_7,axiom,
% 2.83/1.55 fs_name @ $o ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Agent_Oname___Agent_Ofs__name_8,axiom,
% 2.83/1.55 fs_name @ name ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Product__Type_Oprod___Agent_Ofs__name_9,axiom,
% 2.83/1.55 ! [A8: $tType,A9: $tType] :
% 2.83/1.55 ( ( ( fs_name @ A8 )
% 2.83/1.55 & ( fs_name @ A9 ) )
% 2.83/1.55 => ( fs_name @ ( product_prod @ A8 @ A9 ) ) ) ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_10,axiom,
% 2.83/1.55 fs_name @ late_freeRes ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Late__Semantics_Osubject___Agent_Ofs__name_11,axiom,
% 2.83/1.55 fs_name @ late_subject ).
% 2.83/1.55
% 2.83/1.55 thf(tcon_Late__Semantics_Oresidual___Agent_Ofs__name_12,axiom,
% 2.83/1.55 fs_name @ late_residual ).
% 2.83/1.55
% 2.83/1.55 thf(conj_0,conjecture,
% 2.83/1.55 y != x ).
% 2.83/1.55 ------------------------
% 2.83/1.58 % (31949)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/2Mi)
% 2.83/1.58 % (31948)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_31617 for (2999ds/27Mi)
% 2.83/1.58 % (31946)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/183Mi)
% 2.83/1.58 % (31949)Instruction limit reached!
% 2.83/1.58 % (31949)------------------------------
% 2.83/1.58 % (31949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.58 % (31949)Termination reason: Unknown
% 2.83/1.58 % (31949)Termination phase: shuffling
% 2.83/1.58
% 2.83/1.58 % (31949)Memory used [KB]: 1407
% 2.83/1.58 % (31949)Time elapsed: 0.002 s
% 2.83/1.58 % (31949)Instructions burned: 2 (million)
% 2.83/1.58 % (31949)------------------------------
% 2.83/1.58 % (31949)------------------------------
% 2.83/1.58 % (31952)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/18Mi)
% 2.83/1.59 % (31952)Instruction limit reached!
% 2.83/1.59 % (31952)------------------------------
% 2.83/1.59 % (31952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.59 % (31952)Termination reason: Unknown
% 2.83/1.59 % (31952)Termination phase: shuffling
% 2.83/1.59
% 2.83/1.59 % (31952)Memory used [KB]: 1791
% 2.83/1.59 % (31952)Time elapsed: 0.008 s
% 2.83/1.59 % (31952)Instructions burned: 20 (million)
% 2.83/1.59 % (31952)------------------------------
% 2.83/1.59 % (31952)------------------------------
% 2.83/1.59 % (31947)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_31617 for (2999ds/4Mi)
% 2.83/1.59 % (31950)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_31617 for (2999ds/2Mi)
% 2.83/1.59 % (31951)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_31617 for (2999ds/275Mi)
% 2.83/1.59 % (31948)Instruction limit reached!
% 2.83/1.59 % (31948)------------------------------
% 2.83/1.59 % (31948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.59 % (31948)Termination reason: Unknown
% 2.83/1.59 % (31948)Termination phase: shuffling
% 2.83/1.59
% 2.83/1.59 % (31948)Memory used [KB]: 1918
% 2.83/1.59 % (31948)Time elapsed: 0.010 s
% 2.83/1.59 % (31948)Instructions burned: 27 (million)
% 2.83/1.59 % (31948)------------------------------
% 2.83/1.59 % (31948)------------------------------
% 2.83/1.59 % (31950)Instruction limit reached!
% 2.83/1.59 % (31950)------------------------------
% 2.83/1.59 % (31950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.59 % (31950)Termination reason: Unknown
% 2.83/1.59 % (31950)Termination phase: shuffling
% 2.83/1.59
% 2.83/1.59 % (31950)Memory used [KB]: 1407
% 2.83/1.59 % (31950)Time elapsed: 0.004 s
% 2.83/1.59 % (31950)Instructions burned: 3 (million)
% 2.83/1.59 % (31950)------------------------------
% 2.83/1.59 % (31950)------------------------------
% 2.83/1.59 % (31953)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/3Mi)
% 2.83/1.59 % (31947)Instruction limit reached!
% 2.83/1.59 % (31947)------------------------------
% 2.83/1.59 % (31947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.59 % (31947)Termination reason: Unknown
% 2.83/1.59 % (31947)Termination phase: shuffling
% 2.83/1.59
% 2.83/1.59 % (31947)Memory used [KB]: 1535
% 2.83/1.59 % (31947)Time elapsed: 0.005 s
% 2.83/1.59 % (31947)Instructions burned: 5 (million)
% 2.83/1.59 % (31947)------------------------------
% 2.83/1.59 % (31947)------------------------------
% 2.83/1.59 % (31953)Instruction limit reached!
% 2.83/1.59 % (31953)------------------------------
% 2.83/1.59 % (31953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.59 % (31953)Termination reason: Unknown
% 2.83/1.59 % (31953)Termination phase: shuffling
% 2.83/1.59
% 2.83/1.59 % (31953)Memory used [KB]: 1407
% 2.83/1.59 % (31953)Time elapsed: 0.002 s
% 2.83/1.59 % (31953)Instructions burned: 3 (million)
% 2.83/1.59 % (31953)------------------------------
% 2.83/1.59 % (31953)------------------------------
% 2.90/1.60 % (31955)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_31617 for (2999ds/15Mi)
% 2.90/1.60 % (31954)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_31617 for (2999ds/37Mi)
% 2.90/1.60 % (31958)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/7Mi)
% 2.90/1.61 % (31955)Instruction limit reached!
% 2.90/1.61 % (31955)------------------------------
% 2.90/1.61 % (31955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (31955)Termination reason: Unknown
% 2.90/1.61 % (31955)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (31955)Memory used [KB]: 1791
% 2.90/1.61 % (31955)Time elapsed: 0.006 s
% 2.90/1.61 % (31955)Instructions burned: 15 (million)
% 2.90/1.61 % (31955)------------------------------
% 2.90/1.61 % (31955)------------------------------
% 2.90/1.61 % (31958)Instruction limit reached!
% 2.90/1.61 % (31958)------------------------------
% 2.90/1.61 % (31958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (31958)Termination reason: Unknown
% 2.90/1.61 % (31958)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (31958)Memory used [KB]: 1535
% 2.90/1.61 % (31958)Time elapsed: 0.004 s
% 2.90/1.61 % (31958)Instructions burned: 9 (million)
% 2.90/1.61 % (31958)------------------------------
% 2.90/1.61 % (31958)------------------------------
% 2.90/1.61 % (31956)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_31617 for (2999ds/3Mi)
% 2.90/1.61 % (31957)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_31617 for (2999ds/1041Mi)
% 2.90/1.61 % (31956)Instruction limit reached!
% 2.90/1.61 % (31956)------------------------------
% 2.90/1.61 % (31956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (31956)Termination reason: Unknown
% 2.90/1.61 % (31956)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (31956)Memory used [KB]: 1407
% 2.90/1.61 % (31956)Time elapsed: 0.004 s
% 2.90/1.61 % (31956)Instructions burned: 4 (million)
% 2.90/1.61 % (31956)------------------------------
% 2.90/1.61 % (31956)------------------------------
% 2.90/1.61 % (31954)Instruction limit reached!
% 2.90/1.61 % (31954)------------------------------
% 2.90/1.61 % (31954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (31954)Termination reason: Unknown
% 2.90/1.61 % (31954)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (31954)Memory used [KB]: 2174
% 2.90/1.61 % (31954)Time elapsed: 0.012 s
% 2.90/1.61 % (31954)Instructions burned: 37 (million)
% 2.90/1.61 % (31954)------------------------------
% 2.90/1.61 % (31954)------------------------------
% 2.90/1.62 % (31959)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/16Mi)
% 2.90/1.62 % (31960)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_31617 for (2999ds/3Mi)
% 2.90/1.62 % (31951)Refutation not found, incomplete strategy
% 2.90/1.62 % (31951)------------------------------
% 2.90/1.62 % (31951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (31951)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.62
% 2.90/1.62
% 2.90/1.62 % (31951)Memory used [KB]: 6396
% 2.90/1.62 % (31951)Time elapsed: 0.027 s
% 2.90/1.62 % (31951)Instructions burned: 43 (million)
% 2.90/1.62 % (31951)------------------------------
% 2.90/1.62 % (31951)------------------------------
% 2.90/1.62 % (31960)Instruction limit reached!
% 2.90/1.62 % (31960)------------------------------
% 2.90/1.62 % (31960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (31960)Termination reason: Unknown
% 2.90/1.62 % (31960)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (31960)Memory used [KB]: 1407
% 2.90/1.62 % (31960)Time elapsed: 0.002 s
% 2.90/1.62 % (31960)Instructions burned: 3 (million)
% 2.90/1.62 % (31960)------------------------------
% 2.90/1.62 % (31960)------------------------------
% 2.90/1.62 % (31959)Instruction limit reached!
% 2.90/1.62 % (31959)------------------------------
% 2.90/1.62 % (31959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (31959)Termination reason: Unknown
% 2.90/1.62 % (31959)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (31959)Memory used [KB]: 1663
% 2.90/1.62 % (31959)Time elapsed: 0.006 s
% 2.90/1.62 % (31959)Instructions burned: 16 (million)
% 2.90/1.62 % (31959)------------------------------
% 2.90/1.62 % (31959)------------------------------
% 2.90/1.62 % (31962)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/7Mi)
% 2.90/1.62 % (31962)Instruction limit reached!
% 2.90/1.62 % (31962)------------------------------
% 2.90/1.62 % (31962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (31962)Termination reason: Unknown
% 2.90/1.62 % (31962)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (31962)Memory used [KB]: 1535
% 2.90/1.62 % (31962)Time elapsed: 0.004 s
% 2.90/1.62 % (31962)Instructions burned: 9 (million)
% 2.90/1.62 % (31962)------------------------------
% 2.90/1.62 % (31962)------------------------------
% 2.90/1.63 % (31963)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/3Mi)
% 2.90/1.63 % (31963)Instruction limit reached!
% 2.90/1.63 % (31963)------------------------------
% 2.90/1.63 % (31963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.63 % (31963)Termination reason: Unknown
% 2.90/1.63 % (31963)Termination phase: shuffling
% 2.90/1.63
% 2.90/1.63 % (31963)Memory used [KB]: 1407
% 2.90/1.63 % (31963)Time elapsed: 0.002 s
% 2.90/1.63 % (31963)Instructions burned: 4 (million)
% 2.90/1.63 % (31963)------------------------------
% 2.90/1.63 % (31963)------------------------------
% 2.90/1.63 % (31965)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/18Mi)
% 2.90/1.63 % (31961)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_31617 for (2999ds/3Mi)
% 2.90/1.63 % (31961)Instruction limit reached!
% 2.90/1.63 % (31961)------------------------------
% 2.90/1.63 % (31961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.63 % (31961)Termination reason: Unknown
% 2.90/1.63 % (31961)Termination phase: shuffling
% 2.90/1.63
% 2.90/1.63 % (31961)Memory used [KB]: 1407
% 2.90/1.63 % (31961)Time elapsed: 0.004 s
% 2.90/1.63 % (31961)Instructions burned: 4 (million)
% 2.90/1.63 % (31961)------------------------------
% 2.90/1.63 % (31961)------------------------------
% 2.90/1.63 % (31966)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/710Mi)
% 2.90/1.63 % (31964)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/4Mi)
% 2.90/1.64 % (31965)Instruction limit reached!
% 2.90/1.64 % (31965)------------------------------
% 2.90/1.64 % (31965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.64 % (31965)Termination reason: Unknown
% 2.90/1.64 % (31965)Termination phase: shuffling
% 2.90/1.64
% 2.90/1.64 % (31965)Memory used [KB]: 1791
% 2.90/1.64 % (31965)Time elapsed: 0.007 s
% 2.90/1.64 % (31965)Instructions burned: 19 (million)
% 2.90/1.64 % (31965)------------------------------
% 2.90/1.64 % (31965)------------------------------
% 2.90/1.64 % (31967)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/6Mi)
% 2.90/1.64 % (31964)Instruction limit reached!
% 2.90/1.64 % (31964)------------------------------
% 2.90/1.64 % (31964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.64 % (31964)Termination reason: Unknown
% 2.90/1.64 % (31964)Termination phase: shuffling
% 2.90/1.64
% 2.90/1.64 % (31964)Memory used [KB]: 1407
% 2.90/1.64 % (31964)Time elapsed: 0.004 s
% 2.90/1.64 % (31964)Instructions burned: 4 (million)
% 2.90/1.64 % (31964)------------------------------
% 2.90/1.64 % (31964)------------------------------
% 2.90/1.64 % (31967)Instruction limit reached!
% 2.90/1.64 % (31967)------------------------------
% 2.90/1.64 % (31967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.64 % (31967)Termination reason: Unknown
% 2.90/1.64 % (31967)Termination phase: shuffling
% 2.90/1.64
% 2.90/1.64 % (31967)Memory used [KB]: 1535
% 2.90/1.64 % (31967)Time elapsed: 0.003 s
% 2.90/1.64 % (31967)Instructions burned: 6 (million)
% 2.90/1.64 % (31967)------------------------------
% 2.90/1.64 % (31967)------------------------------
% 2.90/1.64 % (31946)Instruction limit reached!
% 2.90/1.64 % (31946)------------------------------
% 2.90/1.64 % (31946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.64 % (31946)Termination reason: Unknown
% 2.90/1.64 % (31946)Termination phase: Saturation
% 2.90/1.64
% 2.90/1.64 % (31946)Memory used [KB]: 7675
% 2.90/1.64 % (31946)Time elapsed: 0.057 s
% 2.90/1.64 % (31946)Instructions burned: 183 (million)
% 2.90/1.64 % (31946)------------------------------
% 2.90/1.64 % (31946)------------------------------
% 2.90/1.64 % (31969)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_31617 for (2999ds/21Mi)
% 2.90/1.65 % (31968)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_31617 for (2999ds/902Mi)
% 2.90/1.65 % (31971)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_31617 for (2999ds/6Mi)
% 2.90/1.65 % (31966)Refutation not found, incomplete strategy
% 2.90/1.65 % (31966)------------------------------
% 2.90/1.65 % (31966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.65 % (31970)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/5Mi)
% 2.90/1.65 % (31966)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.65
% 2.90/1.65
% 2.90/1.65 % (31966)Memory used [KB]: 6524
% 2.90/1.65 % (31966)Time elapsed: 0.015 s
% 2.90/1.65 % (31966)Instructions burned: 45 (million)
% 2.90/1.65 % (31966)------------------------------
% 2.90/1.65 % (31966)------------------------------
% 2.90/1.65 % (31971)Instruction limit reached!
% 2.90/1.65 % (31971)------------------------------
% 2.90/1.65 % (31971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.65 % (31971)Termination reason: Unknown
% 2.90/1.65 % (31971)Termination phase: shuffling
% 2.90/1.65
% 2.90/1.65 % (31971)Memory used [KB]: 1535
% 2.90/1.65 % (31971)Time elapsed: 0.003 s
% 2.90/1.65 % (31971)Instructions burned: 7 (million)
% 2.90/1.65 % (31971)------------------------------
% 2.90/1.65 % (31971)------------------------------
% 2.90/1.65 % (31972)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/377Mi)
% 2.90/1.65 % (31970)Instruction limit reached!
% 2.90/1.65 % (31970)------------------------------
% 2.90/1.65 % (31970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.65 % (31970)Termination reason: Unknown
% 2.90/1.65 % (31970)Termination phase: shuffling
% 2.90/1.65
% 2.90/1.65 % (31970)Memory used [KB]: 1535
% 2.90/1.65 % (31970)Time elapsed: 0.003 s
% 2.90/1.65 % (31970)Instructions burned: 6 (million)
% 2.90/1.65 % (31970)------------------------------
% 2.90/1.65 % (31970)------------------------------
% 2.90/1.65 % (31969)Instruction limit reached!
% 2.90/1.65 % (31969)------------------------------
% 2.90/1.65 % (31969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.65 % (31969)Termination reason: Unknown
% 2.90/1.65 % (31969)Termination phase: shuffling
% 2.90/1.65
% 2.90/1.65 % (31969)Memory used [KB]: 1918
% 2.90/1.65 % (31969)Time elapsed: 0.008 s
% 2.90/1.65 % (31969)Instructions burned: 22 (million)
% 2.90/1.65 % (31969)------------------------------
% 2.90/1.65 % (31969)------------------------------
% 2.90/1.66 % (31973)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_31617 for (2999ds/779Mi)
% 2.90/1.66 % (31974)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_31617 for (2999ds/19Mi)
% 2.90/1.66 % (31975)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/879Mi)
% 2.90/1.66 % (31976)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/17Mi)
% 2.90/1.66 % (31974)Instruction limit reached!
% 2.90/1.66 % (31974)------------------------------
% 2.90/1.66 % (31974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.66 % (31974)Termination reason: Unknown
% 2.90/1.66 % (31974)Termination phase: shuffling
% 2.90/1.66
% 2.90/1.66 % (31974)Memory used [KB]: 1918
% 2.90/1.66 % (31974)Time elapsed: 0.007 s
% 2.90/1.66 % (31974)Instructions burned: 22 (million)
% 2.90/1.66 % (31974)------------------------------
% 2.90/1.66 % (31974)------------------------------
% 2.90/1.67 % (31976)Instruction limit reached!
% 2.90/1.67 % (31976)------------------------------
% 2.90/1.67 % (31976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.67 % (31976)Termination reason: Unknown
% 2.90/1.67 % (31976)Termination phase: shuffling
% 2.90/1.67
% 2.90/1.67 % (31976)Memory used [KB]: 1791
% 2.90/1.67 % (31976)Time elapsed: 0.007 s
% 2.90/1.67 % (31976)Instructions burned: 18 (million)
% 2.90/1.67 % (31976)------------------------------
% 2.90/1.67 % (31976)------------------------------
% 2.90/1.67 % (31977)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_31617 for (2999ds/3Mi)
% 2.90/1.68 % (31977)Instruction limit reached!
% 2.90/1.68 % (31977)------------------------------
% 2.90/1.68 % (31977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.68 % (31977)Termination reason: Unknown
% 2.90/1.68 % (31977)Termination phase: shuffling
% 2.90/1.68
% 2.90/1.68 % (31977)Memory used [KB]: 1407
% 2.90/1.68 % (31977)Time elapsed: 0.002 s
% 2.90/1.68 % (31977)Instructions burned: 3 (million)
% 2.90/1.68 % (31977)------------------------------
% 2.90/1.68 % (31977)------------------------------
% 2.90/1.68 % (31975)Refutation not found, incomplete strategy
% 2.90/1.68 % (31975)------------------------------
% 2.90/1.68 % (31975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.68 % (31975)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.68
% 2.90/1.68
% 2.90/1.68 % (31975)Memory used [KB]: 6396
% 2.90/1.68 % (31975)Time elapsed: 0.017 s
% 2.90/1.68 % (31975)Instructions burned: 52 (million)
% 2.90/1.68 % (31975)------------------------------
% 2.90/1.68 % (31975)------------------------------
% 2.90/1.68 % (31978)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_31617 for (2998ds/30Mi)
% 2.90/1.68 % (31979)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_31617 for (2998ds/127Mi)
% 2.90/1.69 % (31980)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_31617 for (2998ds/100Mi)
% 2.90/1.69 % (31978)Instruction limit reached!
% 2.90/1.69 % (31978)------------------------------
% 2.90/1.69 % (31978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.69 % (31978)Termination reason: Unknown
% 2.90/1.69 % (31978)Termination phase: shuffling
% 2.90/1.69
% 2.90/1.69 % (31978)Memory used [KB]: 2046
% 2.90/1.69 % (31978)Time elapsed: 0.011 s
% 2.90/1.69 % (31978)Instructions burned: 30 (million)
% 2.90/1.69 % (31978)------------------------------
% 2.90/1.69 % (31978)------------------------------
% 2.90/1.70 % (31981)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_31617 for (2998ds/3Mi)
% 2.90/1.70 % (31981)Instruction limit reached!
% 2.90/1.70 % (31981)------------------------------
% 2.90/1.70 % (31981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.70 % (31981)Termination reason: Unknown
% 2.90/1.70 % (31981)Termination phase: shuffling
% 2.90/1.70
% 2.90/1.70 % (31981)Memory used [KB]: 1407
% 2.90/1.70 % (31981)Time elapsed: 0.002 s
% 2.90/1.70 % (31981)Instructions burned: 4 (million)
% 2.90/1.70 % (31981)------------------------------
% 2.90/1.70 % (31981)------------------------------
% 2.90/1.71 % (31982)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_31617 for (2998ds/20Mi)
% 2.90/1.71 % (31980)Instruction limit reached!
% 2.90/1.71 % (31980)------------------------------
% 2.90/1.71 % (31980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.71 % (31980)Termination reason: Unknown
% 2.90/1.71 % (31980)Termination phase: Property scanning
% 2.90/1.71
% 2.90/1.71 % (31980)Memory used [KB]: 2686
% 2.90/1.71 % (31980)Time elapsed: 0.028 s
% 2.90/1.71 % (31980)Instructions burned: 101 (million)
% 2.90/1.71 % (31980)------------------------------
% 2.90/1.71 % (31980)------------------------------
% 2.90/1.71 % (31982)Instruction limit reached!
% 2.90/1.71 % (31982)------------------------------
% 2.90/1.71 % (31982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.71 % (31982)Termination reason: Unknown
% 2.90/1.71 % (31982)Termination phase: shuffling
% 2.90/1.71
% 2.90/1.71 % (31982)Memory used [KB]: 1791
% 2.90/1.71 % (31982)Time elapsed: 0.008 s
% 2.90/1.71 % (31982)Instructions burned: 21 (million)
% 2.90/1.71 % (31982)------------------------------
% 2.90/1.71 % (31982)------------------------------
% 2.90/1.72 % (31979)Instruction limit reached!
% 2.90/1.72 % (31979)------------------------------
% 2.90/1.72 % (31979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.72 % (31979)Termination reason: Unknown
% 2.90/1.72 % (31979)Termination phase: Saturation
% 2.90/1.72
% 2.90/1.72 % (31979)Memory used [KB]: 7036
% 2.90/1.72 % (31979)Time elapsed: 0.037 s
% 2.90/1.72 % (31979)Instructions burned: 128 (million)
% 2.90/1.72 % (31979)------------------------------
% 2.90/1.72 % (31979)------------------------------
% 2.90/1.72 % (31983)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_31617 for (2998ds/86Mi)
% 2.90/1.72 % (31984)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_31617 for (2998ds/107Mi)
% 2.90/1.73 % (31985)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_31617 for (2998ds/39Mi)
% 2.90/1.74 % (31985)Instruction limit reached!
% 2.90/1.74 % (31985)------------------------------
% 2.90/1.74 % (31985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.74 % (31985)Termination reason: Unknown
% 2.90/1.74 % (31985)Termination phase: shuffling
% 2.90/1.74
% 2.90/1.74 % (31985)Memory used [KB]: 2302
% 2.90/1.74 % (31985)Time elapsed: 0.012 s
% 2.90/1.74 % (31985)Instructions burned: 41 (million)
% 2.90/1.74 % (31985)------------------------------
% 2.90/1.74 % (31985)------------------------------
% 2.90/1.75 % (31983)Instruction limit reached!
% 2.90/1.75 % (31983)------------------------------
% 2.90/1.75 % (31983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.75 % (31983)Termination reason: Unknown
% 2.90/1.75 % (31983)Termination phase: Function definition elimination
% 2.90/1.75
% 2.90/1.75 % (31983)Memory used [KB]: 2558
% 2.90/1.75 % (31983)Time elapsed: 0.026 s
% 2.90/1.75 % (31983)Instructions burned: 87 (million)
% 2.90/1.75 % (31983)------------------------------
% 2.90/1.75 % (31983)------------------------------
% 2.90/1.75 % (31986)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_31617 for (2998ds/448Mi)
% 2.90/1.75 % (31984)Instruction limit reached!
% 2.90/1.75 % (31984)------------------------------
% 2.90/1.75 % (31984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.75 % (31984)Termination reason: Unknown
% 2.90/1.75 % (31984)Termination phase: Saturation
% 2.90/1.75
% 2.90/1.75 % (31984)Memory used [KB]: 7036
% 2.90/1.75 % (31984)Time elapsed: 0.032 s
% 2.90/1.75 % (31984)Instructions burned: 108 (million)
% 2.90/1.75 % (31984)------------------------------
% 2.90/1.75 % (31984)------------------------------
% 2.90/1.76 % (31987)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_31617 for (2998ds/46Mi)
% 2.90/1.76 % (31988)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_31617 for (2998ds/98Mi)
% 2.90/1.77 % (31972)Instruction limit reached!
