%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP184^1 : 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:14 AM UTC 2026
% Result : Theorem 2.92s 1.63s
% Output : Refutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 255 ( 10 ~; 3 |; 4 &; 238 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 27 ( 26 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 113 ( 110 usr; 13 con; 0-5 aty)
% Number of variables : 6 ( 0 ^; 2 !; 4 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
pi: $tType ).
thf(type_def_7,type,
name: $tType ).
thf(type_def_8,type,
late_freeRes: $tType ).
thf(type_def_9,type,
late_subject: $tType ).
thf(type_def_10,type,
late_residual: $tType ).
thf(type_def_11,type,
noption_name: $tType ).
thf(type_def_12,type,
noption_pi: $tType ).
thf(type_def_13,type,
noption_Late_freeRes: $tType ).
thf(type_def_14,type,
noption_Late_subject: $tType ).
thf(type_def_15,type,
produc1462499409ion_pi: $tType ).
thf(type_def_16,type,
produc405342261i_name: $tType ).
thf(type_def_17,type,
produc629157763_pi_pi: $tType ).
thf(type_def_18,type,
produc1834551554reeRes: $tType ).
thf(type_def_19,type,
produc691362330ubject: $tType ).
thf(type_def_20,type,
produc2008547984reeRes: $tType ).
thf(type_def_21,type,
produc865358760ubject: $tType ).
thf(type_def_22,type,
product_prod_pi_pi: $tType ).
thf(type_def_23,type,
produc2052722628s_name: $tType ).
thf(type_def_24,type,
produc992857746Res_pi: $tType ).
thf(type_def_25,type,
produc1357834675reeRes: $tType ).
thf(type_def_26,type,
produc214645451ubject: $tType ).
thf(type_def_27,type,
produc1998742700t_name: $tType ).
thf(type_def_28,type,
produc140253050ect_pi: $tType ).
thf(type_def_29,type,
produc355105483reeRes: $tType ).
thf(type_def_30,type,
produc1359399907ubject: $tType ).
thf(type_def_31,type,
set_Pr1834926343_pi_pi: $tType ).
thf(func_def_0,type,
produc1462499409ion_pi: $tType ).
thf(func_def_1,type,
produc691362330ubject: $tType ).
thf(func_def_2,type,