% 2.90/1.77 % (31972)------------------------------
% 2.90/1.77 % (31972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.77 % (31972)Termination reason: Unknown
% 2.90/1.77 % (31972)Termination phase: Saturation
% 2.90/1.77
% 2.90/1.77 % (31972)Memory used [KB]: 8827
% 2.90/1.77 % (31972)Time elapsed: 0.122 s
% 2.90/1.77 % (31972)Instructions burned: 379 (million)
% 2.90/1.77 % (31972)------------------------------
% 2.90/1.77 % (31972)------------------------------
% 2.90/1.77 % (31987)Instruction limit reached!
% 2.90/1.77 % (31987)------------------------------
% 2.90/1.77 % (31987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.77 % (31987)Termination reason: Unknown
% 2.90/1.77 % (31987)Termination phase: SInE selection
% 2.90/1.77
% 2.90/1.77 % (31987)Memory used [KB]: 1918
% 2.90/1.77 % (31987)Time elapsed: 0.015 s
% 2.90/1.77 % (31987)Instructions burned: 47 (million)
% 2.90/1.77 % (31987)------------------------------
% 2.90/1.77 % (31987)------------------------------
% 2.90/1.78 % (31990)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_31617 for (2997ds/149Mi)
% 2.90/1.78 % (31989)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_31617 for (2997ds/507Mi)
% 2.90/1.79 % (31988)Instruction limit reached!
% 2.90/1.79 % (31988)------------------------------
% 2.90/1.79 % (31988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.79 % (31988)Termination reason: Unknown
% 2.90/1.79 % (31988)Termination phase: Property scanning
% 2.90/1.79
% 2.90/1.79 % (31988)Memory used [KB]: 2686
% 2.90/1.79 % (31988)Time elapsed: 0.027 s
% 2.90/1.79 % (31988)Instructions burned: 98 (million)
% 2.90/1.79 % (31988)------------------------------
% 2.90/1.79 % (31988)------------------------------
% 2.90/1.80 % (31991)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_31617 for (2997ds/39Mi)
% 2.90/1.81 % (31991)Instruction limit reached!
% 2.90/1.81 % (31991)------------------------------
% 2.90/1.81 % (31991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.81 % (31991)Termination reason: Unknown
% 2.90/1.81 % (31991)Termination phase: Preprocessing 1
% 2.90/1.81
% 2.90/1.81 % (31991)Memory used [KB]: 1918
% 2.90/1.81 % (31991)Time elapsed: 0.014 s
% 2.90/1.81 % (31991)Instructions burned: 41 (million)
% 2.90/1.81 % (31991)------------------------------
% 2.90/1.81 % (31991)------------------------------
% 2.90/1.82 % (31990)Instruction limit reached!
% 2.90/1.82 % (31990)------------------------------
% 2.90/1.82 % (31990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.82 % (31990)Termination reason: Unknown
% 2.90/1.82 % (31990)Termination phase: Property scanning
% 2.90/1.82
% 2.90/1.82 % (31990)Memory used [KB]: 2558
% 2.90/1.82 % (31990)Time elapsed: 0.042 s
% 2.90/1.82 % (31990)Instructions burned: 152 (million)
% 2.90/1.82 % (31990)------------------------------
% 2.90/1.82 % (31990)------------------------------
% 2.90/1.82 % (31992)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_31617 for (2997ds/6Mi)
% 2.90/1.82 % (31992)Instruction limit reached!
% 2.90/1.82 % (31992)------------------------------
% 2.90/1.82 % (31992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.82 % (31992)Termination reason: Unknown
% 2.90/1.82 % (31992)Termination phase: shuffling
% 2.90/1.82
% 2.90/1.82 % (31992)Memory used [KB]: 1535
% 2.90/1.82 % (31992)Time elapsed: 0.003 s
% 2.90/1.82 % (31992)Instructions burned: 7 (million)
% 2.90/1.82 % (31992)------------------------------
% 2.90/1.82 % (31992)------------------------------
% 2.90/1.83 % (31993)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_31617 for (2997ds/1087Mi)
% 2.90/1.83 % (31994)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_31617 for (2997ds/47Mi)
% 2.90/1.84 % (31993)Refutation not found, incomplete strategy
% 2.90/1.84 % (31993)------------------------------
% 2.90/1.84 % (31993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.84 % (31993)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.84
% 2.90/1.84
% 2.90/1.84 % (31993)Memory used [KB]: 6396
% 2.90/1.84 % (31993)Time elapsed: 0.015 s
% 2.90/1.84 % (31993)Instructions burned: 47 (million)
% 2.90/1.84 % (31993)------------------------------
% 2.90/1.84 % (31993)------------------------------
% 2.90/1.85 % (31994)Instruction limit reached!
% 2.90/1.85 % (31994)------------------------------
% 2.90/1.85 % (31994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.85 % (31994)Termination reason: Unknown
% 2.90/1.85 % (31994)Termination phase: Preprocessing 3
% 2.90/1.85
% 2.90/1.85 % (31994)Memory used [KB]: 2174
% 2.90/1.85 % (31994)Time elapsed: 0.016 s
% 2.90/1.85 % (31994)Instructions burned: 49 (million)
% 2.90/1.85 % (31994)------------------------------
% 2.90/1.85 % (31994)------------------------------
% 2.90/1.85 % (31995)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_31617 for (2997ds/44Mi)
% 2.90/1.86 % (31996)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_31617 for (2997ds/432Mi)
% 2.90/1.87 % (31995)Instruction limit reached!
% 2.90/1.87 % (31995)------------------------------
% 2.90/1.87 % (31995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.87 % (31995)Termination reason: Unknown
% 2.90/1.87 % (31995)Termination phase: shuffling
% 2.90/1.87
% 2.90/1.87 % (31995)Memory used [KB]: 2302
% 2.90/1.87 % (31995)Time elapsed: 0.013 s
% 2.90/1.87 % (31995)Instructions burned: 44 (million)
% 2.90/1.87 % (31995)------------------------------
% 2.90/1.87 % (31995)------------------------------
% 2.90/1.88 % (31997)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_31617 for (2996ds/62Mi)
% 2.90/1.88 % (31986)Instruction limit reached!
% 2.90/1.88 % (31986)------------------------------
% 2.90/1.88 % (31986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.88 % (31986)Termination reason: Unknown
% 2.90/1.88 % (31986)Termination phase: Saturation
% 2.90/1.88
% 2.90/1.88 % (31986)Memory used [KB]: 9083
% 2.90/1.88 % (31986)Time elapsed: 0.155 s
% 2.90/1.88 % (31986)Instructions burned: 450 (million)
% 2.90/1.88 % (31986)------------------------------
% 2.90/1.88 % (31986)------------------------------
% 2.90/1.89 % (31998)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_31617 for (2996ds/31Mi)
% 2.90/1.89 % (31997)Instruction limit reached!
% 2.90/1.89 % (31997)------------------------------
% 2.90/1.89 % (31997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.89 % (31997)Termination reason: Unknown
% 2.90/1.89 % (31997)Termination phase: Property scanning
% 2.90/1.89
% 2.90/1.89 % (31997)Memory used [KB]: 2430
% 2.90/1.89 % (31997)Time elapsed: 0.018 s
% 2.90/1.89 % (31997)Instructions burned: 64 (million)
% 2.90/1.89 % (31997)------------------------------
% 2.90/1.89 % (31997)------------------------------
% 2.90/1.90 % (31973)Instruction limit reached!
% 2.90/1.90 % (31973)------------------------------
% 2.90/1.90 % (31973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.90 % (31973)Termination reason: Unknown
% 2.90/1.90 % (31973)Termination phase: Saturation
% 2.90/1.90
% 2.90/1.90 % (31973)Memory used [KB]: 9083
% 2.90/1.90 % (31973)Time elapsed: 0.238 s
% 2.90/1.90 % (31973)Instructions burned: 781 (million)
% 2.90/1.90 % (31973)------------------------------
% 2.90/1.90 % (31973)------------------------------
% 2.90/1.90 % (31998)Instruction limit reached!
% 2.90/1.90 % (31998)------------------------------
% 2.90/1.90 % (31998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.90 % (31998)Termination reason: Unknown
% 2.90/1.90 % (31998)Termination phase: Property scanning
% 2.90/1.90
% 2.90/1.90 % (31998)Memory used [KB]: 1918
% 2.90/1.90 % (31998)Time elapsed: 0.011 s
% 2.90/1.90 % (31998)Instructions burned: 32 (million)
% 2.90/1.90 % (31998)------------------------------
% 2.90/1.90 % (31998)------------------------------
% 2.90/1.90 % (31999)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_31617 for (2996ds/96Mi)
% 2.90/1.91 % (32000)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_31617 for (2996ds/453Mi)
% 2.90/1.91 % (32001)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_31617 for (2996ds/71Mi)
% 2.90/1.93 % (31999)Instruction limit reached!
% 2.90/1.93 % (31999)------------------------------
% 2.90/1.93 % (31999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.93 % (31999)Termination reason: Unknown
% 2.90/1.93 % (31999)Termination phase: Property scanning
% 2.90/1.93
% 2.90/1.93 % (31999)Memory used [KB]: 2558
% 2.90/1.93 % (31999)Time elapsed: 0.030 s
% 2.90/1.93 % (31999)Instructions burned: 99 (million)
% 2.90/1.93 % (31999)------------------------------
% 2.90/1.93 % (31999)------------------------------
% 2.90/1.93 % (32001)Instruction limit reached!
% 2.90/1.93 % (32001)------------------------------
% 2.90/1.93 % (32001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.93 % (32001)Termination reason: Unknown
% 2.90/1.93 % (32001)Termination phase: Property scanning
% 2.90/1.93
% 2.90/1.93 % (32001)Memory used [KB]: 2558
% 2.90/1.93 % (32001)Time elapsed: 0.023 s
% 2.90/1.93 % (32001)Instructions burned: 71 (million)
% 2.90/1.93 % (32001)------------------------------
% 2.90/1.93 % (32001)------------------------------
% 2.90/1.94 % (31968)Instruction limit reached!
% 2.90/1.94 % (31968)------------------------------
% 2.90/1.94 % (31968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.94 % (31968)Termination reason: Unknown
% 2.90/1.94 % (31968)Termination phase: Saturation
% 2.90/1.94
% 2.90/1.94 % (31968)Memory used [KB]: 9466
% 2.90/1.94 % (31968)Time elapsed: 0.295 s
% 2.90/1.94 % (31968)Instructions burned: 904 (million)
% 2.90/1.94 % (31968)------------------------------
% 2.90/1.94 % (31968)------------------------------
% 2.90/1.94 % (32002)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_31617 for (2996ds/83Mi)
% 2.90/1.94 % (32003)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_31617 for (2996ds/11Mi)
% 2.90/1.94 % (31989)Instruction limit reached!
% 2.90/1.94 % (31989)------------------------------
% 2.90/1.94 % (31989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.94 % (31989)Termination reason: Unknown
% 2.90/1.94 % (31989)Termination phase: Saturation
% 2.90/1.94
% 2.90/1.94 % (31989)Memory used [KB]: 8955
% 2.90/1.94 % (31989)Time elapsed: 0.166 s
% 2.90/1.94 % (31989)Instructions burned: 508 (million)
% 2.90/1.94 % (31989)------------------------------
% 2.90/1.94 % (31989)------------------------------
% 2.90/1.95 % (32003)Instruction limit reached!
% 2.90/1.95 % (32003)------------------------------
% 2.90/1.95 % (32003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.95 % (32003)Termination reason: Unknown
% 2.90/1.95 % (32003)Termination phase: shuffling
% 2.90/1.95
% 2.90/1.95 % (32003)Memory used [KB]: 1663
% 2.90/1.95 % (32003)Time elapsed: 0.004 s
% 2.90/1.95 % (32003)Instructions burned: 12 (million)
% 2.90/1.95 % (32003)------------------------------
% 2.90/1.95 % (32003)------------------------------
% 2.90/1.95 % (32005)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31617 for (2996ds/6Mi)
% 2.90/1.96 % (32006)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_31617 for (2996ds/150Mi)
% 2.90/1.96 % (32002)Refutation not found, incomplete strategy
% 2.90/1.96 % (32002)------------------------------
% 2.90/1.96 % (32002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.96 % (32002)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.96
% 2.90/1.96
% 2.90/1.96 % (32002)Memory used [KB]: 6396
% 2.90/1.96 % (32002)Time elapsed: 0.016 s
% 2.90/1.96 % (32002)Instructions burned: 47 (million)
% 2.90/1.96 % (32002)------------------------------
% 2.90/1.96 % (32002)------------------------------
% 2.90/1.96 % (32005)Instruction limit reached!
% 2.90/1.96 % (32005)------------------------------
% 2.90/1.96 % (32005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.96 % (32005)Termination reason: Unknown
% 2.90/1.96 % (32005)Termination phase: shuffling
% 2.90/1.96
% 2.90/1.96 % (32005)Memory used [KB]: 1407
% 2.90/1.96 % (32005)Time elapsed: 0.003 s
% 2.90/1.96 % (32005)Instructions burned: 6 (million)
% 2.90/1.96 % (32005)------------------------------
% 2.90/1.96 % (32005)------------------------------
% 2.90/1.96 % (32004)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_31617 for (2996ds/41Mi)
% 2.90/1.97 % (32007)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_31617 for (2996ds/343Mi)
% 2.90/1.97 % (32008)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_31617 for (2996ds/109Mi)
% 2.90/1.98 % (32004)Instruction limit reached!
% 2.90/1.98 % (32004)------------------------------
% 2.90/1.98 % (32004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.98 % (32004)Termination reason: Unknown
% 2.90/1.98 % (32004)Termination phase: shuffling
% 2.90/1.98
% 2.90/1.98 % (32004)Memory used [KB]: 2302
% 2.90/1.98 % (32004)Time elapsed: 0.024 s
% 2.90/1.98 % (32004)Instructions burned: 42 (million)
% 2.90/1.98 % (32004)------------------------------
% 2.90/1.98 % (32004)------------------------------
% 2.90/1.98 % (31996)Instruction limit reached!
% 2.90/1.98 % (31996)------------------------------
% 2.90/1.98 % (31996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.98 % (31996)Termination reason: Unknown
% 2.90/1.98 % (31996)Termination phase: Saturation
% 2.90/1.98
% 2.90/1.98 % (31996)Memory used [KB]: 4477
% 2.90/1.98 % (31996)Time elapsed: 0.128 s
% 2.90/1.98 % (31996)Instructions burned: 432 (million)
% 2.90/1.98 % (31996)------------------------------
% 2.90/1.98 % (31996)------------------------------
% 2.90/1.99 % (31957)Instruction limit reached!
% 2.90/1.99 % (31957)------------------------------
% 2.90/1.99 % (31957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.99 % (31957)Termination reason: Unknown
% 2.90/1.99 % (31957)Termination phase: Saturation
% 2.90/1.99
% 2.90/1.99 % (31957)Memory used [KB]: 10234
% 2.90/1.99 % (31957)Time elapsed: 0.379 s
% 2.90/1.99 % (31957)Instructions burned: 1042 (million)
% 2.90/1.99 % (31957)------------------------------
% 2.90/1.99 % (31957)------------------------------
% 2.90/1.99 % (32010)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_31617 for (2995ds/140Mi)
% 2.90/2.00 % (32006)Instruction limit reached!
% 2.90/2.00 % (32006)------------------------------
% 2.90/2.00 % (32006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/2.00 % (32006)Termination reason: Unknown
% 2.90/2.00 % (32006)Termination phase: Saturation
% 2.90/2.00
% 2.90/2.00 % (32006)Memory used [KB]: 7164
% 2.90/2.00 % (32006)Time elapsed: 0.043 s
% 2.90/2.00 % (32006)Instructions burned: 153 (million)
% 2.90/2.00 % (32006)------------------------------
% 2.90/2.00 % (32006)------------------------------
% 2.90/2.00 % (32008)Instruction limit reached!
% 2.90/2.00 % (32008)------------------------------
% 2.90/2.00 % (32008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/2.00 % (32008)Termination reason: Unknown
% 2.90/2.00 % (32008)Termination phase: Property scanning
% 2.90/2.00
% 2.90/2.00 % (32008)Memory used [KB]: 2430
% 2.90/2.00 % (32008)Time elapsed: 0.033 s
% 2.90/2.00 % (32008)Instructions burned: 112 (million)
% 2.90/2.00 % (32008)------------------------------
% 2.90/2.00 % (32008)------------------------------
% 2.90/2.00 % (32009)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_31617 for (2995ds/253Mi)
% 2.90/2.00 % (32011)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_31617 for (2995ds/614Mi)
% 2.90/2.01 % (32012)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_31617 for (2995ds/202Mi)
% 2.90/2.01 % (32013)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_31617 for (2995ds/339Mi)
% 2.90/2.01 % (32010)Refutation not found, incomplete strategy
% 2.90/2.01 % (32010)------------------------------
% 2.90/2.01 % (32010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/2.01 % (32010)Termination reason: Refutation not found, incomplete strategy
% 2.90/2.01
% 2.90/2.01
% 2.90/2.01 % (32010)Memory used [KB]: 6524
% 2.90/2.01 % (32010)Time elapsed: 0.016 s
% 2.90/2.01 % (32010)Instructions burned: 50 (million)
% 2.90/2.01 % (32010)------------------------------
% 2.90/2.01 % (32010)------------------------------
% 5.93/2.02 % (32014)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_31617 for (2995ds/283Mi)
% 5.93/2.02 % (32012)Refutation not found, incomplete strategy
% 5.93/2.02 % (32012)------------------------------
% 5.93/2.02 % (32012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.02 % (32012)Termination reason: Refutation not found, incomplete strategy
% 5.93/2.02
% 5.93/2.02
% 5.93/2.02 % (32012)Memory used [KB]: 6524
% 5.93/2.02 % (32012)Time elapsed: 0.015 s
% 5.93/2.02 % (32012)Instructions burned: 46 (million)
% 5.93/2.02 % (32012)------------------------------
% 5.93/2.02 % (32012)------------------------------
% 5.93/2.02 % (32009)Refutation not found, incomplete strategy
% 5.93/2.02 % (32009)------------------------------
% 5.93/2.02 % (32009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.02 % (32009)Termination reason: Refutation not found, incomplete strategy
% 5.93/2.02
% 5.93/2.02
% 5.93/2.02 % (32009)Memory used [KB]: 6396
% 5.93/2.02 % (32009)Time elapsed: 0.027 s
% 5.93/2.02 % (32009)Instructions burned: 43 (million)
% 5.93/2.02 % (32009)------------------------------
% 5.93/2.02 % (32009)------------------------------
% 5.93/2.03 % (32015)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_31617 for (2995ds/134Mi)
% 5.93/2.04 % (32000)Instruction limit reached!
% 5.93/2.04 % (32000)------------------------------
% 5.93/2.04 % (32000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.04 % (32000)Termination reason: Unknown
% 5.93/2.04 % (32000)Termination phase: Saturation
% 5.93/2.04
% 5.93/2.04 % (32000)Memory used [KB]: 8187
% 5.93/2.04 % (32000)Time elapsed: 0.132 s
% 5.93/2.04 % (32000)Instructions burned: 453 (million)
% 5.93/2.04 % (32000)------------------------------
% 5.93/2.04 % (32000)------------------------------
% 5.93/2.04 % (32016)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_31617 for (2995ds/298Mi)
% 5.93/2.05 % (32017)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_31617 for (2995ds/192Mi)
% 5.93/2.07 % (32015)Instruction limit reached!
% 5.93/2.07 % (32015)------------------------------
% 5.93/2.07 % (32015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.07 % (32015)Termination reason: Unknown
% 5.93/2.07 % (32015)Termination phase: Saturation
% 5.93/2.07
% 5.93/2.07 % (32015)Memory used [KB]: 7164
% 5.93/2.07 % (32015)Time elapsed: 0.039 s
% 5.93/2.07 % (32015)Instructions burned: 136 (million)
% 5.93/2.07 % (32015)------------------------------
% 5.93/2.07 % (32015)------------------------------
% 5.93/2.07 % (32007)Instruction limit reached!
% 5.93/2.07 % (32007)------------------------------
% 5.93/2.07 % (32007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.07 % (32007)Termination reason: Unknown
% 5.93/2.07 % (32007)Termination phase: Saturation
% 5.93/2.07
% 5.93/2.07 % (32007)Memory used [KB]: 8059
% 5.93/2.07 % (32007)Time elapsed: 0.107 s
% 5.93/2.07 % (32007)Instructions burned: 345 (million)
% 5.93/2.07 % (32007)------------------------------
% 5.93/2.07 % (32007)------------------------------
% 5.93/2.08 % (32018)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_31617 for (2994ds/258Mi)
% 5.93/2.08 % (32019)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_31617 for (2994ds/90Mi)
% 5.93/2.10 % (32014)Instruction limit reached!
% 5.93/2.10 % (32014)------------------------------
% 5.93/2.10 % (32014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.10 % (32014)Termination reason: Unknown
% 5.93/2.10 % (32014)Termination phase: Saturation
% 5.93/2.10
% 5.93/2.10 % (32014)Memory used [KB]: 7675
% 5.93/2.10 % (32014)Time elapsed: 0.081 s
% 5.93/2.10 % (32014)Instructions burned: 285 (million)
% 5.93/2.10 % (32014)------------------------------
% 5.93/2.10 % (32014)------------------------------
% 5.93/2.10 % (32017)Instruction limit reached!
% 5.93/2.10 % (32017)------------------------------
% 5.93/2.10 % (32017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.10 % (32017)Termination reason: Unknown
% 5.93/2.10 % (32017)Termination phase: Saturation
% 5.93/2.10
% 5.93/2.10 % (32017)Memory used [KB]: 3965
% 5.93/2.10 % (32017)Time elapsed: 0.057 s
% 5.93/2.10 % (32017)Instructions burned: 192 (million)
% 5.93/2.10 % (32017)------------------------------
% 5.93/2.10 % (32017)------------------------------
% 5.93/2.11 % (32019)Instruction limit reached!
% 5.93/2.11 % (32019)------------------------------
% 5.93/2.11 % (32019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.11 % (32019)Termination reason: Unknown
% 5.93/2.11 % (32019)Termination phase: Property scanning
% 5.93/2.11
% 5.93/2.11 % (32019)Memory used [KB]: 2558
% 5.93/2.11 % (32019)Time elapsed: 0.028 s
% 5.93/2.11 % (32019)Instructions burned: 93 (million)
% 5.93/2.11 % (32019)------------------------------
% 5.93/2.11 % (32019)------------------------------
% 5.93/2.11 % (32020)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_31617 for (2994ds/231Mi)
% 5.93/2.11 % (32013)Instruction limit reached!
% 5.93/2.11 % (32013)------------------------------
% 5.93/2.11 % (32013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.11 % (32013)Termination reason: Unknown
% 5.93/2.11 % (32013)Termination phase: Saturation
% 5.93/2.11
% 5.93/2.11 % (32013)Memory used [KB]: 7547
% 5.93/2.11 % (32013)Time elapsed: 0.105 s
% 5.93/2.11 % (32013)Instructions burned: 339 (million)
% 5.93/2.11 % (32013)------------------------------
% 5.93/2.11 % (32013)------------------------------
% 6.40/2.11 % (32021)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_31617 for (2994ds/458Mi)
% 6.40/2.12 % (32022)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_31617 for (2994ds/31Mi)
% 6.40/2.12 % (32023)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_31617 for (2994ds/297Mi)
% 6.40/2.13 % (32022)Instruction limit reached!
% 6.40/2.13 % (32022)------------------------------
% 6.40/2.13 % (32022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.13 % (32022)Termination reason: Unknown
% 6.40/2.13 % (32022)Termination phase: Property scanning
% 6.40/2.13
% 6.40/2.13 % (32022)Memory used [KB]: 1918
% 6.40/2.13 % (32022)Time elapsed: 0.011 s
% 6.40/2.13 % (32022)Instructions burned: 32 (million)
% 6.40/2.13 % (32022)------------------------------
% 6.40/2.13 % (32022)------------------------------
% 6.40/2.13 % (32016)Instruction limit reached!
% 6.40/2.13 % (32016)------------------------------
% 6.40/2.13 % (32016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.13 % (32016)Termination reason: Unknown
% 6.40/2.13 % (32016)Termination phase: Saturation
% 6.40/2.13
% 6.40/2.13 % (32016)Memory used [KB]: 7803
% 6.40/2.13 % (32016)Time elapsed: 0.092 s
% 6.40/2.13 % (32016)Instructions burned: 301 (million)
% 6.40/2.13 % (32016)------------------------------
% 6.40/2.13 % (32016)------------------------------
% 6.40/2.14 % (32024)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_31617 for (2994ds/987Mi)
% 6.40/2.14 % (32025)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_31617 for (2994ds/182Mi)
% 6.40/2.15 % (32023)Refutation not found, incomplete strategy
% 6.40/2.15 % (32023)------------------------------
% 6.40/2.15 % (32023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.15 % (32023)Termination reason: Refutation not found, incomplete strategy
% 6.40/2.15
% 6.40/2.15
% 6.40/2.15 % (32023)Memory used [KB]: 6908
% 6.40/2.15 % (32023)Time elapsed: 0.029 s
% 6.40/2.15 % (32023)Instructions burned: 104 (million)
% 6.40/2.15 % (32023)------------------------------
% 6.40/2.15 % (32023)------------------------------
% 6.40/2.16 % (32018)Instruction limit reached!
% 6.40/2.16 % (32018)------------------------------
% 6.40/2.16 % (32018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.16 % (32018)Termination reason: Unknown
% 6.40/2.16 % (32018)Termination phase: Saturation
% 6.40/2.16
% 6.40/2.16 % (32018)Memory used [KB]: 7291
% 6.40/2.16 % (32018)Time elapsed: 0.080 s
% 6.40/2.16 % (32018)Instructions burned: 258 (million)
% 6.40/2.16 % (32018)------------------------------
% 6.40/2.16 % (32018)------------------------------
% 6.40/2.16 % (32026)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_31617 for (2994ds/182Mi)
% 6.40/2.17 % (32027)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_31617 for (2994ds/154Mi)
% 6.40/2.17 % (32020)Instruction limit reached!
% 6.40/2.17 % (32020)------------------------------
% 6.40/2.17 % (32020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.17 % (32020)Termination reason: Unknown
% 6.40/2.17 % (32020)Termination phase: Saturation
% 6.40/2.17
% 6.40/2.17 % (32020)Memory used [KB]: 7291
% 6.40/2.17 % (32020)Time elapsed: 0.062 s
% 6.40/2.17 % (32020)Instructions burned: 233 (million)
% 6.40/2.17 % (32020)------------------------------
% 6.40/2.17 % (32020)------------------------------
% 6.40/2.18 % (32028)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_31617 for (2993ds/79Mi)
% 6.40/2.19 % (32011)Instruction limit reached!
% 6.40/2.19 % (32011)------------------------------
% 6.40/2.19 % (32011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.19 % (32011)Termination reason: Unknown
% 6.40/2.19 % (32011)Termination phase: Saturation
% 6.40/2.19
% 6.40/2.19 % (32011)Memory used [KB]: 9978
% 6.40/2.19 % (32011)Time elapsed: 0.193 s
% 6.40/2.19 % (32011)Instructions burned: 614 (million)
% 6.40/2.19 % (32011)------------------------------
% 6.40/2.19 % (32011)------------------------------
% 6.40/2.19 % (32025)Instruction limit reached!
% 6.40/2.19 % (32025)------------------------------
% 6.40/2.19 % (32025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.19 % (32025)Termination reason: Unknown
% 6.40/2.19 % (32025)Termination phase: Property scanning
% 6.40/2.19
% 6.40/2.19 % (32025)Memory used [KB]: 2558
% 6.40/2.19 % (32025)Time elapsed: 0.054 s
% 6.40/2.19 % (32025)Instructions burned: 184 (million)
% 6.40/2.19 % (32025)------------------------------
% 6.40/2.19 % (32025)------------------------------
% 6.99/2.20 % (32029)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_31617 for (2993ds/216Mi)
% 6.99/2.20 % (32028)Instruction limit reached!
% 6.99/2.20 % (32028)------------------------------
% 6.99/2.20 % (32028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.20 % (32028)Termination reason: Unknown
% 6.99/2.20 % (32028)Termination phase: Property scanning
% 6.99/2.20
% 6.99/2.20 % (32028)Memory used [KB]: 2430
% 6.99/2.20 % (32028)Time elapsed: 0.024 s
% 6.99/2.20 % (32028)Instructions burned: 79 (million)
% 6.99/2.20 % (32028)------------------------------
% 6.99/2.20 % (32028)------------------------------
% 6.99/2.20 % (32030)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_31617 for (2993ds/114Mi)
% 6.99/2.21 % (32027)Instruction limit reached!
% 6.99/2.21 % (32027)------------------------------
% 6.99/2.21 % (32027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.21 % (32027)Termination reason: Unknown
% 6.99/2.21 % (32027)Termination phase: Property scanning
% 6.99/2.21
% 6.99/2.21 % (32027)Memory used [KB]: 2686
% 6.99/2.21 % (32027)Time elapsed: 0.042 s
% 6.99/2.21 % (32027)Instructions burned: 157 (million)
% 6.99/2.21 % (32027)------------------------------
% 6.99/2.21 % (32027)------------------------------
% 6.99/2.21 % (32031)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_31617 for (2993ds/922Mi)
% 6.99/2.21 % (32026)Instruction limit reached!
% 6.99/2.21 % (32026)------------------------------
% 6.99/2.21 % (32026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.21 % (32026)Termination reason: Unknown
% 6.99/2.21 % (32026)Termination phase: Saturation
% 6.99/2.21
% 6.99/2.21 % (32026)Memory used [KB]: 7419
% 6.99/2.21 % (32026)Time elapsed: 0.057 s
% 6.99/2.21 % (32026)Instructions burned: 184 (million)
% 6.99/2.21 % (32026)------------------------------
% 6.99/2.21 % (32026)------------------------------
% 6.99/2.22 % (32032)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_31617 for (2993ds/182Mi)
% 6.99/2.22 % (32033)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_31617 for (2993ds/164Mi)
% 6.99/2.24 % (32030)Instruction limit reached!
% 6.99/2.24 % (32030)------------------------------
% 6.99/2.24 % (32030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.24 % (32030)Termination reason: Unknown
% 6.99/2.24 % (32030)Termination phase: Property scanning
% 6.99/2.24
% 6.99/2.24 % (32030)Memory used [KB]: 2558
% 6.99/2.24 % (32030)Time elapsed: 0.037 s
% 6.99/2.24 % (32030)Instructions burned: 116 (million)
% 6.99/2.24 % (32030)------------------------------
% 6.99/2.24 % (32030)------------------------------
% 6.99/2.25 % (32021)Instruction limit reached!
% 6.99/2.25 % (32021)------------------------------
% 6.99/2.25 % (32021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.25 % (32021)Termination reason: Unknown
% 6.99/2.25 % (32021)Termination phase: Saturation
% 6.99/2.25
% 6.99/2.25 % (32021)Memory used [KB]: 8955
% 6.99/2.25 % (32021)Time elapsed: 0.138 s
% 6.99/2.25 % (32021)Instructions burned: 460 (million)
% 6.99/2.25 % (32021)------------------------------
% 6.99/2.25 % (32021)------------------------------
% 6.99/2.25 % (32034)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_31617 for (2993ds/50Mi)
% 6.99/2.25 % (32033)Refutation not found, incomplete strategy
% 6.99/2.25 % (32033)------------------------------
% 6.99/2.25 % (32033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.25 % (32033)Termination reason: Refutation not found, incomplete strategy
% 6.99/2.25
% 6.99/2.25
% 6.99/2.25 % (32033)Memory used [KB]: 2430
% 6.99/2.25 % (32033)Time elapsed: 0.029 s
% 6.99/2.25 % (32033)Instructions burned: 102 (million)
% 6.99/2.25 % (32033)------------------------------
% 6.99/2.25 % (32033)------------------------------
% 6.99/2.26 % (32035)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_31617 for (2993ds/368Mi)
% 6.99/2.26 % (32029)Instruction limit reached!
% 6.99/2.26 % (32029)------------------------------
% 6.99/2.26 % (32029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.26 % (32029)Termination reason: Unknown
% 6.99/2.26 % (32029)Termination phase: Saturation
% 6.99/2.26
% 6.99/2.26 % (32029)Memory used [KB]: 7675
% 6.99/2.26 % (32029)Time elapsed: 0.061 s
% 6.99/2.26 % (32029)Instructions burned: 219 (million)
% 6.99/2.26 % (32029)------------------------------
% 6.99/2.26 % (32029)------------------------------
% 6.99/2.26 % (32036)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_31617 for (2992ds/1021Mi)
% 6.99/2.27 % (32034)Instruction limit reached!
% 6.99/2.27 % (32034)------------------------------
% 6.99/2.27 % (32034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.27 % (32034)Termination reason: Unknown
% 6.99/2.27 % (32034)Termination phase: shuffling
% 6.99/2.27
% 6.99/2.27 % (32034)Memory used [KB]: 2430
% 6.99/2.27 % (32034)Time elapsed: 0.017 s
% 6.99/2.27 % (32034)Instructions burned: 52 (million)
% 6.99/2.27 % (32034)------------------------------
% 6.99/2.27 % (32034)------------------------------
% 6.99/2.27 % (32032)Instruction limit reached!
% 6.99/2.27 % (32032)------------------------------
% 6.99/2.27 % (32032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.27 % (32032)Termination reason: Unknown
% 6.99/2.27 % (32032)Termination phase: Saturation
% 6.99/2.27
% 6.99/2.27 % (32032)Memory used [KB]: 7164
% 6.99/2.27 % (32032)Time elapsed: 0.049 s
% 6.99/2.27 % (32032)Instructions burned: 184 (million)
% 6.99/2.27 % (32032)------------------------------
% 6.99/2.27 % (32032)------------------------------
% 6.99/2.27 % (32037)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_31617 for (2992ds/267Mi)
% 6.99/2.28 % (32038)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_31617 for (2992ds/204Mi)
% 6.99/2.28 % (32039)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_31617 for (2992ds/26Mi)
% 6.99/2.28 % (32039)Instruction limit reached!
% 6.99/2.28 % (32039)------------------------------
% 6.99/2.28 % (32039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.28 % (32039)Termination reason: Unknown
% 6.99/2.28 % (32039)Termination phase: shuffling
% 6.99/2.28
% 6.99/2.28 % (32039)Memory used [KB]: 2046
% 6.99/2.28 % (32039)Time elapsed: 0.009 s
% 6.99/2.28 % (32039)Instructions burned: 28 (million)
% 6.99/2.28 % (32039)------------------------------
% 6.99/2.28 % (32039)------------------------------
% 6.99/2.29 % (32040)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_31617 for (2992ds/53Mi)
% 7.55/2.31 % (32040)Instruction limit reached!
% 7.55/2.31 % (32040)------------------------------
% 7.55/2.31 % (32040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.55/2.31 % (32040)Termination reason: Unknown
% 7.55/2.31 % (32040)Termination phase: Property scanning
% 7.55/2.31
% 7.55/2.31 % (32040)Memory used [KB]: 2430
% 7.55/2.31 % (32040)Time elapsed: 0.016 s
% 7.55/2.31 % (32040)Instructions burned: 56 (million)
% 7.55/2.31 % (32040)------------------------------
% 7.55/2.31 % (32040)------------------------------
% 7.55/2.32 % (32041)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_31617 for (2992ds/4436Mi)
% 7.55/2.33 % (32041)Refutation not found, incomplete strategy
% 7.55/2.33 % (32041)------------------------------
% 7.55/2.33 % (32041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.55/2.33 % (32041)Termination reason: Refutation not found, incomplete strategy
% 7.55/2.33
% 7.55/2.33
% 7.55/2.33 % (32041)Memory used [KB]: 6524
% 7.55/2.33 % (32041)Time elapsed: 0.015 s
% 7.55/2.33 % (32041)Instructions burned: 46 (million)
% 7.55/2.33 % (32041)------------------------------
% 7.55/2.33 % (32041)------------------------------
% 7.55/2.34 % (32038)Instruction limit reached!
% 7.55/2.34 % (32038)------------------------------
% 7.55/2.34 % (32038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.55/2.34 % (32038)Termination reason: Unknown
% 7.55/2.34 % (32038)Termination phase: Saturation
% 7.55/2.34
% 7.55/2.34 % (32038)Memory used [KB]: 7547
% 7.55/2.34 % (32038)Time elapsed: 0.064 s
% 7.55/2.34 % (32038)Instructions burned: 205 (million)
% 7.55/2.34 % (32038)------------------------------
% 7.55/2.34 % (32038)------------------------------
% 7.55/2.34 % (32042)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_31617 for (2992ds/1539Mi)
% 7.55/2.34 % (32037)Instruction limit reached!
% 7.55/2.34 % (32037)------------------------------
% 7.55/2.34 % (32037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.55/2.34 % (32037)Termination reason: Unknown
% 7.55/2.34 % (32037)Termination phase: Saturation
% 7.55/2.34
% 7.55/2.34 % (32037)Memory used [KB]: 7547
% 7.55/2.34 % (32037)Time elapsed: 0.075 s
% 7.55/2.34 % (32037)Instructions burned: 267 (million)
% 7.55/2.34 % (32037)------------------------------
% 7.55/2.34 % (32037)------------------------------
% 7.55/2.35 % (32043)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_31617 for (2992ds/408Mi)
% 7.55/2.35 % (32044)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_31617 for (2992ds/5205Mi)
% 7.55/2.37 % (32035)Instruction limit reached!
% 7.55/2.37 % (32035)------------------------------
% 7.55/2.37 % (32035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.55/2.37 % (32035)Termination reason: Unknown
% 7.55/2.37 % (32035)Termination phase: Saturation
% 7.55/2.37
% 7.55/2.37 % (32035)Memory used [KB]: 9210
% 7.55/2.37 % (32035)Time elapsed: 0.112 s
% 7.55/2.37 % (32035)Instructions burned: 369 (million)
% 7.55/2.37 % (32035)------------------------------
% 7.55/2.37 % (32035)------------------------------
% 7.55/2.38 % (32045)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_31617 for (2991ds/1913Mi)
% 7.87/2.44 % (32024)Instruction limit reached!
% 7.87/2.44 % (32024)------------------------------
% 7.87/2.44 % (32024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.44 % (32024)Termination reason: Unknown
% 7.87/2.44 % (32024)Termination phase: Saturation
% 7.87/2.44
% 7.87/2.44 % (32024)Memory used [KB]: 10874
% 7.87/2.44 % (32024)Time elapsed: 0.306 s
% 7.87/2.44 % (32024)Instructions burned: 987 (million)
% 7.87/2.44 % (32024)------------------------------
% 7.87/2.44 % (32024)------------------------------
% 7.87/2.45 % (32046)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_31617 for (2991ds/4350Mi)
% 7.87/2.47 % (32046)Refutation not found, incomplete strategy
% 7.87/2.47 % (32046)------------------------------
% 7.87/2.47 % (32046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.47 % (32046)Termination reason: Refutation not found, incomplete strategy
% 7.87/2.47
% 7.87/2.47
% 7.87/2.47 % (32046)Memory used [KB]: 6524
% 7.87/2.47 % (32046)Time elapsed: 0.015 s
% 7.87/2.47 % (32046)Instructions burned: 46 (million)
% 7.87/2.47 % (32046)------------------------------
% 7.87/2.47 % (32046)------------------------------
% 7.87/2.48 % (32043)Instruction limit reached!
% 7.87/2.48 % (32043)------------------------------
% 7.87/2.48 % (32043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.48 % (32043)Termination reason: Unknown
% 7.87/2.48 % (32043)Termination phase: Saturation
% 7.87/2.48
% 7.87/2.48 % (32043)Memory used [KB]: 8955
% 7.87/2.48 % (32043)Time elapsed: 0.130 s
% 7.87/2.48 % (32043)Instructions burned: 410 (million)
% 7.87/2.48 % (32043)------------------------------
% 7.87/2.48 % (32043)------------------------------
% 7.87/2.48 % (32047)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_31617 for (2990ds/68Mi)
% 7.87/2.49 % (32048)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_31617 for (2990ds/358Mi)
% 7.87/2.49 % (32031)Instruction limit reached!
% 7.87/2.49 % (32031)------------------------------
% 7.87/2.49 % (32031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.49 % (32031)Termination reason: Unknown
% 7.87/2.49 % (32031)Termination phase: Saturation
% 7.87/2.49
% 7.87/2.49 % (32031)Memory used [KB]: 7931
% 7.87/2.49 % (32031)Time elapsed: 0.300 s
% 7.87/2.49 % (32031)Instructions burned: 923 (million)
% 7.87/2.49 % (32031)------------------------------
% 7.87/2.49 % (32031)------------------------------
% 8.64/2.50 % (32047)Instruction limit reached!
% 8.64/2.50 % (32047)------------------------------
% 8.64/2.50 % (32047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.50 % (32047)Termination reason: Unknown
% 8.64/2.50 % (32047)Termination phase: Preprocessing 3
% 8.64/2.50
% 8.64/2.50 % (32047)Memory used [KB]: 2430
% 8.64/2.50 % (32047)Time elapsed: 0.022 s
% 8.64/2.50 % (32047)Instructions burned: 69 (million)
% 8.64/2.50 % (32047)------------------------------
% 8.64/2.50 % (32047)------------------------------
% 8.64/2.50 % (32049)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_31617 for (2990ds/31Mi)
% 8.64/2.51 % (32050)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_31617 for (2990ds/279Mi)
% 8.64/2.51 % (32049)Instruction limit reached!
% 8.64/2.51 % (32049)------------------------------
% 8.64/2.51 % (32049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.51 % (32049)Termination reason: Unknown
% 8.64/2.51 % (32049)Termination phase: Property scanning
% 8.64/2.51
% 8.64/2.51 % (32049)Memory used [KB]: 1918
% 8.64/2.51 % (32049)Time elapsed: 0.011 s
% 8.64/2.51 % (32049)Instructions burned: 32 (million)
% 8.64/2.51 % (32049)------------------------------
% 8.64/2.51 % (32049)------------------------------
% 8.64/2.52 % (32051)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_31617 for (2990ds/258Mi)
% 8.64/2.54 % (32050)Refutation not found, incomplete strategy
% 8.64/2.54 % (32050)------------------------------
% 8.64/2.54 % (32050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.54 % (32050)Termination reason: Refutation not found, incomplete strategy
% 8.64/2.54
% 8.64/2.54
% 8.64/2.54 % (32050)Memory used [KB]: 7291
% 8.64/2.54 % (32050)Time elapsed: 0.035 s
% 8.64/2.54 % (32050)Instructions burned: 122 (million)
% 8.64/2.54 % (32050)------------------------------
% 8.64/2.54 % (32050)------------------------------
% 8.64/2.55 % (32052)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_31617 for (2990ds/26Mi)
% 8.64/2.56 % (32052)Instruction limit reached!
% 8.64/2.56 % (32052)------------------------------
% 8.64/2.56 % (32052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.56 % (32052)Termination reason: Unknown
% 8.64/2.56 % (32052)Termination phase: shuffling
% 8.64/2.56
% 8.64/2.56 % (32052)Memory used [KB]: 2046
% 8.64/2.56 % (32052)Time elapsed: 0.008 s
% 8.64/2.56 % (32052)Instructions burned: 26 (million)
% 8.64/2.56 % (32052)------------------------------
% 8.64/2.56 % (32052)------------------------------
% 8.64/2.57 % (32053)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_31617 for (2990ds/995Mi)
% 8.64/2.58 % (32036)Instruction limit reached!
% 8.64/2.58 % (32036)------------------------------
% 8.64/2.58 % (32036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.58 % (32036)Termination reason: Unknown
% 8.64/2.58 % (32036)Termination phase: Saturation
% 8.64/2.58
% 8.64/2.58 % (32036)Memory used [KB]: 9594
% 8.64/2.58 % (32036)Time elapsed: 0.313 s
% 8.64/2.58 % (32036)Instructions burned: 1023 (million)
% 8.64/2.58 % (32036)------------------------------
% 8.64/2.58 % (32036)------------------------------
% 8.64/2.58 % (32054)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_31617 for (2989ds/373Mi)
% 9.08/2.60 % (32051)Instruction limit reached!
% 9.08/2.60 % (32051)------------------------------
% 9.08/2.60 % (32051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.60 % (32051)Termination reason: Unknown
% 9.08/2.60 % (32051)Termination phase: Saturation
% 9.08/2.60
% 9.08/2.60 % (32051)Memory used [KB]: 8187
% 9.08/2.60 % (32051)Time elapsed: 0.079 s
% 9.08/2.60 % (32051)Instructions burned: 259 (million)
% 9.08/2.60 % (32051)------------------------------
% 9.08/2.60 % (32051)------------------------------
% 9.08/2.60 % (32048)Instruction limit reached!
% 9.08/2.60 % (32048)------------------------------
% 9.08/2.60 % (32048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.60 % (32048)Termination reason: Unknown
% 9.08/2.60 % (32048)Termination phase: Saturation
% 9.08/2.60
% 9.08/2.60 % (32048)Memory used [KB]: 7675
% 9.08/2.60 % (32048)Time elapsed: 0.112 s
% 9.08/2.60 % (32048)Instructions burned: 359 (million)
% 9.08/2.60 % (32048)------------------------------
% 9.08/2.60 % (32048)------------------------------
% 9.08/2.61 % (32055)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_31617 for (2989ds/253Mi)
% 9.08/2.61 % (32056)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_31617 for (2989ds/832Mi)
% 9.08/2.68 % (32055)Instruction limit reached!
% 9.08/2.68 % (32055)------------------------------
% 9.08/2.68 % (32055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.68 % (32055)Termination reason: Unknown
% 9.08/2.68 % (32055)Termination phase: Saturation
% 9.08/2.68
% 9.08/2.68 % (32055)Memory used [KB]: 7803
% 9.08/2.68 % (32055)Time elapsed: 0.071 s
% 9.08/2.68 % (32055)Instructions burned: 253 (million)
% 9.08/2.68 % (32055)------------------------------
% 9.08/2.68 % (32055)------------------------------
% 9.08/2.69 % (32057)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_31617 for (2988ds/668Mi)
% 9.37/2.70 % (32054)Instruction limit reached!
% 9.37/2.70 % (32054)------------------------------
% 9.37/2.70 % (32054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.37/2.70 % (32054)Termination reason: Unknown
% 9.37/2.70 % (32054)Termination phase: Saturation
% 9.37/2.70
% 9.37/2.70 % (32054)Memory used [KB]: 8827
% 9.37/2.70 % (32054)Time elapsed: 0.117 s
% 9.37/2.70 % (32054)Instructions burned: 373 (million)
% 9.37/2.70 % (32054)------------------------------
% 9.37/2.70 % (32054)------------------------------
% 9.37/2.71 % (32058)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_31617 for (2988ds/40Mi)
% 9.37/2.72 % (32058)Instruction limit reached!
% 9.37/2.72 % (32058)------------------------------
% 9.37/2.72 % (32058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.37/2.72 % (32058)Termination reason: Unknown
% 9.37/2.72 % (32058)Termination phase: shuffling
% 9.37/2.72
% 9.37/2.72 % (32058)Memory used [KB]: 2302
% 9.37/2.72 % (32058)Time elapsed: 0.013 s
% 9.37/2.72 % (32058)Instructions burned: 41 (million)
% 9.37/2.72 % (32058)------------------------------
% 9.37/2.72 % (32058)------------------------------
% 9.37/2.73 % (32059)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_31617 for (2988ds/294Mi)
% 9.37/2.76 % (32059)Refutation not found, incomplete strategy
% 9.37/2.76 % (32059)------------------------------
% 9.37/2.76 % (32059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.37/2.76 % (32059)Termination reason: Refutation not found, incomplete strategy
% 9.37/2.76
% 9.37/2.76
% 9.37/2.76 % (32059)Memory used [KB]: 7036
% 9.37/2.76 % (32059)Time elapsed: 0.027 s
% 9.37/2.76 % (32059)Instructions burned: 95 (million)
% 9.37/2.76 % (32059)------------------------------
% 9.37/2.76 % (32059)------------------------------
% 9.37/2.77 % (32060)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_31617 for (2988ds/187Mi)
% 9.55/2.82 % (32042)Instruction limit reached!
% 9.55/2.82 % (32042)------------------------------
% 9.55/2.82 % (32042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.82 % (32042)Termination reason: Unknown
% 9.55/2.82 % (32042)Termination phase: Saturation
% 9.55/2.82
% 9.55/2.82 % (32042)Memory used [KB]: 11257
% 9.55/2.82 % (32042)Time elapsed: 0.477 s
% 9.55/2.82 % (32042)Instructions burned: 1540 (million)
% 9.55/2.82 % (32042)------------------------------
% 9.55/2.82 % (32042)------------------------------
% 9.55/2.82 % (32060)Instruction limit reached!
% 9.55/2.82 % (32060)------------------------------
% 9.55/2.82 % (32060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.82 % (32060)Termination reason: Unknown
% 9.55/2.82 % (32060)Termination phase: Saturation
% 9.55/2.82
% 9.55/2.82 % (32060)Memory used [KB]: 7675
% 9.55/2.82 % (32060)Time elapsed: 0.054 s
% 9.55/2.82 % (32060)Instructions burned: 190 (million)
% 9.55/2.82 % (32060)------------------------------
% 9.55/2.82 % (32060)------------------------------
% 9.55/2.83 % (32061)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_31617 for (2987ds/371Mi)
% 9.55/2.83 % (32062)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_31617 for (2987ds/1827Mi)
% 9.55/2.85 % (32053)Instruction limit reached!
% 9.55/2.85 % (32053)------------------------------
% 9.55/2.85 % (32053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.85 % (32053)Termination reason: Unknown
% 9.55/2.85 % (32053)Termination phase: Saturation
% 9.55/2.85
% 9.55/2.85 % (32053)Memory used [KB]: 9083
% 9.55/2.85 % (32053)Time elapsed: 0.287 s
% 9.55/2.85 % (32053)Instructions burned: 997 (million)
% 9.55/2.85 % (32053)------------------------------
% 9.55/2.85 % (32053)------------------------------
% 9.55/2.86 % (32063)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_31617 for (2987ds/70Mi)
% 9.55/2.87 % (32056)Instruction limit reached!
% 9.55/2.87 % (32056)------------------------------
% 9.55/2.87 % (32056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.87 % (32056)Termination reason: Unknown
% 9.55/2.87 % (32056)Termination phase: Saturation
% 9.55/2.87
% 9.55/2.87 % (32056)Memory used [KB]: 9083
% 9.55/2.87 % (32056)Time elapsed: 0.267 s
% 9.55/2.87 % (32056)Instructions burned: 832 (million)
% 9.55/2.87 % (32056)------------------------------
% 9.55/2.87 % (32056)------------------------------
% 9.55/2.88 % (32057)Instruction limit reached!
% 9.55/2.88 % (32057)------------------------------
% 9.55/2.88 % (32057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.88 % (32057)Termination reason: Unknown
% 9.55/2.88 % (32057)Termination phase: Saturation
% 9.55/2.88
% 9.55/2.88 % (32057)Memory used [KB]: 14328
% 9.55/2.88 % (32057)Time elapsed: 0.196 s
% 9.55/2.88 % (32057)Instructions burned: 669 (million)
% 9.55/2.88 % (32057)------------------------------
% 9.55/2.88 % (32057)------------------------------
% 9.55/2.88 % (32063)Instruction limit reached!
% 9.55/2.88 % (32063)------------------------------
% 9.55/2.88 % (32063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.88 % (32063)Termination reason: Unknown
% 9.55/2.88 % (32063)Termination phase: Property scanning
% 9.55/2.88
% 9.55/2.88 % (32063)Memory used [KB]: 2430
% 9.55/2.88 % (32063)Time elapsed: 0.020 s
% 9.55/2.88 % (32063)Instructions burned: 72 (million)
% 9.55/2.88 % (32063)------------------------------
% 9.55/2.88 % (32063)------------------------------
% 9.55/2.88 % (32064)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_31617 for (2986ds/316Mi)
% 9.55/2.89 % (32065)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_31617 for (2986ds/932Mi)
% 9.55/2.89 % (32066)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_31617 for (2986ds/4714Mi)
% 10.91/2.92 % (32045)Instruction limit reached!
% 10.91/2.92 % (32045)------------------------------
% 10.91/2.92 % (32045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.91/2.92 % (32045)Termination reason: Unknown
% 10.91/2.92 % (32045)Termination phase: Saturation
% 10.91/2.92
% 10.91/2.92 % (32045)Memory used [KB]: 5245
% 10.91/2.92 % (32045)Time elapsed: 0.540 s
% 10.91/2.92 % (32045)Instructions burned: 1915 (million)
% 10.91/2.92 % (32045)------------------------------
% 10.91/2.92 % (32045)------------------------------
% 10.91/2.93 % (32067)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_31617 for (2986ds/8250Mi)
% 10.91/2.94 % (32061)Instruction limit reached!
% 10.91/2.94 % (32061)------------------------------
% 10.91/2.94 % (32061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.91/2.94 % (32061)Termination reason: Unknown
% 10.91/2.94 % (32061)Termination phase: Saturation
% 10.91/2.94
% 10.91/2.94 % (32061)Memory used [KB]: 8059
% 10.91/2.94 % (32061)Time elapsed: 0.118 s
% 10.91/2.94 % (32061)Instructions burned: 371 (million)
% 10.91/2.94 % (32061)------------------------------
% 10.91/2.94 % (32061)------------------------------
% 10.91/2.95 % (32064)Refutation not found, incomplete strategy
% 10.91/2.95 % (32064)------------------------------
% 10.91/2.95 % (32064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.91/2.95 % (32064)Termination reason: Refutation not found, incomplete strategy
% 10.91/2.95
% 10.91/2.95
% 10.91/2.95 % (32064)Memory used [KB]: 7675
% 10.91/2.95 % (32064)Time elapsed: 0.067 s
% 10.91/2.95 % (32064)Instructions burned: 241 (million)
% 10.91/2.95 % (32064)------------------------------
% 10.91/2.95 % (32064)------------------------------
% 10.91/2.95 % (32068)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_31617 for (2986ds/770Mi)
% 10.91/2.96 % (32069)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_31617 for (2986ds/794Mi)
% 10.91/2.96 % (32066)Refutation not found, incomplete strategy
% 10.91/2.96 % (32066)------------------------------
% 10.91/2.96 % (32066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.91/2.96 % (32066)Termination reason: Refutation not found, incomplete strategy
% 10.91/2.96
% 10.91/2.96
% 10.91/2.96 % (32066)Memory used [KB]: 7803
% 10.91/2.96 % (32066)Time elapsed: 0.071 s
% 10.91/2.96 % (32066)Instructions burned: 256 (million)
% 10.91/2.96 % (32066)------------------------------
% 10.91/2.96 % (32066)------------------------------
% 10.91/2.97 % (32068)Refutation not found, incomplete strategy
% 10.91/2.97 % (32068)------------------------------
% 10.91/2.97 % (32068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.91/2.97 % (32068)Termination reason: Refutation not found, incomplete strategy
% 10.91/2.97
% 10.91/2.97
% 10.91/2.97 % (32068)Memory used [KB]: 6524
% 10.91/2.97 % (32068)Time elapsed: 0.016 s
% 10.91/2.97 % (32068)Instructions burned: 49 (million)
% 10.91/2.97 % (32068)------------------------------
% 10.91/2.97 % (32068)------------------------------
% 10.91/2.98 % (32071)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_31617 for (2985ds/1376Mi)
% 10.91/2.98 % (32070)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_31617 for (2986ds/464Mi)
% 13.73/3.13 % (32070)Instruction limit reached!
% 13.73/3.13 % (32070)------------------------------
% 13.73/3.13 % (32070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.73/3.13 % (32070)Termination reason: Unknown
% 13.73/3.13 % (32070)Termination phase: Saturation
% 13.73/3.13
% 13.73/3.13 % (32070)Memory used [KB]: 8059
% 13.73/3.13 % (32070)Time elapsed: 0.173 s
% 13.73/3.13 % (32070)Instructions burned: 466 (million)
% 13.73/3.13 % (32070)------------------------------
% 13.73/3.13 % (32070)------------------------------
% 13.73/3.14 % (32072)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_31617 for (2984ds/906Mi)
% 13.73/3.17 % (32065)Instruction limit reached!
% 13.73/3.17 % (32065)------------------------------
% 13.73/3.17 % (32065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.73/3.17 % (32065)Termination reason: Unknown
% 13.73/3.17 % (32065)Termination phase: Saturation
% 13.73/3.17
% 13.73/3.17 % (32065)Memory used [KB]: 10746
% 13.73/3.17 % (32065)Time elapsed: 0.285 s
% 13.73/3.17 % (32065)Instructions burned: 932 (million)
% 13.73/3.17 % (32065)------------------------------
% 13.73/3.17 % (32065)------------------------------
% 13.73/3.18 % (32073)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_31617 for (2983ds/434Mi)
% 14.17/3.20 % (32073)Refutation not found, incomplete strategy
% 14.17/3.20 % (32073)------------------------------
% 14.17/3.20 % (32073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.17/3.20 % (32073)Termination reason: Refutation not found, incomplete strategy
% 14.17/3.20
% 14.17/3.20
% 14.17/3.20 % (32073)Memory used [KB]: 6396
% 14.17/3.20 % (32073)Time elapsed: 0.014 s
% 14.17/3.20 % (32073)Instructions burned: 42 (million)
% 14.17/3.20 % (32073)------------------------------
% 14.17/3.20 % (32073)------------------------------
% 14.17/3.21 % (32069)Instruction limit reached!
% 14.17/3.21 % (32069)------------------------------
% 14.17/3.21 % (32069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.17/3.21 % (32069)Termination reason: Unknown
% 14.17/3.21 % (32069)Termination phase: Saturation
% 14.17/3.21
% 14.17/3.21 % (32069)Memory used [KB]: 6652
% 14.17/3.21 % (32069)Time elapsed: 0.271 s
% 14.17/3.21 % (32069)Instructions burned: 794 (million)
% 14.17/3.21 % (32069)------------------------------
% 14.17/3.21 % (32069)------------------------------
% 14.17/3.21 % (32074)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_31617 for (2983ds/865Mi)
% 14.17/3.22 % (32075)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_31617 for (2983ds/593Mi)
% 14.61/3.38 % (32075)Instruction limit reached!
% 14.61/3.38 % (32075)------------------------------
% 14.61/3.38 % (32075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.61/3.38 % (32075)Termination reason: Unknown
% 14.61/3.38 % (32075)Termination phase: Saturation
% 14.61/3.38
% 14.61/3.38 % (32075)Memory used [KB]: 8827
% 14.61/3.38 % (32075)Time elapsed: 0.163 s
% 14.61/3.38 % (32075)Instructions burned: 594 (million)
% 14.61/3.38 % (32075)------------------------------
% 14.61/3.38 % (32075)------------------------------
% 14.61/3.39 % (32076)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_31617 for (2981ds/443Mi)
% 15.18/3.42 % (32062)Instruction limit reached!
% 15.18/3.42 % (32062)------------------------------
% 15.18/3.42 % (32062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/3.42 % (32062)Termination reason: Unknown
% 15.18/3.42 % (32062)Termination phase: Saturation
% 15.18/3.42
% 15.18/3.42 % (32062)Memory used [KB]: 11129
% 15.18/3.42 % (32062)Time elapsed: 0.589 s
% 15.18/3.42 % (32062)Instructions burned: 1827 (million)
% 15.18/3.42 % (32062)------------------------------
% 15.18/3.42 % (32062)------------------------------
% 15.18/3.42 % (32071)Instruction limit reached!
% 15.18/3.42 % (32071)------------------------------
% 15.18/3.42 % (32071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/3.42 % (32071)Termination reason: Unknown
% 15.18/3.42 % (32071)Termination phase: Saturation
% 15.18/3.42
% 15.18/3.42 % (32071)Memory used [KB]: 14328
% 15.18/3.42 % (32071)Time elapsed: 0.444 s
% 15.18/3.42 % (32071)Instructions burned: 1376 (million)
% 15.18/3.42 % (32071)------------------------------
% 15.18/3.42 % (32071)------------------------------
% 15.18/3.43 % (32077)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_31617 for (2981ds/594Mi)
% 15.18/3.43 % (32078)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_31617 for (2981ds/327Mi)
% 15.18/3.46 % (32074)Instruction limit reached!
% 15.18/3.46 % (32074)------------------------------
% 15.18/3.46 % (32074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/3.46 % (32074)Termination reason: Unknown
% 15.18/3.46 % (32074)Termination phase: Saturation
% 15.18/3.46
% 15.18/3.46 % (32074)Memory used [KB]: 9722
% 15.18/3.46 % (32074)Time elapsed: 0.257 s
% 15.18/3.46 % (32074)Instructions burned: 865 (million)
% 15.18/3.46 % (32074)------------------------------
% 15.18/3.46 % (32074)------------------------------
% 15.18/3.47 % (32072)Instruction limit reached!
% 15.18/3.47 % (32072)------------------------------
% 15.18/3.47 % (32072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/3.47 % (32072)Termination reason: Unknown
% 15.18/3.47 % (32072)Termination phase: Saturation
% 15.18/3.47
% 15.18/3.47 % (32072)Memory used [KB]: 12920
% 15.18/3.47 % (32072)Time elapsed: 0.332 s
% 15.18/3.47 % (32072)Instructions burned: 907 (million)
% 15.18/3.47 % (32072)------------------------------
% 15.18/3.47 % (32072)------------------------------
% 15.18/3.47 % (32079)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_31617 for (2980ds/5411Mi)
% 15.18/3.48 % (32080)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_31617 for (2980ds/1762Mi)
% 15.18/3.49 % (32079)Refutation not found, incomplete strategy
% 15.18/3.49 % (32079)------------------------------
% 15.18/3.49 % (32079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.18/3.49 % (32079)Termination reason: Refutation not found, incomplete strategy
% 15.18/3.49
% 15.18/3.49
% 15.18/3.49 % (32079)Memory used [KB]: 6396
% 15.18/3.49 % (32079)Time elapsed: 0.014 s
% 15.18/3.49 % (32079)Instructions burned: 42 (million)
% 15.18/3.49 % (32079)------------------------------
% 15.18/3.49 % (32079)------------------------------
% 16.08/3.50 % (32081)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_31617 for (2980ds/96Mi)
% 16.08/3.52 % (32081)Instruction limit reached!
% 16.08/3.52 % (32081)------------------------------
% 16.08/3.52 % (32081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.08/3.52 % (32081)Termination reason: Unknown
% 16.08/3.52 % (32081)Termination phase: Property scanning
% 16.08/3.52
% 16.08/3.52 % (32081)Memory used [KB]: 2686
% 16.08/3.52 % (32081)Time elapsed: 0.027 s
% 16.08/3.52 % (32081)Instructions burned: 97 (million)
% 16.08/3.52 % (32081)------------------------------
% 16.08/3.52 % (32081)------------------------------
% 16.08/3.53 % (32076)Instruction limit reached!
% 16.08/3.53 % (32076)------------------------------
% 16.08/3.53 % (32076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.08/3.53 % (32076)Termination reason: Unknown
% 16.08/3.53 % (32076)Termination phase: Saturation
% 16.08/3.53
% 16.08/3.53 % (32076)Memory used [KB]: 8059
% 16.08/3.53 % (32076)Time elapsed: 0.137 s
% 16.08/3.53 % (32076)Instructions burned: 443 (million)
% 16.08/3.53 % (32076)------------------------------
% 16.08/3.53 % (32076)------------------------------
% 16.08/3.53 % (32082)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_31617 for (2980ds/503Mi)
% 16.08/3.54 % (32083)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_31617 for (2980ds/90Mi)
% 16.08/3.54 % (32078)Instruction limit reached!
% 16.08/3.54 % (32078)------------------------------
% 16.08/3.54 % (32078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.08/3.54 % (32078)Termination reason: Unknown
% 16.08/3.54 % (32078)Termination phase: Saturation
% 16.08/3.54
% 16.08/3.54 % (32078)Memory used [KB]: 8315
% 16.08/3.54 % (32078)Time elapsed: 0.104 s
% 16.08/3.54 % (32078)Instructions burned: 329 (million)
% 16.08/3.54 % (32078)------------------------------
% 16.08/3.54 % (32078)------------------------------
% 16.08/3.55 % (32084)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_31617 for (2980ds/593Mi)
% 16.08/3.55 % (32082)Refutation not found, incomplete strategy
% 16.08/3.55 % (32082)------------------------------
% 16.08/3.55 % (32082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.08/3.55 % (32082)Termination reason: Refutation not found, incomplete strategy
% 16.08/3.55
% 16.08/3.55
% 16.08/3.55 % (32082)Memory used [KB]: 6396
% 16.08/3.55 % (32082)Time elapsed: 0.014 s
% 16.08/3.55 % (32082)Instructions burned: 43 (million)
% 16.08/3.55 % (32082)------------------------------
% 16.08/3.55 % (32082)------------------------------
% 16.08/3.56 % (32085)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_31617 for (2980ds/1512Mi)
% 16.08/3.56 % (32083)Instruction limit reached!
% 16.08/3.56 % (32083)------------------------------
% 16.08/3.56 % (32083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.08/3.56 % (32083)Termination reason: Unknown
% 16.08/3.56 % (32083)Termination phase: Twee Goal Transformation
% 16.08/3.56
% 16.08/3.56 % (32083)Memory used [KB]: 2558
% 16.08/3.56 % (32083)Time elapsed: 0.027 s
% 16.08/3.56 % (32083)Instructions burned: 90 (million)
% 16.08/3.56 % (32083)------------------------------
% 16.08/3.56 % (32083)------------------------------
% 16.08/3.57 % (32086)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_31617 for (2979ds/569Mi)
% 16.64/3.62 % (32077)Instruction limit reached!
% 16.64/3.62 % (32077)------------------------------
% 16.64/3.62 % (32077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.64/3.62 % (32077)Termination reason: Unknown
% 16.64/3.62 % (32077)Termination phase: Saturation
% 16.64/3.62
% 16.64/3.62 % (32077)Memory used [KB]: 7931
% 16.64/3.62 % (32077)Time elapsed: 0.191 s
% 16.64/3.62 % (32077)Instructions burned: 597 (million)
% 16.64/3.62 % (32077)------------------------------
% 16.64/3.62 % (32077)------------------------------
% 16.64/3.63 % (32087)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_31617 for (2979ds/501Mi)
% 17.05/3.73 % (32084)Instruction limit reached!
% 17.05/3.73 % (32084)------------------------------
% 17.05/3.73 % (32084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.73 % (32084)Termination reason: Unknown
% 17.05/3.73 % (32084)Termination phase: Saturation
% 17.05/3.73
% 17.05/3.73 % (32084)Memory used [KB]: 9978
% 17.05/3.73 % (32084)Time elapsed: 0.182 s
% 17.05/3.73 % (32084)Instructions burned: 595 (million)
% 17.05/3.73 % (32084)------------------------------
% 17.05/3.73 % (32084)------------------------------
% 17.05/3.73 % (32086)Instruction limit reached!
% 17.05/3.73 % (32086)------------------------------
% 17.05/3.73 % (32086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.73 % (32086)Termination reason: Unknown
% 17.05/3.73 % (32086)Termination phase: Saturation
% 17.05/3.73
% 17.05/3.73 % (32086)Memory used [KB]: 8827
% 17.05/3.73 % (32086)Time elapsed: 0.164 s
% 17.05/3.73 % (32086)Instructions burned: 571 (million)
% 17.05/3.73 % (32086)------------------------------
% 17.05/3.73 % (32086)------------------------------
% 17.05/3.74 % (32088)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_31617 for (2978ds/562Mi)
% 17.05/3.74 % (32089)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_31617 for (2978ds/406Mi)
% 17.05/3.78 % (32087)Instruction limit reached!
% 17.05/3.78 % (32087)------------------------------
% 17.05/3.78 % (32087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.78 % (32087)Termination reason: Unknown
% 17.05/3.78 % (32087)Termination phase: Saturation
% 17.05/3.78
% 17.05/3.78 % (32087)Memory used [KB]: 9722
% 17.05/3.78 % (32087)Time elapsed: 0.148 s
% 17.05/3.78 % (32087)Instructions burned: 503 (million)
% 17.05/3.78 % (32087)------------------------------
% 17.05/3.78 % (32087)------------------------------
% 17.05/3.79 % (32090)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_31617 for (2977ds/582Mi)
% 17.77/3.87 % (32089)Instruction limit reached!
% 17.77/3.87 % (32089)------------------------------
% 17.77/3.87 % (32089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.77/3.87 % (32089)Termination reason: Unknown
% 17.77/3.87 % (32089)Termination phase: Saturation
% 17.77/3.87
% 17.77/3.87 % (32089)Memory used [KB]: 8699
% 17.77/3.87 % (32089)Time elapsed: 0.128 s
% 17.77/3.87 % (32089)Instructions burned: 407 (million)
% 17.77/3.87 % (32089)------------------------------
% 17.77/3.87 % (32089)------------------------------
% 17.77/3.88 % (32091)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_31617 for (2976ds/456Mi)
% 18.10/3.91 % (32088)Instruction limit reached!
% 18.10/3.91 % (32088)------------------------------
% 18.10/3.91 % (32088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.10/3.91 % (32088)Termination reason: Unknown
% 18.10/3.91 % (32088)Termination phase: Saturation
% 18.10/3.91
% 18.10/3.91 % (32088)Memory used [KB]: 8827
% 18.10/3.91 % (32088)Time elapsed: 0.172 s
% 18.10/3.91 % (32088)Instructions burned: 565 (million)
% 18.10/3.91 % (32088)------------------------------
% 18.10/3.91 % (32088)------------------------------
% 18.10/3.92 % (32092)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_31617 for (2976ds/393Mi)
% 18.10/3.95 % (32044)Instruction limit reached!
% 18.10/3.95 % (32044)------------------------------
% 18.10/3.95 % (32044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.10/3.95 % (32044)Termination reason: Unknown
% 18.10/3.95 % (32044)Termination phase: Saturation
% 18.10/3.95
% 18.10/3.95 % (32044)Memory used [KB]: 19445
% 18.10/3.95 % (32044)Time elapsed: 1.599 s
% 18.10/3.95 % (32044)Instructions burned: 5206 (million)
% 18.10/3.95 % (32044)------------------------------
% 18.10/3.95 % (32044)------------------------------
% 18.10/3.96 % (32090)Instruction limit reached!
% 18.10/3.96 % (32090)------------------------------
% 18.10/3.96 % (32090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.10/3.96 % (32090)Termination reason: Unknown
% 18.10/3.96 % (32090)Termination phase: Saturation
% 18.10/3.96
% 18.10/3.96 % (32090)Memory used [KB]: 9210
% 18.10/3.96 % (32090)Time elapsed: 0.177 s
% 18.10/3.96 % (32090)Instructions burned: 584 (million)
% 18.10/3.96 % (32090)------------------------------
% 18.10/3.96 % (32090)------------------------------
% 18.10/3.96 % (32093)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_31617 for (2976ds/1335Mi)
% 18.10/3.97 % (32094)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_31617 for (2976ds/3373Mi)
% 18.10/4.00 % (32080)Instruction limit reached!
% 18.10/4.00 % (32080)------------------------------
% 18.10/4.00 % (32080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.10/4.00 % (32080)Termination reason: Unknown
% 18.10/4.00 % (32080)Termination phase: Saturation
% 18.10/4.00
% 18.10/4.00 % (32080)Memory used [KB]: 12025
% 18.10/4.00 % (32080)Time elapsed: 0.522 s
% 18.10/4.00 % (32080)Instructions burned: 1763 (million)
% 18.10/4.00 % (32080)------------------------------
% 18.10/4.00 % (32080)------------------------------
% 18.10/4.01 % (32095)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_31617 for (2975ds/474Mi)
% 18.10/4.02 % (32091)Instruction limit reached!
% 18.10/4.02 % (32091)------------------------------
% 18.10/4.02 % (32091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.10/4.02 % (32091)Termination reason: Unknown
% 18.10/4.02 % (32091)Termination phase: Saturation
% 18.10/4.02
% 18.10/4.02 % (32091)Memory used [KB]: 7675
% 18.10/4.02 % (32091)Time elapsed: 0.144 s
% 18.10/4.02 % (32091)Instructions burned: 459 (million)
% 18.10/4.02 % (32091)------------------------------
% 18.10/4.02 % (32091)------------------------------
% 20.03/4.03 % (32092)Instruction limit reached!
% 20.03/4.03 % (32092)------------------------------
% 20.03/4.03 % (32092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.03 % (32092)Termination reason: Unknown
% 20.03/4.03 % (32092)Termination phase: Saturation
% 20.03/4.03
% 20.03/4.03 % (32092)Memory used [KB]: 7931
% 20.03/4.03 % (32092)Time elapsed: 0.111 s
% 20.03/4.03 % (32092)Instructions burned: 393 (million)
% 20.03/4.03 % (32092)------------------------------
% 20.03/4.03 % (32092)------------------------------
% 20.03/4.03 % (32085)Instruction limit reached!
% 20.03/4.03 % (32085)------------------------------
% 20.03/4.03 % (32085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.03 % (32085)Termination reason: Unknown
% 20.03/4.03 % (32085)Termination phase: Saturation
% 20.03/4.03
% 20.03/4.03 % (32085)Memory used [KB]: 9210
% 20.03/4.03 % (32085)Time elapsed: 0.474 s
% 20.03/4.03 % (32085)Instructions burned: 1513 (million)
% 20.03/4.03 % (32085)------------------------------
% 20.03/4.03 % (32085)------------------------------
% 20.03/4.04 % (32097)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_31617 for (2975ds/590Mi)
% 20.03/4.04 % (32098)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_31617 for (2975ds/104Mi)
% 20.03/4.04 % (32096)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_31617 for (2975ds/157Mi)
% 20.03/4.07 % (32098)Instruction limit reached!
% 20.03/4.07 % (32098)------------------------------
% 20.03/4.07 % (32098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.07 % (32098)Termination reason: Unknown
% 20.03/4.07 % (32098)Termination phase: Property scanning
% 20.03/4.07
% 20.03/4.07 % (32098)Memory used [KB]: 2558
% 20.03/4.07 % (32098)Time elapsed: 0.031 s
% 20.03/4.07 % (32098)Instructions burned: 107 (million)
% 20.03/4.07 % (32098)------------------------------
% 20.03/4.07 % (32098)------------------------------
% 20.03/4.08 % (32099)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_31617 for (2975ds/414Mi)
% 20.03/4.11 % (32096)Instruction limit reached!
% 20.03/4.11 % (32096)------------------------------
% 20.03/4.11 % (32096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.11 % (32096)Termination reason: Unknown
% 20.03/4.11 % (32096)Termination phase: Property scanning
% 20.03/4.11
% 20.03/4.11 % (32096)Memory used [KB]: 2686
% 20.03/4.11 % (32096)Time elapsed: 0.069 s
% 20.03/4.11 % (32096)Instructions burned: 159 (million)
% 20.03/4.11 % (32096)------------------------------
% 20.03/4.11 % (32096)------------------------------
% 20.03/4.12 % (32100)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_31617 for (2974ds/715Mi)
% 20.48/4.15 % (32095)Instruction limit reached!
% 20.48/4.15 % (32095)------------------------------
% 20.48/4.15 % (32095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.48/4.15 % (32095)Termination reason: Unknown
% 20.48/4.15 % (32095)Termination phase: Saturation
% 20.48/4.15
% 20.48/4.15 % (32095)Memory used [KB]: 9210
% 20.48/4.15 % (32095)Time elapsed: 0.141 s
% 20.48/4.15 % (32095)Instructions burned: 474 (million)
% 20.48/4.15 % (32095)------------------------------
% 20.48/4.15 % (32095)------------------------------
% 20.48/4.16 % (32101)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_31617 for (2974ds/961Mi)
% 20.86/4.20 % (32099)Instruction limit reached!
% 20.86/4.20 % (32099)------------------------------
% 20.86/4.20 % (32099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.20 % (32099)Termination reason: Unknown
% 20.86/4.20 % (32099)Termination phase: Saturation
% 20.86/4.20
% 20.86/4.20 % (32099)Memory used [KB]: 7931
% 20.86/4.20 % (32099)Time elapsed: 0.143 s
% 20.86/4.20 % (32099)Instructions burned: 416 (million)
% 20.86/4.20 % (32099)------------------------------
% 20.86/4.20 % (32099)------------------------------
% 20.86/4.21 % (32102)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_31617 for (2973ds/1213Mi)
% 20.86/4.22 % (32097)Instruction limit reached!
% 20.86/4.22 % (32097)------------------------------
% 20.86/4.22 % (32097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.22 % (32097)Termination reason: Unknown
% 20.86/4.22 % (32097)Termination phase: Saturation
% 20.86/4.22
% 20.86/4.22 % (32097)Memory used [KB]: 8443
% 20.86/4.22 % (32097)Time elapsed: 0.203 s
% 20.86/4.22 % (32097)Instructions burned: 593 (million)
% 20.86/4.22 % (32097)------------------------------
% 20.86/4.22 % (32097)------------------------------
% 20.86/4.23 % (32103)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_31617 for (2973ds/1979Mi)
% 21.47/4.33 % (32093)Instruction limit reached!
% 21.47/4.33 % (32093)------------------------------
% 21.47/4.33 % (32093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.47/4.33 % (32093)Termination reason: Unknown
% 21.47/4.33 % (32093)Termination phase: Saturation
% 21.47/4.33
% 21.47/4.33 % (32093)Memory used [KB]: 9850
% 21.47/4.33 % (32093)Time elapsed: 0.368 s
% 21.47/4.33 % (32093)Instructions burned: 1339 (million)
% 21.47/4.33 % (32093)------------------------------
% 21.47/4.33 % (32093)------------------------------
% 21.47/4.34 % (32104)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_31617 for (2972ds/481Mi)
% 21.47/4.35 % (32100)Instruction limit reached!
% 21.47/4.35 % (32100)------------------------------
% 21.47/4.35 % (32100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.47/4.35 % (32100)Termination reason: Unknown
% 21.47/4.35 % (32100)Termination phase: Saturation
% 21.47/4.35
% 21.47/4.35 % (32100)Memory used [KB]: 5884
% 21.47/4.35 % (32100)Time elapsed: 0.261 s
% 21.47/4.35 % (32100)Instructions burned: 717 (million)
% 21.47/4.35 % (32100)------------------------------
% 21.47/4.35 % (32100)------------------------------
% 21.47/4.36 % (32105)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_31617 for (2972ds/783Mi)
% 21.47/4.38 % (32105)Refutation not found, incomplete strategy
% 21.47/4.38 % (32105)------------------------------
% 21.47/4.38 % (32105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.47/4.38 % (32105)Termination reason: Refutation not found, incomplete strategy
% 21.47/4.38
% 21.47/4.38
% 21.47/4.38 % (32105)Memory used [KB]: 6524
% 21.47/4.38 % (32105)Time elapsed: 0.018 s
% 21.47/4.38 % (32105)Instructions burned: 48 (million)
% 21.47/4.38 % (32105)------------------------------
% 21.47/4.38 % (32105)------------------------------
% 21.47/4.39 % (32106)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_31617 for (2971ds/432Mi)
% 21.98/4.41 % (32106)Refutation not found, incomplete strategy
% 21.98/4.41 % (32106)------------------------------
% 21.98/4.41 % (32106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.98/4.41 % (32106)Termination reason: Refutation not found, incomplete strategy
% 21.98/4.41
% 21.98/4.41
% 21.98/4.41 % (32106)Memory used [KB]: 6396
% 21.98/4.41 % (32106)Time elapsed: 0.017 s
% 21.98/4.41 % (32106)Instructions burned: 45 (million)
% 21.98/4.41 % (32106)------------------------------
% 21.98/4.41 % (32106)------------------------------
% 21.98/4.42 % (32107)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_31617 for (2971ds/1670Mi)
% 21.98/4.46 % (32101)Instruction limit reached!
% 21.98/4.46 % (32101)------------------------------
% 21.98/4.46 % (32101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.98/4.46 % (32101)Termination reason: Unknown
% 21.98/4.46 % (32101)Termination phase: Saturation
% 21.98/4.46
% 21.98/4.46 % (32101)Memory used [KB]: 8443
% 21.98/4.46 % (32101)Time elapsed: 0.295 s
% 21.98/4.46 % (32101)Instructions burned: 963 (million)
% 21.98/4.46 % (32101)------------------------------
% 21.98/4.46 % (32101)------------------------------
% 21.98/4.47 % (32108)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_31617 for (2971ds/90Mi)
% 21.98/4.48 % (32104)Instruction limit reached!
% 21.98/4.48 % (32104)------------------------------
% 21.98/4.48 % (32104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.98/4.48 % (32104)Termination reason: Unknown
% 21.98/4.48 % (32104)Termination phase: Saturation
% 21.98/4.48
% 21.98/4.48 % (32104)Memory used [KB]: 8443
% 21.98/4.48 % (32104)Time elapsed: 0.144 s
% 21.98/4.48 % (32104)Instructions burned: 481 (million)
% 21.98/4.48 % (32104)------------------------------
% 21.98/4.48 % (32104)------------------------------
% 21.98/4.49 % (32109)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_31617 for (2970ds/346Mi)
% 21.98/4.49 % (32108)Instruction limit reached!
% 21.98/4.49 % (32108)------------------------------
% 21.98/4.49 % (32108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.98/4.49 % (32108)Termination reason: Unknown
% 21.98/4.49 % (32108)Termination phase: Property scanning
% 21.98/4.49
% 21.98/4.49 % (32108)Memory used [KB]: 2558
% 21.98/4.49 % (32108)Time elapsed: 0.027 s
% 21.98/4.49 % (32108)Instructions burned: 90 (million)
% 21.98/4.49 % (32108)------------------------------
% 21.98/4.49 % (32108)------------------------------
% 22.70/4.50 % (32110)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_31617 for (2970ds/401Mi)
% 22.70/4.58 % (32102)Instruction limit reached!
% 22.70/4.58 % (32102)------------------------------
% 22.70/4.58 % (32102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.70/4.58 % (32102)Termination reason: Unknown
% 22.70/4.58 % (32102)Termination phase: Saturation
% 22.70/4.58
% 22.70/4.58 % (32102)Memory used [KB]: 8955
% 22.70/4.58 % (32102)Time elapsed: 0.376 s
% 22.70/4.58 % (32102)Instructions burned: 1214 (million)
% 22.70/4.58 % (32102)------------------------------
% 22.70/4.58 % (32102)------------------------------
% 22.70/4.59 % (32109)Instruction limit reached!
% 22.70/4.59 % (32109)------------------------------
% 22.70/4.59 % (32109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.70/4.59 % (32109)Termination reason: Unknown
% 22.70/4.59 % (32109)Termination phase: Saturation
% 22.70/4.59
% 22.70/4.59 % (32109)Memory used [KB]: 8059
% 22.70/4.59 % (32109)Time elapsed: 0.100 s
% 22.70/4.59 % (32109)Instructions burned: 348 (million)
% 22.70/4.59 % (32109)------------------------------
% 22.70/4.59 % (32109)------------------------------
% 22.70/4.59 % (32111)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_31617 for (2969ds/6454Mi)
% 23.40/4.60 % (32112)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_31617 for (2969ds/283Mi)
% 23.40/4.61 % (32110)Instruction limit reached!
% 23.40/4.61 % (32110)------------------------------
% 23.40/4.61 % (32110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.40/4.61 % (32110)Termination reason: Unknown
% 23.40/4.61 % (32110)Termination phase: Saturation
% 23.40/4.61
% 23.40/4.61 % (32110)Memory used [KB]: 8699
% 23.40/4.61 % (32110)Time elapsed: 0.108 s
% 23.40/4.61 % (32110)Instructions burned: 402 (million)
% 23.40/4.61 % (32110)------------------------------
% 23.40/4.61 % (32110)------------------------------
% 23.40/4.61 % (32111)Refutation not found, incomplete strategy
% 23.40/4.61 % (32111)------------------------------
% 23.40/4.61 % (32111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.40/4.61 % (32111)Termination reason: Refutation not found, incomplete strategy
% 23.40/4.61
% 23.40/4.61
% 23.40/4.61 % (32111)Memory used [KB]: 6524
% 23.40/4.61 % (32111)Time elapsed: 0.017 s
% 23.40/4.61 % (32111)Instructions burned: 50 (million)
% 23.40/4.61 % (32111)------------------------------
% 23.40/4.61 % (32111)------------------------------
% 23.40/4.62 % (32113)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_31617 for (2969ds/865Mi)
% 23.40/4.62 % (32114)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_31617 for (2969ds/4528Mi)
% 23.40/4.63 % (32114)Refutation not found, incomplete strategy
% 23.40/4.63 % (32114)------------------------------
% 23.40/4.63 % (32114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.40/4.63 % (32114)Termination reason: Refutation not found, incomplete strategy
% 23.40/4.63
% 23.40/4.63
% 23.40/4.63 % (32114)Memory used [KB]: 2046
% 23.40/4.63 % (32114)Time elapsed: 0.015 s
% 23.40/4.63 % (32114)Instructions burned: 46 (million)
% 23.40/4.63 % (32114)------------------------------
% 23.40/4.63 % (32114)------------------------------
% 23.40/4.64 % (32115)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_31617 for (2969ds/1001Mi)
% 23.40/4.68 % (32112)Instruction limit reached!
% 23.40/4.68 % (32112)------------------------------
% 23.40/4.68 % (32112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.40/4.68 % (32112)Termination reason: Unknown
% 23.40/4.68 % (32112)Termination phase: Saturation
% 23.40/4.68
% 23.40/4.68 % (32112)Memory used [KB]: 8059
% 23.40/4.68 % (32112)Time elapsed: 0.084 s
% 23.40/4.68 % (32112)Instructions burned: 283 (million)
% 23.40/4.68 % (32112)------------------------------
% 23.40/4.68 % (32112)------------------------------
% 23.40/4.69 % (32116)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_31617 for (2968ds/102Mi)
% 23.86/4.72 % (32116)Instruction limit reached!
% 23.86/4.72 % (32116)------------------------------
% 23.86/4.72 % (32116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.86/4.72 % (32116)Termination reason: Unknown
% 23.86/4.72 % (32116)Termination phase: Property scanning
% 23.86/4.72
% 23.86/4.72 % (32116)Memory used [KB]: 2686
% 23.86/4.72 % (32116)Time elapsed: 0.029 s
% 23.86/4.72 % (32116)Instructions burned: 105 (million)
% 23.86/4.72 % (32116)------------------------------
% 23.86/4.72 % (32116)------------------------------
% 23.86/4.73 % (32117)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_31617 for (2968ds/952Mi)
% 24.09/4.82 % (32103)Instruction limit reached!
% 24.09/4.82 % (32103)------------------------------
% 24.09/4.82 % (32103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.09/4.82 % (32103)Termination reason: Unknown
% 24.09/4.82 % (32103)Termination phase: Saturation
% 24.09/4.82
% 24.09/4.82 % (32103)Memory used [KB]: 9594
% 24.09/4.82 % (32103)Time elapsed: 0.594 s
% 24.09/4.82 % (32103)Instructions burned: 1979 (million)
% 24.09/4.82 % (32103)------------------------------
% 24.09/4.82 % (32103)------------------------------
% 24.09/4.83 % (32118)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_31617 for (2967ds/578Mi)
% 24.09/4.89 % (32113)Instruction limit reached!
% 24.09/4.89 % (32113)------------------------------
% 24.09/4.89 % (32113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.09/4.89 % (32113)Termination reason: Unknown
% 24.09/4.89 % (32113)Termination phase: Saturation
% 24.09/4.89
% 24.09/4.89 % (32113)Memory used [KB]: 10362
% 24.09/4.89 % (32113)Time elapsed: 0.271 s
% 24.09/4.89 % (32113)Instructions burned: 866 (million)
% 24.09/4.89 % (32113)------------------------------
% 24.09/4.89 % (32113)------------------------------
% 24.09/4.90 % (32107)Instruction limit reached!
% 24.09/4.90 % (32107)------------------------------
% 24.09/4.90 % (32107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.09/4.90 % (32107)Termination reason: Unknown
% 24.09/4.90 % (32107)Termination phase: Saturation
% 24.09/4.90
% 24.09/4.90 % (32107)Memory used [KB]: 8955
% 24.09/4.90 % (32107)Time elapsed: 0.481 s
% 24.09/4.90 % (32107)Instructions burned: 1672 (million)
% 24.09/4.90 % (32107)------------------------------
% 24.09/4.90 % (32107)------------------------------
% 25.20/4.90 % (32119)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_31617 for (2966ds/643Mi)
% 25.20/4.91 % (32120)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_31617 for (2966ds/865Mi)
% 25.20/4.91 % (32115)Instruction limit reached!
% 25.20/4.91 % (32115)------------------------------
% 25.20/4.91 % (32115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.20/4.91 % (32115)Termination reason: Unknown
% 25.20/4.91 % (32115)Termination phase: Saturation
% 25.20/4.91
% 25.20/4.91 % (32115)Memory used [KB]: 8571
% 25.20/4.91 % (32115)Time elapsed: 0.267 s
% 25.20/4.91 % (32115)Instructions burned: 1003 (million)
% 25.20/4.91 % (32115)------------------------------
% 25.20/4.91 % (32115)------------------------------
% 25.20/4.92 % (32121)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_31617 for (2966ds/1174Mi)
% 25.20/5.00 % (32118)Instruction limit reached!
% 25.20/5.00 % (32118)------------------------------
% 25.20/5.00 % (32118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.20/5.00 % (32118)Termination reason: Unknown
% 25.20/5.00 % (32118)Termination phase: Saturation
% 25.20/5.00
% 25.20/5.00 % (32118)Memory used [KB]: 9466
% 25.20/5.00 % (32118)Time elapsed: 0.173 s
% 25.20/5.00 % (32118)Instructions burned: 580 (million)
% 25.20/5.00 % (32118)------------------------------
% 25.20/5.00 % (32118)------------------------------
% 25.20/5.00 % (32094)Instruction limit reached!
% 25.20/5.00 % (32094)------------------------------
% 25.20/5.00 % (32094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.20/5.00 % (32094)Termination reason: Unknown
% 25.20/5.00 % (32094)Termination phase: Saturation
% 25.20/5.00
% 25.20/5.00 % (32094)Memory used [KB]: 15223
% 25.20/5.00 % (32094)Time elapsed: 1.032 s
% 25.20/5.00 % (32094)Instructions burned: 3374 (million)
% 25.20/5.00 % (32094)------------------------------
% 25.20/5.00 % (32094)------------------------------
% 26.96/5.01 % (32123)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_31617 for (2965ds/1201Mi)
% 26.96/5.02 % (32122)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_31617 for (2965ds/644Mi)
% 26.96/5.02 % (32117)Instruction limit reached!
% 26.96/5.02 % (32117)------------------------------
% 26.96/5.02 % (32117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.96/5.02 % (32117)Termination reason: Unknown
% 26.96/5.02 % (32117)Termination phase: Saturation
% 26.96/5.02
% 26.96/5.02 % (32117)Memory used [KB]: 10746
% 26.96/5.02 % (32117)Time elapsed: 0.291 s
% 26.96/5.02 % (32117)Instructions burned: 952 (million)
% 26.96/5.02 % (32117)------------------------------
% 26.96/5.02 % (32117)------------------------------
% 26.96/5.03 % (32124)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_31617 for (2965ds/1046Mi)
% 26.96/5.07 % (32119)Instruction limit reached!
% 26.96/5.07 % (32119)------------------------------
% 26.96/5.07 % (32119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.96/5.07 % (32119)Termination reason: Unknown
% 26.96/5.07 % (32119)Termination phase: Saturation
% 26.96/5.07
% 26.96/5.07 % (32119)Memory used [KB]: 9338
% 26.96/5.07 % (32119)Time elapsed: 0.178 s
% 26.96/5.07 % (32119)Instructions burned: 646 (million)
% 26.96/5.07 % (32119)------------------------------
% 26.96/5.07 % (32119)------------------------------
% 26.96/5.08 % (32125)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_31617 for (2964ds/222Mi)
% 27.35/5.14 % (32125)Instruction limit reached!
% 27.35/5.14 % (32125)------------------------------
% 27.35/5.14 % (32125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.35/5.14 % (32125)Termination reason: Unknown
% 27.35/5.14 % (32125)Termination phase: Saturation
% 27.35/5.14
% 27.35/5.14 % (32125)Memory used [KB]: 7419
% 27.35/5.14 % (32125)Time elapsed: 0.059 s
% 27.35/5.14 % (32125)Instructions burned: 224 (million)
% 27.35/5.14 % (32125)------------------------------
% 27.35/5.14 % (32125)------------------------------
% 27.35/5.15 % (32126)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_31617 for (2964ds/68Mi)
% 27.35/5.17 % (32126)Instruction limit reached!
% 27.35/5.17 % (32126)------------------------------
% 27.35/5.17 % (32126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.35/5.17 % (32126)Termination reason: Unknown
% 27.35/5.17 % (32126)Termination phase: Preprocessing 3
% 27.35/5.17
% 27.35/5.17 % (32126)Memory used [KB]: 2430
% 27.35/5.17 % (32126)Time elapsed: 0.023 s
% 27.35/5.17 % (32126)Instructions burned: 69 (million)
% 27.35/5.17 % (32126)------------------------------
% 27.35/5.17 % (32126)------------------------------
% 27.35/5.18 % (32120)Instruction limit reached!
% 27.35/5.18 % (32120)------------------------------
% 27.35/5.18 % (32120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.35/5.18 % (32120)Termination reason: Unknown
% 27.35/5.18 % (32120)Termination phase: Saturation
% 27.35/5.18
% 27.35/5.18 % (32120)Memory used [KB]: 10362
% 27.35/5.18 % (32120)Time elapsed: 0.271 s
% 27.35/5.18 % (32120)Instructions burned: 866 (million)
% 27.35/5.18 % (32120)------------------------------
% 27.35/5.18 % (32120)------------------------------
% 27.35/5.18 % (32127)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_31617 for (2963ds/454Mi)
% 27.35/5.19 % (32128)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_31617 for (2963ds/360Mi)
% 27.70/5.26 % (32122)Instruction limit reached!
% 27.70/5.26 % (32122)------------------------------
% 27.70/5.26 % (32122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.70/5.26 % (32122)Termination reason: Unknown
% 27.70/5.26 % (32122)Termination phase: Saturation
% 27.70/5.26
% 27.70/5.26 % (32122)Memory used [KB]: 10106
% 27.70/5.26 % (32122)Time elapsed: 0.247 s
% 27.70/5.26 % (32122)Instructions burned: 644 (million)
% 27.70/5.26 % (32122)------------------------------
% 27.70/5.26 % (32122)------------------------------
% 27.70/5.28 % (32129)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_31617 for (2963ds/157Mi)
% 27.70/5.29 % (32121)Instruction limit reached!
% 27.70/5.29 % (32121)------------------------------
% 27.70/5.29 % (32121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.70/5.29 % (32121)Termination reason: Unknown
% 27.70/5.29 % (32121)Termination phase: Saturation
% 27.70/5.29
% 27.70/5.29 % (32121)Memory used [KB]: 11513
% 27.70/5.29 % (32121)Time elapsed: 0.368 s
% 27.70/5.29 % (32121)Instructions burned: 1174 (million)
% 27.70/5.29 % (32121)------------------------------
% 27.70/5.29 % (32121)------------------------------
% 27.70/5.29 % (32128)Instruction limit reached!
% 27.70/5.29 % (32128)------------------------------
% 27.70/5.29 % (32128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.70/5.29 % (32128)Termination reason: Unknown
% 27.70/5.29 % (32128)Termination phase: Saturation
% 27.70/5.29
% 27.70/5.29 % (32128)Memory used [KB]: 8443
% 27.70/5.29 % (32128)Time elapsed: 0.099 s
% 27.70/5.29 % (32128)Instructions burned: 360 (million)
% 27.70/5.29 % (32128)------------------------------
% 27.70/5.29 % (32128)------------------------------
% 27.70/5.30 % (32130)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_31617 for (2962ds/5061Mi)
% 28.28/5.30 % (32131)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_31617 for (2962ds/2401Mi)
% 28.28/5.31 % (32127)Instruction limit reached!
% 28.28/5.31 % (32127)------------------------------
% 28.28/5.31 % (32127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.28/5.31 % (32127)Termination reason: Unknown
% 28.28/5.31 % (32127)Termination phase: Saturation
% 28.28/5.31
% 28.28/5.31 % (32127)Memory used [KB]: 13304
% 28.28/5.31 % (32127)Time elapsed: 0.132 s
% 28.28/5.31 % (32127)Instructions burned: 455 (million)
% 28.28/5.31 % (32127)------------------------------
% 28.28/5.31 % (32127)------------------------------
% 28.28/5.32 % (32129)Instruction limit reached!
% 28.28/5.32 % (32129)------------------------------
% 28.28/5.32 % (32129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.28/5.32 % (32129)Termination reason: Unknown
% 28.28/5.32 % (32129)Termination phase: Property scanning
% 28.28/5.32
% 28.28/5.32 % (32129)Memory used [KB]: 2686
% 28.28/5.32 % (32129)Time elapsed: 0.043 s
% 28.28/5.32 % (32129)Instructions burned: 157 (million)
% 28.28/5.32 % (32129)------------------------------
% 28.28/5.32 % (32129)------------------------------
% 28.28/5.32 % (32132)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_31617 for (2962ds/5798Mi)
% 28.28/5.33 % (32133)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_31617 for (2962ds/346Mi)
% 28.28/5.34 % (32124)Instruction limit reached!
% 28.28/5.34 % (32124)------------------------------
% 28.28/5.34 % (32124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.28/5.34 % (32124)Termination reason: Unknown
% 28.28/5.34 % (32124)Termination phase: Saturation
% 28.28/5.34
% 28.28/5.34 % (32124)Memory used [KB]: 9338
% 28.28/5.34 % (32124)Time elapsed: 0.307 s
% 28.28/5.34 % (32124)Instructions burned: 1049 (million)
% 28.28/5.34 % (32124)------------------------------
% 28.28/5.34 % (32124)------------------------------
% 28.28/5.35 % (32134)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_31617 for (2962ds/1321Mi)
% 28.28/5.35 % (32123)Instruction limit reached!
% 28.28/5.35 % (32123)------------------------------
% 28.28/5.35 % (32123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.28/5.35 % (32123)Termination reason: Unknown
% 28.28/5.35 % (32123)Termination phase: Saturation
% 28.28/5.35
% 28.28/5.35 % (32123)Memory used [KB]: 11641
% 28.28/5.35 % (32123)Time elapsed: 0.340 s
% 28.28/5.35 % (32123)Instructions burned: 1202 (million)
% 28.28/5.35 % (32123)------------------------------
% 28.28/5.35 % (32123)------------------------------
% 28.28/5.36 % (32135)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_31617 for (2962ds/1312Mi)
% 29.25/5.43 % (32133)Instruction limit reached!
% 29.25/5.43 % (32133)------------------------------
% 29.25/5.43 % (32133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.25/5.43 % (32133)Termination reason: Unknown
% 29.25/5.43 % (32133)Termination phase: Saturation
% 29.25/5.43
% 29.25/5.43 % (32133)Memory used [KB]: 7931
% 29.25/5.43 % (32133)Time elapsed: 0.123 s
% 29.25/5.43 % (32133)Instructions burned: 348 (million)
% 29.25/5.43 % (32133)------------------------------
% 29.25/5.43 % (32133)------------------------------
% 29.25/5.44 % (32136)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_31617 for (2961ds/672Mi)
% 29.25/5.45 % (32136)Refutation not found, incomplete strategy
% 29.25/5.45 % (32136)------------------------------
% 29.25/5.45 % (32136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.25/5.45 % (32136)Termination reason: Refutation not found, incomplete strategy
% 29.25/5.45
% 29.25/5.45
% 29.25/5.45 % (32136)Memory used [KB]: 6524
% 29.25/5.45 % (32136)Time elapsed: 0.016 s
% 29.25/5.45 % (32136)Instructions burned: 48 (million)
% 29.25/5.45 % (32136)------------------------------
% 29.25/5.45 % (32136)------------------------------
% 29.25/5.46 % (32137)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_31617 for (2961ds/1897Mi)
% 29.25/5.47 % (32067)Instruction limit reached!
% 29.25/5.47 % (32067)------------------------------
% 29.25/5.47 % (32067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.25/5.47 % (32067)Termination reason: Unknown
% 29.25/5.47 % (32067)Termination phase: Saturation
% 29.25/5.47
% 29.25/5.47 % (32067)Memory used [KB]: 19317
% 29.25/5.47 % (32067)Time elapsed: 2.546 s
% 29.25/5.47 % (32067)Instructions burned: 8253 (million)
% 29.25/5.47 % (32067)------------------------------
% 29.25/5.47 % (32067)------------------------------
% 29.25/5.47 % (32137)Refutation not found, incomplete strategy
% 29.25/5.47 % (32137)------------------------------
% 29.25/5.47 % (32137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.25/5.47 % (32137)Termination reason: Refutation not found, incomplete strategy
% 29.25/5.47
% 29.25/5.47
% 29.25/5.47 % (32137)Memory used [KB]: 6396
% 29.25/5.47 % (32137)Time elapsed: 0.015 s
% 29.25/5.47 % (32137)Instructions burned: 44 (million)
% 29.25/5.47 % (32137)------------------------------
% 29.25/5.47 % (32137)------------------------------
% 29.25/5.48 % (32138)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_31617 for (2960ds/1202Mi)
% 29.25/5.48 % (32139)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_31617 for (2960ds/1493Mi)
% 29.49/5.51 % (32139)Refutation not found, incomplete strategy
% 29.49/5.51 % (32139)------------------------------
% 29.49/5.51 % (32139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.49/5.51 % (32139)Termination reason: Refutation not found, incomplete strategy
% 29.49/5.51
% 29.49/5.51
% 29.49/5.51 % (32139)Memory used [KB]: 6908
% 29.49/5.51 % (32139)Time elapsed: 0.026 s
% 29.49/5.51 % (32139)Instructions burned: 94 (million)
% 29.49/5.51 % (32139)------------------------------
% 29.49/5.51 % (32139)------------------------------
% 29.49/5.52 % (32140)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_31617 for (2960ds/7679Mi)
% 29.49/5.54 % (32140)Refutation not found, incomplete strategy
% 29.49/5.54 % (32140)------------------------------
% 29.49/5.54 % (32140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.49/5.54 % (32140)Termination reason: Refutation not found, incomplete strategy
% 29.49/5.54
% 29.49/5.54
% 29.49/5.54 % (32140)Memory used [KB]: 1918
% 29.49/5.54 % (32140)Time elapsed: 0.016 s
% 29.49/5.54 % (32140)Instructions burned: 47 (million)
% 29.49/5.54 % (32140)------------------------------
% 29.49/5.54 % (32140)------------------------------
% 29.49/5.54 % (32141)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_31617 for (2960ds/340Mi)
% 29.55/5.64 % (32141)Instruction limit reached!
% 29.55/5.64 % (32141)------------------------------
% 29.55/5.64 % (32141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.55/5.64 % (32141)Termination reason: Unknown
% 29.55/5.64 % (32141)Termination phase: Saturation
% 29.55/5.64
% 29.55/5.64 % (32141)Memory used [KB]: 8443
% 29.55/5.64 % (32141)Time elapsed: 0.095 s
% 29.55/5.64 % (32141)Instructions burned: 342 (million)
% 29.55/5.64 % (32141)------------------------------
% 29.55/5.64 % (32141)------------------------------
% 29.55/5.65 % (32142)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_31617 for (2959ds/3672Mi)
% 29.65/5.74 % (32135)Instruction limit reached!
% 29.65/5.74 % (32135)------------------------------
% 29.65/5.74 % (32135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.65/5.74 % (32135)Termination reason: Unknown
% 29.65/5.74 % (32135)Termination phase: Saturation
% 29.65/5.74
% 29.65/5.74 % (32135)Memory used [KB]: 10362
% 29.65/5.74 % (32135)Time elapsed: 0.385 s
% 29.65/5.74 % (32135)Instructions burned: 1314 (million)
% 29.65/5.74 % (32135)------------------------------
% 29.65/5.74 % (32135)------------------------------
% 29.65/5.75 % (32134)Instruction limit reached!
% 29.65/5.75 % (32134)------------------------------
% 29.65/5.75 % (32134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.65/5.75 % (32134)Termination reason: Unknown
% 29.65/5.75 % (32134)Termination phase: Saturation
% 29.65/5.75
% 29.65/5.75 % (32134)Memory used [KB]: 5884
% 29.65/5.75 % (32134)Time elapsed: 0.424 s
% 29.65/5.75 % (32134)Instructions burned: 1321 (million)
% 29.65/5.75 % (32134)------------------------------
% 29.65/5.75 % (32134)------------------------------
% 29.65/5.76 % (32143)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_31617 for (2958ds/1535Mi)
% 29.65/5.76 % (32144)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_31617 for (2958ds/4637Mi)
% 29.65/5.77 % (32144)Refutation not found, incomplete strategy
% 29.65/5.77 % (32144)------------------------------
% 29.65/5.77 % (32144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.65/5.77 % (32144)Termination reason: Refutation not found, incomplete strategy
% 29.65/5.77
% 29.65/5.77
% 29.65/5.77 % (32144)Memory used [KB]: 6524
% 29.65/5.77 % (32144)Time elapsed: 0.015 s
% 29.65/5.77 % (32144)Instructions burned: 46 (million)
% 29.65/5.77 % (32144)------------------------------
% 29.65/5.77 % (32144)------------------------------
% 29.65/5.78 % (32145)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_31617 for (2957ds/3174Mi)
% 30.49/5.85 % (32138)Instruction limit reached!
% 30.49/5.85 % (32138)------------------------------
% 30.49/5.85 % (32138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.49/5.85 % (32138)Termination reason: Unknown
% 30.49/5.85 % (32138)Termination phase: Saturation
% 30.49/5.85
% 30.49/5.85 % (32138)Memory used [KB]: 5628
% 30.49/5.85 % (32138)Time elapsed: 0.368 s
% 30.49/5.85 % (32138)Instructions burned: 1202 (million)
% 30.49/5.85 % (32138)------------------------------
% 30.49/5.85 % (32138)------------------------------
% 30.49/5.86 % (32146)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_31617 for (2957ds/307Mi)
% 30.87/5.94 % (32146)Instruction limit reached!
% 30.87/5.94 % (32146)------------------------------
% 30.87/5.94 % (32146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.87/5.94 % (32146)Termination reason: Unknown
% 30.87/5.94 % (32146)Termination phase: Saturation
% 30.87/5.94
% 30.87/5.94 % (32146)Memory used [KB]: 7675
% 30.87/5.94 % (32146)Time elapsed: 0.083 s
% 30.87/5.94 % (32146)Instructions burned: 309 (million)
% 30.87/5.94 % (32146)------------------------------
% 30.87/5.94 % (32146)------------------------------
% 30.87/5.95 % (32147)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_31617 for (2956ds/3619Mi)
% 34.07/6.03 % (32131)Instruction limit reached!
% 34.07/6.03 % (32131)------------------------------
% 34.07/6.03 % (32131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.07/6.03 % (32131)Termination reason: Unknown
% 34.07/6.03 % (32131)Termination phase: Saturation
% 34.07/6.03
% 34.07/6.03 % (32131)Memory used [KB]: 8059
% 34.07/6.03 % (32131)Time elapsed: 0.759 s
% 34.07/6.03 % (32131)Instructions burned: 2401 (million)
% 34.07/6.03 % (32131)------------------------------
% 34.07/6.03 % (32131)------------------------------
% 34.07/6.04 % (32148)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_31617 for (2955ds/2325Mi)
% 35.12/6.20 % (32143)Instruction limit reached!
% 35.12/6.20 % (32143)------------------------------
% 35.12/6.20 % (32143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.12/6.20 % (32143)Termination reason: Unknown
% 35.12/6.20 % (32143)Termination phase: Saturation
% 35.12/6.20
% 35.12/6.20 % (32143)Memory used [KB]: 12665
% 35.12/6.20 % (32143)Time elapsed: 0.449 s
% 35.12/6.20 % (32143)Instructions burned: 1535 (million)
% 35.12/6.20 % (32143)------------------------------
% 35.12/6.20 % (32143)------------------------------
% 35.12/6.21 % (32149)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_31617 for (2953ds/2341Mi)
% 37.65/6.71 % (32145)Instruction limit reached!
% 37.65/6.71 % (32145)------------------------------
% 37.65/6.71 % (32145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.65/6.71 % (32145)Termination reason: Unknown
% 37.65/6.71 % (32145)Termination phase: Saturation
% 37.65/6.71
% 37.65/6.71 % (32145)Memory used [KB]: 13304
% 37.65/6.71 % (32145)Time elapsed: 0.934 s
% 37.65/6.71 % (32145)Instructions burned: 3176 (million)
% 37.65/6.71 % (32145)------------------------------
% 37.65/6.71 % (32145)------------------------------
% 37.65/6.73 % (32150)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_31617 for (2948ds/7257Mi)
% 37.65/6.74 % (32150)Refutation not found, incomplete strategy
% 37.65/6.74 % (32150)------------------------------
% 37.65/6.74 % (32150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.65/6.74 % (32150)Termination reason: Refutation not found, incomplete strategy
% 37.65/6.74
% 37.65/6.74
% 37.65/6.74 % (32150)Memory used [KB]: 6524
% 37.65/6.74 % (32150)Time elapsed: 0.016 s
% 37.65/6.74 % (32150)Instructions burned: 48 (million)
% 37.65/6.74 % (32150)------------------------------
% 37.65/6.74 % (32150)------------------------------
% 37.65/6.75 % (32151)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_31617 for (2948ds/3710Mi)
% 37.65/6.76 % (32148)Instruction limit reached!
% 37.65/6.76 % (32148)------------------------------
% 37.65/6.76 % (32148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.65/6.76 % (32148)Termination reason: Unknown
% 37.65/6.76 % (32148)Termination phase: Saturation
% 37.65/6.76
% 37.65/6.76 % (32148)Memory used [KB]: 12409
% 37.65/6.76 % (32148)Time elapsed: 0.722 s
% 37.65/6.76 % (32148)Instructions burned: 2325 (million)
% 37.65/6.76 % (32148)------------------------------
% 37.65/6.76 % (32148)------------------------------
% 37.65/6.77 % (32152)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_31617 for (2947ds/326Mi)
% 37.65/6.79 % (32152)Refutation not found, incomplete strategy
% 37.65/6.79 % (32152)------------------------------
% 37.65/6.79 % (32152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.65/6.79 % (32152)Termination reason: Refutation not found, incomplete strategy
% 37.65/6.79
% 37.65/6.79
% 37.65/6.79 % (32152)Memory used [KB]: 6396
% 37.65/6.79 % (32152)Time elapsed: 0.014 s
% 37.65/6.79 % (32152)Instructions burned: 43 (million)
% 37.65/6.79 % (32152)------------------------------
% 37.65/6.79 % (32152)------------------------------
% 37.65/6.79 % (32142)Instruction limit reached!
% 37.65/6.79 % (32142)------------------------------
% 37.65/6.79 % (32142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.65/6.79 % (32142)Termination reason: Unknown
% 37.65/6.79 % (32142)Termination phase: Saturation
% 37.65/6.79
% 37.65/6.79 % (32142)Memory used [KB]: 13688
% 37.65/6.79 % (32142)Time elapsed: 1.142 s
% 37.65/6.79 % (32142)Instructions burned: 3673 (million)
% 37.65/6.79 % (32142)------------------------------
% 37.65/6.79 % (32142)------------------------------
% 38.87/6.80 % (32153)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_31617 for (2947ds/1100Mi)
% 38.87/6.80 % (32130)Instruction limit reached!
% 38.87/6.80 % (32130)------------------------------
% 38.87/6.80 % (32130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.87/6.80 % (32130)Termination reason: Unknown
% 38.87/6.80 % (32130)Termination phase: Saturation
% 38.87/6.80
% 38.87/6.80 % (32130)Memory used [KB]: 12920
% 38.87/6.80 % (32130)Time elapsed: 1.504 s
% 38.87/6.80 % (32130)Instructions burned: 5061 (million)
% 38.87/6.80 % (32130)------------------------------
% 38.87/6.80 % (32130)------------------------------
% 38.87/6.80 % (32154)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_31617 for (2947ds/406Mi)
% 38.87/6.81 % (32155)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_31617 for (2947ds/1871Mi)
% 39.08/6.93 % (32154)Instruction limit reached!
% 39.08/6.93 % (32154)------------------------------
% 39.08/6.93 % (32154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.08/6.93 % (32154)Termination reason: Unknown
% 39.08/6.93 % (32154)Termination phase: Saturation
% 39.08/6.93
% 39.08/6.93 % (32154)Memory used [KB]: 8827
% 39.08/6.93 % (32154)Time elapsed: 0.128 s
% 39.08/6.93 % (32154)Instructions burned: 406 (million)
% 39.08/6.93 % (32154)------------------------------
% 39.08/6.93 % (32154)------------------------------
% 39.08/6.94 % (32156)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_31617 for (2946ds/1194Mi)
% 39.08/6.95 % (32149)Instruction limit reached!
% 39.08/6.95 % (32149)------------------------------
% 39.08/6.95 % (32149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.08/6.95 % (32149)Termination reason: Unknown
% 39.08/6.95 % (32149)Termination phase: Saturation
% 39.08/6.95
% 39.08/6.95 % (32149)Memory used [KB]: 9083
% 39.08/6.95 % (32149)Time elapsed: 0.735 s
% 39.08/6.95 % (32149)Instructions burned: 2342 (million)
% 39.08/6.95 % (32149)------------------------------
% 39.08/6.95 % (32149)------------------------------
% 39.08/6.96 % (32157)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_31617 for (2946ds/474Mi)
% 39.08/7.02 % (32147)Instruction limit reached!
% 39.08/7.02 % (32147)------------------------------
% 39.08/7.02 % (32147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.08/7.02 % (32147)Termination reason: Unknown
% 39.08/7.02 % (32147)Termination phase: Saturation
% 39.08/7.02
% 39.08/7.02 % (32147)Memory used [KB]: 11897
% 39.08/7.02 % (32147)Time elapsed: 1.065 s
% 39.08/7.02 % (32147)Instructions burned: 3621 (million)
% 39.08/7.02 % (32147)------------------------------
% 39.08/7.02 % (32147)------------------------------
% 41.10/7.03 % (32158)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_31617 for (2945ds/3115Mi)
% 41.10/7.09 % (32132)Instruction limit reached!
% 41.10/7.09 % (32132)------------------------------
% 41.10/7.09 % (32132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.10/7.09 % (32132)Termination reason: Unknown
% 41.10/7.09 % (32132)Termination phase: Saturation
% 41.10/7.09
% 41.10/7.09 % (32132)Memory used [KB]: 15351
% 41.10/7.09 % (32132)Time elapsed: 1.791 s
% 41.10/7.09 % (32132)Instructions burned: 5800 (million)
% 41.10/7.09 % (32132)------------------------------
% 41.10/7.09 % (32132)------------------------------
% 41.10/7.09 % (32157)Instruction limit reached!
% 41.10/7.09 % (32157)------------------------------
% 41.10/7.09 % (32157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.10/7.09 % (32157)Termination reason: Unknown
% 41.10/7.09 % (32157)Termination phase: Saturation
% 41.10/7.09
% 41.10/7.09 % (32157)Memory used [KB]: 9338
% 41.10/7.09 % (32157)Time elapsed: 0.139 s
% 41.10/7.09 % (32157)Instructions burned: 477 (million)
% 41.10/7.09 % (32157)------------------------------
% 41.10/7.09 % (32157)------------------------------
% 41.10/7.10 % (32159)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_31617 for (2944ds/831Mi)
% 41.10/7.10 % (32160)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_31617 for (2944ds/1188Mi)
% 41.66/7.14 % (32153)Instruction limit reached!
% 41.66/7.14 % (32153)------------------------------
% 41.66/7.14 % (32153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.66/7.14 % (32153)Termination reason: Unknown
% 41.66/7.14 % (32153)Termination phase: Saturation
% 41.66/7.14
% 41.66/7.14 % (32153)Memory used [KB]: 11641
% 41.66/7.14 % (32153)Time elapsed: 0.342 s
% 41.66/7.14 % (32153)Instructions burned: 1101 (million)
% 41.66/7.14 % (32153)------------------------------
% 41.66/7.14 % (32153)------------------------------
% 41.66/7.15 % (32161)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_31617 for (2944ds/2868Mi)
% 41.90/7.22 % (32161)Refutation not found, incomplete strategy
% 41.90/7.22 % (32161)------------------------------
% 41.90/7.22 % (32161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.90/7.22 % (32161)Termination reason: Refutation not found, incomplete strategy
% 41.90/7.22
% 41.90/7.22
% 41.90/7.22 % (32161)Memory used [KB]: 7803
% 41.90/7.22 % (32161)Time elapsed: 0.069 s
% 41.90/7.22 % (32161)Instructions burned: 256 (million)
% 41.90/7.22 % (32161)------------------------------
% 41.90/7.22 % (32161)------------------------------
% 41.90/7.23 % (32162)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_31617 for (2943ds/1516Mi)
% 41.90/7.24 % (32162)Refutation not found, incomplete strategy
% 41.90/7.24 % (32162)------------------------------
% 41.90/7.24 % (32162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.90/7.24 % (32162)Termination reason: Refutation not found, incomplete strategy
% 41.90/7.24
% 41.90/7.24
% 41.90/7.24 % (32162)Memory used [KB]: 6396
% 41.90/7.24 % (32162)Time elapsed: 0.015 s
% 41.90/7.24 % (32162)Instructions burned: 43 (million)
% 41.90/7.24 % (32162)------------------------------
% 41.90/7.24 % (32162)------------------------------
% 41.90/7.25 % (32163)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_31617 for (2943ds/2321Mi)
% 42.30/7.30 % (32156)Instruction limit reached!
% 42.30/7.30 % (32156)------------------------------
% 42.30/7.30 % (32156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.30/7.30 % (32156)Termination reason: Unknown
% 42.30/7.30 % (32156)Termination phase: Saturation
% 42.30/7.30
% 42.30/7.30 % (32156)Memory used [KB]: 9978
% 42.30/7.30 % (32156)Time elapsed: 0.369 s
% 42.30/7.30 % (32156)Instructions burned: 1194 (million)
% 42.30/7.30 % (32156)------------------------------
% 42.30/7.30 % (32156)------------------------------
% 42.30/7.32 % (32164)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_31617 for (2942ds/2812Mi)
% 42.30/7.32 % (32163)Refutation not found, incomplete strategy
% 42.30/7.32 % (32163)------------------------------
% 42.30/7.32 % (32163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.30/7.32 % (32163)Termination reason: Refutation not found, incomplete strategy
% 42.30/7.32
% 42.30/7.32
% 42.30/7.32 % (32163)Memory used [KB]: 7931
% 42.30/7.32 % (32163)Time elapsed: 0.071 s
% 42.30/7.32 % (32163)Instructions burned: 259 (million)
% 42.30/7.32 % (32163)------------------------------
% 42.30/7.32 % (32163)------------------------------
% 42.30/7.34 % (32165)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_31617 for (2942ds/4604Mi)
% 42.30/7.35 % (32159)Instruction limit reached!
% 42.30/7.35 % (32159)------------------------------
% 42.30/7.35 % (32159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.30/7.35 % (32159)Termination reason: Unknown
% 42.30/7.35 % (32159)Termination phase: Saturation
% 42.30/7.35
% 42.30/7.35 % (32159)Memory used [KB]: 10874
% 42.30/7.35 % (32159)Time elapsed: 0.253 s
% 42.30/7.35 % (32159)Instructions burned: 831 (million)
% 42.30/7.35 % (32159)------------------------------
% 42.30/7.35 % (32159)------------------------------
% 42.30/7.36 % (32166)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_31617 for (2942ds/2678Mi)
% 42.30/7.37 % (32165)Refutation not found, incomplete strategy
% 42.30/7.37 % (32165)------------------------------
% 42.30/7.37 % (32165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.30/7.37 % (32165)Termination reason: Refutation not found, incomplete strategy
% 42.30/7.37
% 42.30/7.37
% 42.30/7.37 % (32165)Memory used [KB]: 6524
% 42.30/7.37 % (32165)Time elapsed: 0.029 s
% 42.30/7.37 % (32165)Instructions burned: 47 (million)
% 42.30/7.37 % (32165)------------------------------
% 42.30/7.37 % (32165)------------------------------
% 42.30/7.39 % (32167)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_31617 for (2941ds/643Mi)
% 42.92/7.40 % (32155)Instruction limit reached!
% 42.92/7.40 % (32155)------------------------------
% 42.92/7.40 % (32155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.92/7.40 % (32155)Termination reason: Unknown
% 42.92/7.40 % (32155)Termination phase: Saturation
% 42.92/7.40
% 42.92/7.40 % (32155)Memory used [KB]: 12665
% 42.92/7.40 % (32155)Time elapsed: 0.591 s
% 42.92/7.40 % (32155)Instructions burned: 1871 (million)
% 42.92/7.40 % (32155)------------------------------
% 42.92/7.40 % (32155)------------------------------
% 42.92/7.41 % (32168)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_31617 for (2941ds/458Mi)
% 42.92/7.46 % (32160)Instruction limit reached!
% 42.92/7.46 % (32160)------------------------------
% 42.92/7.46 % (32160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.92/7.46 % (32160)Termination reason: Unknown
% 42.92/7.46 % (32160)Termination phase: Saturation
% 42.92/7.46
% 42.92/7.46 % (32160)Memory used [KB]: 11257
% 42.92/7.46 % (32160)Time elapsed: 0.358 s
% 42.92/7.46 % (32160)Instructions burned: 1189 (million)
% 42.92/7.46 % (32160)------------------------------
% 42.92/7.46 % (32160)------------------------------
% 42.92/7.47 % (32169)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_31617 for (2940ds/2546Mi)
% 43.40/7.54 % (32168)Instruction limit reached!
% 43.40/7.54 % (32168)------------------------------
% 43.40/7.54 % (32168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.40/7.54 % (32168)Termination reason: Unknown
% 43.40/7.54 % (32168)Termination phase: Saturation
% 43.40/7.54
% 43.40/7.54 % (32168)Memory used [KB]: 8571
% 43.40/7.54 % (32168)Time elapsed: 0.128 s
% 43.40/7.54 % (32168)Instructions burned: 458 (million)
% 43.40/7.54 % (32168)------------------------------
% 43.40/7.54 % (32168)------------------------------
% 43.40/7.55 % (32170)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_31617 for (2940ds/1432Mi)
% 43.63/7.60 % (32167)Instruction limit reached!
% 43.63/7.60 % (32167)------------------------------
% 43.63/7.60 % (32167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.63/7.60 % (32167)Termination reason: Unknown
% 43.63/7.60 % (32167)Termination phase: Saturation
% 43.63/7.60
% 43.63/7.60 % (32167)Memory used [KB]: 9722
% 43.63/7.60 % (32167)Time elapsed: 0.213 s
% 43.63/7.60 % (32167)Instructions burned: 643 (million)
% 43.63/7.60 % (32167)------------------------------
% 43.63/7.60 % (32167)------------------------------
% 43.63/7.61 % (32171)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_31617 for (2939ds/386Mi)
% 43.96/7.72 % (32171)Instruction limit reached!
% 43.96/7.72 % (32171)------------------------------
% 43.96/7.72 % (32171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.96/7.72 % (32171)Termination reason: Unknown
% 43.96/7.72 % (32171)Termination phase: Saturation
% 43.96/7.72
% 43.96/7.72 % (32171)Memory used [KB]: 8571
% 43.96/7.72 % (32171)Time elapsed: 0.114 s
% 43.96/7.72 % (32171)Instructions burned: 388 (million)
% 43.96/7.72 % (32171)------------------------------
% 43.96/7.72 % (32171)------------------------------
% 43.96/7.73 % (32172)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_31617 for (2938ds/360Mi)
% 44.19/7.84 % (32172)Instruction limit reached!
% 44.19/7.84 % (32172)------------------------------
% 44.19/7.84 % (32172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.19/7.84 % (32172)Termination reason: Unknown
% 44.19/7.84 % (32172)Termination phase: Saturation
% 44.19/7.84
% 44.19/7.84 % (32172)Memory used [KB]: 8571
% 44.19/7.84 % (32172)Time elapsed: 0.105 s
% 44.19/7.84 % (32172)Instructions burned: 360 (million)
% 44.19/7.84 % (32172)------------------------------
% 44.19/7.84 % (32172)------------------------------
% 44.19/7.85 % (32173)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_31617 for (2937ds/5446Mi)
% 44.19/7.88 % (32170)Instruction limit reached!
% 44.19/7.88 % (32170)------------------------------
% 44.19/7.88 % (32170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.19/7.88 % (32170)Termination reason: Unknown
% 44.19/7.88 % (32170)Termination phase: Saturation
% 44.19/7.88
% 44.19/7.88 % (32170)Memory used [KB]: 12153
% 44.19/7.88 % (32170)Time elapsed: 0.333 s
% 44.19/7.88 % (32170)Instructions burned: 1435 (million)
% 44.19/7.88 % (32170)------------------------------
% 44.19/7.88 % (32170)------------------------------
% 44.19/7.89 % (32174)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_31617 for (2936ds/2573Mi)
% 44.75/7.92 % (32151)Instruction limit reached!
% 44.75/7.92 % (32151)------------------------------
% 44.75/7.92 % (32151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.75/7.92 % (32151)Termination reason: Unknown
% 44.75/7.92 % (32151)Termination phase: Saturation
% 44.75/7.92
% 44.75/7.92 % (32151)Memory used [KB]: 20596
% 44.75/7.92 % (32151)Time elapsed: 1.172 s
% 44.75/7.92 % (32151)Instructions burned: 3710 (million)
% 44.75/7.92 % (32151)------------------------------
% 44.75/7.92 % (32151)------------------------------
% 44.75/7.93 % (32175)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_31617 for (2936ds/2655Mi)
% 44.75/7.98 % (32158)Instruction limit reached!
% 44.75/7.98 % (32158)------------------------------
% 44.75/7.98 % (32158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.75/7.98 % (32158)Termination reason: Unknown
% 44.75/7.98 % (32158)Termination phase: Saturation
% 44.75/7.98
% 44.75/7.98 % (32158)Memory used [KB]: 15223
% 44.75/7.98 % (32158)Time elapsed: 0.978 s
% 44.75/7.98 % (32158)Instructions burned: 3117 (million)
% 44.75/7.98 % (32158)------------------------------
% 44.75/7.98 % (32158)------------------------------
% 44.75/7.99 % (32176)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_31617 for (2935ds/2781Mi)
% 48.77/8.15 % (32166)Instruction limit reached!
% 48.77/8.15 % (32166)------------------------------
% 48.77/8.15 % (32166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.77/8.15 % (32166)Termination reason: Unknown
% 48.77/8.15 % (32166)Termination phase: Saturation
% 48.77/8.15
% 48.77/8.15 % (32166)Memory used [KB]: 12537
% 48.77/8.15 % (32166)Time elapsed: 0.792 s
% 48.77/8.15 % (32166)Instructions burned: 2680 (million)
% 48.77/8.15 % (32166)------------------------------
% 48.77/8.15 % (32166)------------------------------
% 48.77/8.17 % (32177)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_31617 for (2934ds/307Mi)
% 49.28/8.21 % (32164)Instruction limit reached!
% 49.28/8.21 % (32164)------------------------------
% 49.28/8.21 % (32164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.28/8.21 % (32164)Termination reason: Unknown
% 49.28/8.21 % (32164)Termination phase: Saturation
% 49.28/8.21
% 49.28/8.21 % (32164)Memory used [KB]: 14200
% 49.28/8.21 % (32164)Time elapsed: 0.898 s
% 49.28/8.21 % (32164)Instructions burned: 2814 (million)
% 49.28/8.21 % (32164)------------------------------
% 49.28/8.21 % (32164)------------------------------
% 49.28/8.22 % (32178)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_31617 for (2933ds/1548Mi)
% 49.28/8.24 % (32178)Refutation not found, incomplete strategy
% 49.28/8.24 % (32178)------------------------------
% 49.28/8.24 % (32178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.28/8.24 % (32178)Termination reason: Refutation not found, incomplete strategy
% 49.28/8.24
% 49.28/8.24
% 49.28/8.24 % (32178)Memory used [KB]: 6396
% 49.28/8.24 % (32178)Time elapsed: 0.015 s
% 49.28/8.24 % (32178)Instructions burned: 45 (million)
% 49.28/8.24 % (32178)------------------------------
% 49.28/8.24 % (32178)------------------------------
% 49.28/8.25 % (32179)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_31617 for (2933ds/5214Mi)
% 49.28/8.25 % (32177)Instruction limit reached!
% 49.28/8.25 % (32177)------------------------------
% 49.28/8.25 % (32177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.28/8.25 % (32177)Termination reason: Unknown
% 49.28/8.25 % (32177)Termination phase: Saturation
% 49.28/8.25
% 49.28/8.25 % (32177)Memory used [KB]: 7675
% 49.28/8.25 % (32177)Time elapsed: 0.086 s
% 49.28/8.25 % (32177)Instructions burned: 307 (million)
% 49.28/8.25 % (32177)------------------------------
% 49.28/8.25 % (32177)------------------------------
% 49.28/8.26 % (32180)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_31617 for (2933ds/3201Mi)
% 49.28/8.27 % (32169)Instruction limit reached!
% 49.28/8.27 % (32169)------------------------------
% 49.28/8.27 % (32169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.28/8.27 % (32169)Termination reason: Unknown
% 49.28/8.27 % (32169)Termination phase: Saturation
% 49.28/8.27
% 49.28/8.27 % (32169)Memory used [KB]: 12920
% 49.28/8.27 % (32169)Time elapsed: 0.797 s
% 49.28/8.27 % (32169)Instructions burned: 2546 (million)
% 49.28/8.27 % (32169)------------------------------
% 49.28/8.27 % (32169)------------------------------
% 49.28/8.28 % (32181)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_31617 for (2932ds/454Mi)
% 50.30/8.41 % (32181)Instruction limit reached!
% 50.30/8.41 % (32181)------------------------------
% 50.30/8.41 % (32181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.30/8.41 % (32181)Termination reason: Unknown
% 50.30/8.41 % (32181)Termination phase: Saturation
% 50.30/8.41
% 50.30/8.41 % (32181)Memory used [KB]: 13304
% 50.30/8.41 % (32181)Time elapsed: 0.129 s
% 50.30/8.41 % (32181)Instructions burned: 455 (million)
% 50.30/8.41 % (32181)------------------------------
% 50.30/8.41 % (32181)------------------------------
% 50.30/8.42 % (32182)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_31617 for (2931ds/3049Mi)
% 51.23/8.68 % (32174)Instruction limit reached!
% 51.23/8.68 % (32174)------------------------------
% 51.23/8.68 % (32174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.23/8.68 % (32174)Termination reason: Unknown
% 51.23/8.68 % (32174)Termination phase: Saturation
% 51.23/8.68
% 51.23/8.68 % (32174)Memory used [KB]: 14583
% 51.23/8.68 % (32174)Time elapsed: 0.798 s
% 51.23/8.68 % (32174)Instructions burned: 2574 (million)
% 51.23/8.68 % (32174)------------------------------
% 51.23/8.68 % (32174)------------------------------
% 51.23/8.70 % (32183)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_31617 for (2928ds/7311Mi)
% 51.65/8.71 % (32183)Refutation not found, incomplete strategy
% 51.65/8.71 % (32183)------------------------------
% 51.65/8.71 % (32183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.65/8.71 % (32183)Termination reason: Refutation not found, incomplete strategy
% 51.65/8.71
% 51.65/8.71
% 51.65/8.71 % (32183)Memory used [KB]: 6524
% 51.65/8.71 % (32183)Time elapsed: 0.016 s
% 51.65/8.71 % (32183)Instructions burned: 48 (million)
% 51.65/8.71 % (32183)------------------------------
% 51.65/8.71 % (32183)------------------------------
% 51.65/8.72 % (32184)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_31617 for (2928ds/6804Mi)
% 51.65/8.74 % (32175)Instruction limit reached!
% 51.65/8.74 % (32175)------------------------------
% 51.65/8.74 % (32175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.65/8.74 % (32175)Termination reason: Unknown
% 51.65/8.74 % (32175)Termination phase: Saturation
% 51.65/8.74
% 51.65/8.74 % (32175)Memory used [KB]: 16119
% 51.65/8.74 % (32175)Time elapsed: 0.808 s
% 51.65/8.74 % (32175)Instructions burned: 2657 (million)
% 51.65/8.74 % (32175)------------------------------
% 51.65/8.74 % (32175)------------------------------
% 51.65/8.75 % (32185)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_31617 for (2928ds/1683Mi)
% 51.94/8.86 % (32176)Instruction limit reached!
% 51.94/8.86 % (32176)------------------------------
% 51.94/8.86 % (32176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.94/8.86 % (32176)Termination reason: Unknown
% 51.94/8.86 % (32176)Termination phase: Saturation
% 51.94/8.86
% 51.94/8.86 % (32176)Memory used [KB]: 6396
% 51.94/8.86 % (32176)Time elapsed: 0.865 s
% 51.94/8.86 % (32176)Instructions burned: 2781 (million)
% 51.94/8.86 % (32176)------------------------------
% 51.94/8.86 % (32176)------------------------------
% 51.94/8.87 % (32186)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_31617 for (2927ds/4688Mi)
% 56.30/9.21 % (32180)Instruction limit reached!
% 56.30/9.21 % (32180)------------------------------
% 56.30/9.21 % (32180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.30/9.21 % (32180)Termination reason: Unknown
% 56.30/9.21 % (32180)Termination phase: Saturation
% 56.30/9.21
% 56.30/9.21 % (32180)Memory used [KB]: 13560
% 56.30/9.21 % (32180)Time elapsed: 0.953 s
% 56.30/9.21 % (32180)Instructions burned: 3202 (million)
% 56.30/9.21 % (32180)------------------------------
% 56.30/9.21 % (32180)------------------------------
% 56.30/9.22 % (32187)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_31617 for (2923ds/2207Mi)
% 56.30/9.29 % (32185)Instruction limit reached!
% 56.30/9.29 % (32185)------------------------------
% 56.30/9.29 % (32185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.30/9.29 % (32185)Termination reason: Unknown
% 56.30/9.29 % (32185)Termination phase: Saturation
% 56.30/9.29
% 56.30/9.29 % (32185)Memory used [KB]: 10618
% 56.30/9.29 % (32185)Time elapsed: 0.540 s
% 56.30/9.29 % (32185)Instructions burned: 1685 (million)
% 56.30/9.29 % (32185)------------------------------
% 56.30/9.29 % (32185)------------------------------
% 56.94/9.30 % (32188)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_31617 for (2922ds/8216Mi)
% 56.94/9.34 % (32182)Instruction limit reached!
% 56.94/9.34 % (32182)------------------------------
% 56.94/9.34 % (32182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.94/9.34 % (32182)Termination reason: Unknown
% 56.94/9.34 % (32182)Termination phase: Saturation
% 56.94/9.34
% 56.94/9.34 % (32182)Memory used [KB]: 11001
% 56.94/9.34 % (32182)Time elapsed: 0.930 s
% 56.94/9.34 % (32182)Instructions burned: 3049 (million)
% 56.94/9.34 % (32182)------------------------------
% 56.94/9.34 % (32182)------------------------------
% 56.94/9.35 % (32189)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_31617 for (2922ds/430Mi)
% 57.42/9.47 % (32189)Instruction limit reached!
% 57.42/9.47 % (32189)------------------------------
% 57.42/9.47 % (32189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.42/9.47 % (32189)Termination reason: Unknown
% 57.42/9.47 % (32189)Termination phase: Saturation
% 57.42/9.47
% 57.42/9.47 % (32189)Memory used [KB]: 8443
% 57.42/9.47 % (32189)Time elapsed: 0.118 s
% 57.42/9.47 % (32189)Instructions burned: 430 (million)
% 57.42/9.47 % (32189)------------------------------
% 57.42/9.47 % (32189)------------------------------
% 57.42/9.48 % (32190)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_31617 for (2920ds/2012Mi)
% 58.33/9.68 % (32173)Instruction limit reached!
% 58.33/9.68 % (32173)------------------------------
% 58.33/9.68 % (32173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.33/9.68 % (32173)Termination reason: Unknown
% 58.33/9.68 % (32173)Termination phase: Saturation
% 58.33/9.68
% 58.33/9.68 % (32173)Memory used [KB]: 19317
% 58.33/9.68 % (32173)Time elapsed: 1.837 s
% 58.33/9.68 % (32173)Instructions burned: 5446 (million)
% 58.33/9.68 % (32173)------------------------------
% 58.33/9.68 % (32173)------------------------------
% 58.33/9.69 % (32191)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_31617 for (2918ds/631Mi)
% 59.02/9.82 % (32179)Instruction limit reached!
% 59.02/9.82 % (32179)------------------------------
% 59.02/9.82 % (32179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.02/9.82 % (32179)Termination reason: Unknown
% 59.02/9.82 % (32179)Termination phase: Saturation
% 59.02/9.82
% 59.02/9.82 % (32179)Memory used [KB]: 17398
% 59.02/9.82 % (32179)Time elapsed: 1.575 s
% 59.02/9.82 % (32179)Instructions burned: 5214 (million)
% 59.02/9.82 % (32179)------------------------------
% 59.02/9.82 % (32179)------------------------------
% 59.02/9.83 % (32192)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_31617 for (2917ds/8785Mi)
% 59.02/9.88 % (32191)Instruction limit reached!
% 59.02/9.88 % (32191)------------------------------
% 59.02/9.88 % (32191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.02/9.88 % (32191)Termination reason: Unknown
% 59.02/9.88 % (32191)Termination phase: Saturation
% 59.02/9.88
% 59.02/9.88 % (32191)Memory used [KB]: 10106
% 59.02/9.88 % (32191)Time elapsed: 0.196 s
% 59.02/9.88 % (32191)Instructions burned: 633 (million)
% 59.02/9.88 % (32191)------------------------------
% 59.02/9.88 % (32191)------------------------------
% 59.02/9.89 % (32193)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_31617 for (2916ds/739Mi)
% 59.47/9.91 % (32187)Instruction limit reached!
% 59.47/9.91 % (32187)------------------------------
% 59.47/9.91 % (32187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.47/9.91 % (32187)Termination reason: Unknown
% 59.47/9.91 % (32187)Termination phase: Saturation
% 59.47/9.91
% 59.47/9.91 % (32187)Memory used [KB]: 13944
% 59.47/9.91 % (32187)Time elapsed: 0.687 s
% 59.47/9.91 % (32187)Instructions burned: 2210 (million)
% 59.47/9.91 % (32187)------------------------------
% 59.47/9.91 % (32187)------------------------------
% 59.47/9.92 % (32194)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_31617 for (2916ds/5473Mi)
% 62.11/10.09 % (32190)Instruction limit reached!
% 62.11/10.09 % (32190)------------------------------
% 62.11/10.09 % (32190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.11/10.09 % (32190)Termination reason: Unknown
% 62.11/10.09 % (32190)Termination phase: Saturation
% 62.11/10.09
% 62.11/10.09 % (32190)Memory used [KB]: 19189
% 62.11/10.09 % (32190)Time elapsed: 0.612 s
% 62.11/10.09 % (32190)Instructions burned: 2014 (million)
% 62.11/10.09 % (32190)------------------------------
% 62.11/10.09 % (32190)------------------------------
% 62.11/10.10 % (32195)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_31617 for (2914ds/43570Mi)
% 62.11/10.12 % (32195)Refutation not found, incomplete strategy
% 62.11/10.12 % (32195)------------------------------
% 62.11/10.12 % (32195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.11/10.12 % (32195)Termination reason: Refutation not found, incomplete strategy
% 62.11/10.12
% 62.11/10.12
% 62.11/10.12 % (32195)Memory used [KB]: 6396
% 62.11/10.12 % (32195)Time elapsed: 0.014 s
% 62.11/10.12 % (32195)Instructions burned: 42 (million)
% 62.11/10.12 % (32195)------------------------------
% 62.11/10.12 % (32195)------------------------------
% 62.11/10.12 % (32193)Instruction limit reached!
% 62.11/10.12 % (32193)------------------------------
% 62.11/10.12 % (32193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.11/10.12 % (32193)Termination reason: Unknown
% 62.11/10.12 % (32193)Termination phase: Saturation
% 62.11/10.12
% 62.11/10.12 % (32193)Memory used [KB]: 8827
% 62.11/10.12 % (32193)Time elapsed: 0.233 s
% 62.11/10.12 % (32193)Instructions burned: 739 (million)
% 62.11/10.12 % (32193)------------------------------
% 62.11/10.12 % (32193)------------------------------
% 62.60/10.13 % (32196)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_31617 for (2914ds/8382Mi)
% 62.60/10.13 % (32197)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_31617 for (2914ds/407Mi)
% 62.60/10.17 % (32186)Instruction limit reached!
% 62.60/10.17 % (32186)------------------------------
% 62.60/10.17 % (32186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.60/10.17 % (32186)Termination reason: Unknown
% 62.60/10.17 % (32186)Termination phase: Saturation
% 62.60/10.17
% 62.60/10.17 % (32186)Memory used [KB]: 19317
% 62.60/10.17 % (32186)Time elapsed: 1.308 s
% 62.60/10.17 % (32186)Instructions burned: 4688 (million)
% 62.60/10.17 % (32186)------------------------------
% 62.60/10.17 % (32186)------------------------------
% 62.60/10.18 % (32198)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_31617 for (2913ds/2971Mi)
% 63.19/10.25 % (32198)Refutation not found, incomplete strategy
% 63.19/10.25 % (32198)------------------------------
% 63.19/10.25 % (32198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.19/10.25 % (32198)Termination reason: Refutation not found, incomplete strategy
% 63.19/10.25
% 63.19/10.25
% 63.19/10.25 % (32198)Memory used [KB]: 7803
% 63.19/10.25 % (32198)Time elapsed: 0.069 s
% 63.19/10.25 % (32198)Instructions burned: 255 (million)
% 63.19/10.25 % (32198)------------------------------
% 63.19/10.25 % (32198)------------------------------
% 63.19/10.26 % (32197)Instruction limit reached!
% 63.19/10.26 % (32197)------------------------------
% 63.19/10.26 % (32197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.19/10.26 % (32197)Termination reason: Unknown
% 63.19/10.26 % (32197)Termination phase: Saturation
% 63.19/10.26
% 63.19/10.26 % (32197)Memory used [KB]: 9338
% 63.19/10.26 % (32197)Time elapsed: 0.124 s
% 63.19/10.26 % (32197)Instructions burned: 409 (million)
% 63.19/10.26 % (32197)------------------------------
% 63.19/10.26 % (32197)------------------------------
% 63.19/10.26 % (32199)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_31617 for (2913ds/9822Mi)
% 63.19/10.27 % (32200)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_31617 for (2913ds/8425Mi)
% 65.81/10.84 % (32184)Instruction limit reached!
% 65.81/10.84 % (32184)------------------------------
% 65.81/10.84 % (32184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.81/10.84 % (32184)Termination reason: Unknown
% 65.81/10.84 % (32184)Termination phase: Saturation
% 65.81/10.84
% 65.81/10.84 % (32184)Memory used [KB]: 12537
% 65.81/10.84 % (32184)Time elapsed: 2.124 s
% 65.81/10.84 % (32184)Instructions burned: 6804 (million)
% 65.81/10.84 % (32184)------------------------------
% 65.81/10.84 % (32184)------------------------------
% 65.81/10.85 % (32201)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_31617 for (2907ds/3107Mi)
% 71.77/11.46 % (32188)First to succeed.
% 71.77/11.46 % (32188)Refutation found. Thanks to Tanya!
% 71.77/11.46 % SZS status Theorem for DTF2THF_31617
% 71.77/11.46 % SZS output start Proof for DTF2THF_31617
% 71.77/11.46 thf(type_def_5, type, name: $tType).
% 71.77/11.46 thf(type_def_6, type, pi: $tType).
% 71.77/11.46 thf(type_def_8, type, late_freeRes: $tType).
% 71.77/11.46 thf(type_def_9, type, late_subject: $tType).
% 71.77/11.46 thf(type_def_10, type, late_residual: $tType).
% 71.77/11.46 thf(type_def_11, type, noption: ($tType) > $tType).
% 71.77/11.46 thf(type_def_12, type, product_prod: ($tType * $tType) > $tType).
% 71.77/11.46 thf(type_def_13, type, set: ($tType) > $tType).
% 71.77/11.46 thf(func_def_0, type, late_residual: $tType).
% 71.77/11.46 thf(func_def_1, type, late_subject: $tType).
% 71.77/11.46 thf(func_def_2, type, late_freeRes: $tType).
% 71.77/11.46 thf(func_def_3, type, product_prod: ($tType * $tType) > $tType).
% 71.77/11.46 thf(func_def_4, type, noption: ($tType) > $tType).
% 71.77/11.46 thf(func_def_5, type, name: $tType).
% 71.77/11.46 thf(func_def_6, type, pi: $tType).
% 71.77/11.46 thf(func_def_7, type, set: ($tType) > $tType).
% 71.77/11.46 thf(func_def_8, type, type: !>[X0: $tType]:($o)).
% 71.77/11.46 thf(func_def_9, type, fs_name: !>[X0: $tType]:($o)).
% 71.77/11.46 thf(func_def_10, type, ord: !>[X0: $tType]:($o)).
% 71.77/11.46 thf(func_def_11, type, order: !>[X0: $tType]:($o)).
% 71.77/11.46 thf(func_def_12, type, linorder: !>[X0: $tType]:($o)).
% 71.77/11.46 thf(func_def_13, type, preorder: !>[X0: $tType]:($o)).
% 71.77/11.46 thf(func_def_14, type, input: name > name > pi > pi).
% 71.77/11.46 thf(func_def_15, type, mismatch: name > name > pi > pi).
% 71.77/11.46 thf(func_def_16, type, output: name > name > pi > pi).
% 71.77/11.46 thf(func_def_17, type, par: pi > pi > pi).
% 71.77/11.46 thf(func_def_18, type, piNil: pi).
% 71.77/11.46 thf(func_def_19, type, res: name > pi > pi).
% 71.77/11.46 thf(func_def_20, type, sum: pi > pi > pi).
% 71.77/11.46 thf(func_def_21, type, tau: pi > pi).
% 71.77/11.46 thf(func_def_22, type, subs: pi > name > name > pi).
% 71.77/11.46 thf(func_def_23, type, late_OutputR: name > name > late_freeRes).
% 71.77/11.46 thf(func_def_24, type, late_TauR: late_freeRes).
% 71.77/11.46 thf(func_def_25, type, late_freeRes_rec: !>[X0: $tType]:((name > name > X0) > X0 > late_freeRes > X0)).
% 71.77/11.46 thf(func_def_26, type, late_BoundR: late_subject > name > pi > late_residual).
% 71.77/11.46 thf(func_def_27, type, late_FreeR: late_freeRes > pi > late_residual).
% 71.77/11.46 thf(func_def_28, type, late_BoundOutputS: name > late_subject).
% 71.77/11.46 thf(func_def_29, type, late_InputS: name > late_subject).
% 71.77/11.46 thf(func_def_30, type, late_subject_rec: !>[X0: $tType]:((name > X0) > (name > X0) > late_subject > X0)).
% 71.77/11.46 thf(func_def_31, type, late_transitions: pi > late_residual > $o).
% 71.77/11.46 thf(func_def_32, type, abs_fun: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0 > noption @ X1)).
% 71.77/11.46 thf(func_def_33, type, fresh: !>[X0: $tType, X1: $tType]:(X0 > X1 > $o)).
% 71.77/11.46 thf(func_def_34, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 71.77/11.46 thf(func_def_35, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 71.77/11.46 thf(func_def_36, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 71.77/11.46 thf(func_def_37, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 71.77/11.46 thf(func_def_38, type, eqvt: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 71.77/11.46 thf(func_def_39, type, id: !>[X0: $tType]:(set @ product_prod @ X0 @ X0)).
% 71.77/11.46 thf(func_def_40, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 71.77/11.46 thf(func_def_41, type, strong2129052853vative: pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o).
% 71.77/11.46 thf(func_def_42, type, strong743114133lation: pi > set @ product_prod @ pi @ pi > pi > $o).
% 71.77/11.46 thf(func_def_43, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 71.77/11.46 thf(func_def_44, type, p: pi).
% 71.77/11.46 thf(func_def_45, type, pq: pi).
% 71.77/11.46 thf(func_def_46, type, q: pi).
% 71.77/11.46 thf(func_def_47, type, rel: set @ product_prod @ pi @ pi).
% 71.77/11.46 thf(func_def_48, type, a: late_subject).
% 71.77/11.46 thf(func_def_49, type, x: name).
% 71.77/11.46 thf(func_def_50, type, y: name).
% 71.77/11.46 thf(func_def_73, type, sK1: (late_freeRes > $o) > name).
% 71.77/11.46 thf(func_def_74, type, sK2: (late_freeRes > $o) > name).
% 71.77/11.46 thf(func_def_75, type, sK3: (late_subject > $o) > name).
% 71.77/11.46 thf(func_def_76, type, sK4: (late_subject > $o) > name).
% 71.77/11.46 thf(func_def_77, type, sK5: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 71.77/11.46 thf(func_def_78, type, sK6: !>[X0: $tType]:((X0 > late_freeRes > $o) > X0)).
% 71.77/11.46 thf(func_def_79, type, sK7: !>[X0: $tType]:(product_prod @ X0 @ X0 > X0)).
% 71.77/11.46 thf(func_def_80, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X2 @ X1 > X1)).
% 71.77/11.46 thf(func_def_81, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X1 @ product_prod @ X2 @ X0 > X2)).
% 71.77/11.46 thf(func_def_82, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X1 @ product_prod @ X2 @ X0 > X1)).
% 71.77/11.46 thf(func_def_83, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X1)).
% 71.77/11.46 thf(func_def_84, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X3)).
% 71.77/11.46 thf(func_def_85, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > X2)).
% 71.77/11.46 thf(func_def_86, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > X1)).
% 71.77/11.46 thf(func_def_87, type, sK15: (late_residual > $o) > pi).
% 71.77/11.46 thf(func_def_88, type, sK16: (late_residual > $o) > name).
% 71.77/11.46 thf(func_def_89, type, sK17: (late_residual > $o) > pi).
% 71.77/11.46 thf(func_def_90, type, sK18: (late_residual > $o) > late_freeRes).
% 71.77/11.46 thf(func_def_91, type, sK19: (late_residual > $o) > late_subject).
% 71.77/11.46 thf(func_def_92, type, sK20: (pi > $o) > late_freeRes > pi > name > pi).
% 71.77/11.46 thf(func_def_93, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > $o) > X2)).
% 71.77/11.46 thf(func_def_94, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > $o) > X4)).
% 71.77/11.46 thf(func_def_95, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > $o) > X3)).
% 71.77/11.46 thf(func_def_96, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > $o) > X2)).
% 71.77/11.46 thf(func_def_97, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > $o) > X0)).
% 71.77/11.46 thf(func_def_98, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > X2)).
% 71.77/11.46 thf(func_def_99, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > X4)).
% 71.77/11.46 thf(func_def_100, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > X3)).
% 71.77/11.46 thf(func_def_101, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > X2)).
% 71.77/11.46 thf(func_def_102, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X1 > X0)).
% 71.77/11.46 thf(func_def_103, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ X2 > $o) > X2)).
% 71.77/11.46 thf(func_def_104, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ X3 > $o) > X5)).
% 71.77/11.46 thf(func_def_105, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X2 > $o) > X4)).
% 71.77/11.46 thf(func_def_106, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X2 > $o) > X3)).
% 71.77/11.46 thf(func_def_107, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ X2 > $o) > X1)).
% 71.77/11.46 thf(func_def_108, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ X2 > $o) > X3)).
% 71.77/11.46 thf(func_def_109, type, sK37: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 71.77/11.46 thf(func_def_110, type, sK38: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 71.77/11.46 thf(func_def_111, type, sK39: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 71.77/11.46 thf(func_def_112, type, sK40: !>[X0: $tType]:((X0 > late_subject > $o) > X0)).
% 71.77/11.46 thf(func_def_113, type, sK41: !>[X0: $tType]:((X0 > late_subject > $o) > X0)).
% 71.77/11.46 thf(func_def_114, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X1)).
% 71.77/11.46 thf(func_def_115, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X2)).
% 71.77/11.46 thf(func_def_116, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X1)).
% 71.77/11.46 thf(func_def_117, type, sK45: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X0)).
% 71.77/11.46 thf(func_def_118, type, sK46: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X1)).
% 71.77/11.46 thf(func_def_119, type, sK47: (pi > $o) > name > pi > late_subject > pi > pi).
% 71.77/11.46 thf(func_def_120, type, sK48: (pi > $o) > name > pi > late_subject > pi > pi).
% 71.77/11.46 thf(func_def_121, type, sK49: late_residual > pi > pi).
% 71.77/11.46 thf(func_def_122, type, sK50: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0)).
% 71.77/11.46 thf(func_def_123, type, sK51: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1)).
% 71.77/11.46 thf(func_def_124, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > $o) > X1)).
% 71.77/11.46 thf(func_def_125, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > $o) > X3)).
% 71.77/11.46 thf(func_def_126, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X2)).
% 71.77/11.46 thf(func_def_127, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X1)).
% 71.77/11.46 thf(func_def_128, type, sK56: late_residual > pi > name > name > pi).
% 71.77/11.46 thf(func_def_129, type, sK57: late_residual > pi > name > name > name).
% 71.77/11.46 thf(func_def_130, type, sK58: late_residual > pi > name > name > name).
% 71.77/11.46 thf(func_def_131, type, sK59: late_freeRes > name).
% 71.77/11.46 thf(func_def_132, type, sK60: late_freeRes > name).
% 71.77/11.46 thf(func_def_133, type, sK61: late_subject > name).
% 71.77/11.46 thf(func_def_134, type, sK62: late_subject > name).
% 71.77/11.46 thf(func_def_135, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X4 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X5 @ X2 > X2)).
% 71.77/11.46 thf(func_def_136, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ X3 > X5)).
% 71.77/11.46 thf(func_def_137, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X2 > X4)).
% 71.77/11.46 thf(func_def_138, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X2 > X3)).
% 71.77/11.46 thf(func_def_139, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ X2 > X1)).
% 71.77/11.46 thf(func_def_140, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X5 @ X2 > X3)).
% 71.77/11.46 thf(func_def_141, type, ph69: !>[X0: $tType]:(X0)).
% 71.77/11.46 thf(f7277,plain,(
% 71.77/11.46 $false),
% 71.77/11.46 inference(trivial_inequality_removal,[status(thm)],[f7273])).
% 71.77/11.46 thf(f7273,plain,(
% 71.77/11.46 ($false = $true) | (x != x)),
% 71.77/11.46 inference(superposition,[status(thm)],[f5607,f7254])).
% 71.77/11.46 thf(f7254,plain,(
% 71.77/11.46 ((fresh @ name @ name @ x @ x) = $true)),
% 71.77/11.46 inference(trivial_inequality_removal,[status(thm)],[f7252])).
% 71.77/11.46 thf(f7252,plain,(
% 71.77/11.46 ($false = $true) | ((fresh @ name @ name @ x @ x) = $true)),
% 71.77/11.46 inference(superposition,[status(thm)],[f3854,f2735])).
% 71.77/11.46 thf(f2735,plain,(
% 71.77/11.46 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : X1,X5 : X0] : (($false = (fresh @ X0 @ product_prod @ X1 @ X2 @ X5 @ (product_Pair @ X1 @ X2 @ X4 @ X3))) | ((fresh @ X0 @ X1 @ X5 @ X4) = $true)) )),
% 71.77/11.46 inference(binary_proxy_clausification,[status(thm)],[f2734])).
% 71.77/11.46 thf(f2734,plain,(
% 71.77/11.46 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : X1,X5 : X0] : ((((fresh @ X0 @ product_prod @ X1 @ X2 @ X5 @ (product_Pair @ X1 @ X2 @ X4 @ X3)) => (fresh @ X0 @ X1 @ X5 @ X4)) = $true)) )),
% 71.77/11.46 inference(beta_eta_normalization,[status(thm)],[f2733])).
% 71.77/11.46 thf(f2733,plain,(
% 71.77/11.46 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : X1,X5 : X0] : ((((^[Y0 : X0]: ((fresh @ X0 @ product_prod @ X1 @ X2 @ Y0 @ (product_Pair @ X1 @ X2 @ X4 @ X3)) => (fresh @ X0 @ X1 @ Y0 @ X4))) @ X5) = $true)) )),
% 71.77/11.46 inference(pi_clausification,[status(thm)],[f2732])).
% 71.77/11.46 thf(f2732,plain,(
% 71.77/11.46 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : X1] : (((!! @ X0 @ (^[Y0 : X0]: ((fresh @ X0 @ product_prod @ X1 @ X2 @ Y0 @ (product_Pair @ X1 @ X2 @ X4 @ X3)) => (fresh @ X0 @ X1 @ Y0 @ X4)))) = $true)) )),
% 71.77/11.46 inference(beta_eta_normalization,[status(thm)],[f2731])).
% 71.77/11.46 thf(f2731,plain,(
% 71.77/11.46 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2,X4 : X1] : (($true = ((^[Y0 : X1]: (!! @ X0 @ (^[Y1 : X0]: ((fresh @ X0 @ product_prod @ X1 @ X2 @ Y1 @ (product_Pair @ X1 @ X2 @ Y0 @ X3)) => (fresh @ X0 @ X1 @ Y1 @ Y0))))) @ X4))) )),
% 71.77/11.46 inference(pi_clausification,[status(thm)],[f2730])).
% 71.77/11.46 thf(f2730,plain,(
% 71.77/11.46 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2] : (((!! @ X1 @ (^[Y0 : X1]: (!! @ X0 @ (^[Y1 : X0]: ((fresh @ X0 @ product_prod @ X1 @ X2 @ Y1 @ (product_Pair @ X1 @ X2 @ Y0 @ X3)) => (fresh @ X0 @ X1 @ Y1 @ Y0)))))) = $true)) )),
% 71.77/11.46 inference(beta_eta_normalization,[status(thm)],[f2729])).
% 71.77/11.46 thf(f2729,plain,(
% 71.77/11.46 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2] : (($true = ((^[Y0 : X2]: (!! @ X1 @ (^[Y1 : X1]: (!! @ X0 @ (^[Y2 : X0]: ((fresh @ X0 @ product_prod @ X1 @ X2 @ Y2 @ (product_Pair @ X1 @ X2 @ Y1 @ Y0)) => (fresh @ X0 @ X1 @ Y2 @ Y1))))))) @ X3))) )),
% 71.77/11.46 inference(pi_clausification,[status(thm)],[f917])).
% 71.77/11.46 thf(f917,plain,(
% 71.77/11.46 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (((!! @ X2 @ (^[Y0 : X2]: (!! @ X1 @ (^[Y1 : X1]: (!! @ X0 @ (^[Y2 : X0]: ((fresh @ X0 @ product_prod @ X1 @ X2 @ Y2 @ (product_Pair @ X1 @ X2 @ Y1 @ Y0)) => (fresh @ X0 @ X1 @ Y2 @ Y1)))))))) = $true)) )),
% 71.77/11.46 inference(cnf_transformation,[status(thm)],[f879])).
% 71.77/11.46 thf(f879,plain,(
% 71.77/11.46 ! [X0 : $tType,X1 : $tType,X2 : $tType] : ((!! @ X2 @ (^[Y0 : X2]: (!! @ X1 @ (^[Y1 : X1]: (!! @ X0 @ (^[Y2 : X0]: ((fresh @ X0 @ product_prod @ X1 @ X2 @ Y2 @ (product_Pair @ X1 @ X2 @ Y1 @ Y0)) => (fresh @ X0 @ X1 @ Y2 @ Y1)))))))) = $true)),
% 71.77/11.46 inference(rectify,[status(thm)],[f833])).
% 71.77/11.46 thf(f833,plain,(
% 71.77/11.46 ! [X2 : $tType,X1 : $tType,X0 : $tType] : ((!! @ X0 @ (^[Y0 : X0]: (!! @ X1 @ (^[Y1 : X1]: (!! @ X2 @ (^[Y2 : X2]: ((fresh @ X2 @ product_prod @ X1 @ X0 @ Y2 @ (product_Pair @ X1 @ X0 @ Y1 @ Y0)) => (fresh @ X2 @ X1 @ Y2 @ Y1)))))))) = $true)),
% 71.77/11.46 inference(closure,[status(thm)],[f832])).
% 71.77/11.46 thf(f832,plain,(
% 71.77/11.46 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (((!! @ X0 @ (^[Y0 : X0]: (!! @ X1 @ (^[Y1 : X1]: (!! @ X2 @ (^[Y2 : X2]: ((fresh @ X2 @ product_prod @ X1 @ X0 @ Y2 @ (product_Pair @ X1 @ X0 @ Y1 @ Y0)) => (fresh @ X2 @ X1 @ Y2 @ Y1)))))))) = $true)) )),
% 71.77/11.46 inference(rectify,[status(thm)],[f619])).
% 71.77/11.46 thf(f619,plain,(
% 71.77/11.46 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (((!! @ X0 @ (^[Y0 : X0]: (!! @ X2 @ (^[Y1 : X2]: (!! @ X1 @ (^[Y2 : X1]: ((fresh @ X1 @ product_prod @ X2 @ X0 @ Y2 @ (product_Pair @ X2 @ X0 @ Y1 @ Y0)) => (fresh @ X1 @ X2 @ Y2 @ Y1)))))))) = $true)) )),
% 71.77/11.47 inference(fool_elimination,[status(thm)],[f618])).
% 71.77/11.47 thf(f618,plain,(
% 71.77/11.47 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1,X4 : X2,X5 : X0] : ((fresh @ X1 @ product_prod @ X2 @ X0 @ X3 @ (product_Pair @ X2 @ X0 @ X4 @ X5)) => (fresh @ X1 @ X2 @ X3 @ X4))),
% 71.77/11.47 inference(rectify,[status(thm)],[f13])).
% 71.77/11.47 thf(f13,axiom,(
% 71.77/11.47 ! [X4 : $tType,X0 : $tType,X3 : $tType,X5 : X0,X6 : X3,X7 : X4] : ((fresh @ X0 @ product_prod @ X3 @ X4 @ X5 @ (product_Pair @ X3 @ X4 @ X6 @ X7)) => (fresh @ X0 @ X3 @ X5 @ X6))),
% 71.77/11.47 file('/export/starexec/sandbox/tmp/tmp.xvru83IF3W/DTF2THF_31617.p',fact_12_fresh__prodD_I1_J)).
% 71.77/11.47 thf(f3854,plain,(
% 71.77/11.47 ((fresh @ name @ product_prod @ name @ product_prod @ pi @ pi @ x @ (product_Pair @ name @ product_prod @ pi @ pi @ x @ (product_Pair @ pi @ pi @ p @ q))) = $true)),
% 71.77/11.47 inference(forward_demodulation,[status(thm)],[f1027,f2655])).
% 71.77/11.47 thf(f2655,plain,(
% 71.77/11.47 (y = x)),
% 71.77/11.47 inference(equality_proxy_clausification,[status(thm)],[f1070])).
% 71.77/11.47 thf(f1070,plain,(
% 71.77/11.47 ((y = x) = $true)),
% 71.77/11.47 inference(boolean_simplification,[status(thm)],[f962])).
% 71.77/11.47 thf(f962,plain,(
% 71.77/11.47 ((~ (~ (y = x))) = $true)),
% 71.77/11.47 inference(cnf_transformation,[status(thm)],[f307])).
% 71.77/11.47 thf(f307,plain,(
% 71.77/11.47 ((~ (~ (y = x))) = $true)),
% 71.77/11.47 inference(fool_elimination,[status(thm)],[f275])).
% 71.77/11.47 thf(f275,negated_conjecture,(
% 71.77/11.47 ~(y != x)),
% 71.77/11.47 inference(negated_conjecture,[status(cth)],[f274])).
% 71.77/11.47 thf(f274,conjecture,(
% 71.77/11.47 (y != x)),
% 71.77/11.47 file('/export/starexec/sandbox/tmp/tmp.xvru83IF3W/DTF2THF_31617.p',conj_0)).
% 71.77/11.47 thf(f1027,plain,(
% 71.77/11.47 ((fresh @ name @ product_prod @ name @ product_prod @ pi @ pi @ y @ (product_Pair @ name @ product_prod @ pi @ pi @ x @ (product_Pair @ pi @ pi @ p @ q))) = $true)),
% 71.77/11.47 inference(cnf_transformation,[status(thm)],[f481])).
% 71.77/11.47 thf(f481,plain,(
% 71.77/11.47 ((fresh @ name @ product_prod @ name @ product_prod @ pi @ pi @ y @ (product_Pair @ name @ product_prod @ pi @ pi @ x @ (product_Pair @ pi @ pi @ p @ q))) = $true)),
% 71.77/11.47 inference(fool_elimination,[status(thm)],[f480])).
% 71.77/11.47 thf(f480,plain,(
% 71.77/11.47 (fresh @ name @ product_prod @ name @ product_prod @ pi @ pi @ y @ (product_Pair @ name @ product_prod @ pi @ pi @ x @ (product_Pair @ pi @ pi @ p @ q)))),
% 71.77/11.47 inference(rectify,[status(thm)],[f2])).
% 71.77/11.47 thf(f2,axiom,(
% 71.77/11.47 (fresh @ name @ product_prod @ name @ product_prod @ pi @ pi @ y @ (product_Pair @ name @ product_prod @ pi @ pi @ x @ (product_Pair @ pi @ pi @ p @ q)))),
% 71.77/11.47 file('/export/starexec/sandbox/tmp/tmp.xvru83IF3W/DTF2THF_31617.p',fact_1_Bound_Ohyps_I5_J)).
% 71.77/11.47 thf(f5607,plain,(
% 71.77/11.47 ( ! [X2 : name,X1 : name] : (((fresh @ name @ name @ X1 @ X2) = $false) | (X1 != X2)) )),
% 71.77/11.47 inference(equality_proxy_clausification,[status(thm)],[f5606])).
% 71.77/11.47 thf(f5606,plain,(
% 71.77/11.47 ( ! [X2 : name,X1 : name] : (((fresh @ name @ name @ X1 @ X2) = $false) | ((X1 = X2) = $false)) )),
% 71.77/11.47 inference(not_proxy_clausification,[status(thm)],[f5603])).
% 71.77/11.47 thf(f5603,plain,(
% 71.77/11.47 ( ! [X2 : name,X1 : name] : (((~ (X1 = X2)) = $true) | ((fresh @ name @ name @ X1 @ X2) = $false)) )),
% 71.77/11.47 inference(binary_proxy_clausification,[status(thm)],[f5601])).
% 71.77/11.47 thf(f5601,plain,(
% 71.77/11.47 ( ! [X2 : name,X1 : name] : (((fresh @ name @ name @ X1 @ X2) = (~ (X1 = X2)))) )),
% 71.77/11.47 inference(beta_eta_normalization,[status(thm)],[f5599])).
% 71.77/11.47 thf(f5599,plain,(
% 71.77/11.47 ( ! [X2 : name,X1 : name] : (((fresh @ name @ name @ X1 @ X2) = ((^[Y0 : name]: (~ (X1 = Y0))) @ X2))) )),
% 71.77/11.47 inference(argument_congruence,[status(thm)],[f3214])).
% 71.77/11.47 thf(f3214,plain,(
% 71.77/11.47 ( ! [X1 : name] : (((fresh @ name @ name @ X1) = (^[Y0 : name]: (~ (X1 = Y0))))) )),
% 71.77/11.47 inference(beta_eta_normalization,[status(thm)],[f3213])).
% 71.77/11.47 thf(f3213,plain,(
% 71.77/11.47 ( ! [X1 : name] : (((fresh @ name @ name @ X1) = ((^[Y0 : name]: ((^[Y1 : name]: (~ (Y0 = Y1))))) @ X1))) )),
% 71.77/11.47 inference(argument_congruence,[status(thm)],[f980])).
% 71.77/11.47 thf(f980,plain,(
% 71.77/11.47 (fresh @ name @ name = (^[Y0 : name]: ((^[Y1 : name]: (~ (Y0 = Y1))))))),
% 71.77/11.47 inference(cnf_transformation,[status(thm)],[f787])).
% 71.77/11.47 thf(f787,plain,(
% 71.77/11.47 (fresh @ name @ name = (^[Y0 : name]: ((^[Y1 : name]: (~ (Y0 = Y1))))))),
% 71.77/11.47 inference(fool_elimination,[status(thm)],[f786])).
% 71.77/11.47 thf(f786,plain,(
% 71.77/11.47 ((^[X0 : name, X1 : name] : ((X0 != X1))) = fresh @ name @ name)),
% 71.77/11.47 inference(rectify,[status(thm)],[f170])).
% 71.77/11.47 thf(f170,axiom,(
% 71.77/11.47 ((^[X76 : name, X77 : name] : ((X76 != X77))) = fresh @ name @ name)),
% 71.77/11.47 file('/export/starexec/sandbox/tmp/tmp.xvru83IF3W/DTF2THF_31617.p',fact_169_name__fresh)).
% 71.77/11.47 % SZS output end Proof for DTF2THF_31617
% 71.77/11.47 % (32188)------------------------------
% 71.77/11.47 % (32188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.77/11.47 % (32188)Termination reason: Refutation
% 71.77/11.47
% 71.77/11.47 % (32188)Memory used [KB]: 13176
% 71.77/11.47 % (32188)Time elapsed: 2.165 s
% 71.77/11.47 % (32188)Instructions burned: 7261 (million)
% 71.77/11.47 % (32188)------------------------------
% 71.77/11.47 % (32188)------------------------------
% 71.77/11.47 % (31945)Success in time 9.888 s
%------------------------------------------------------------------------------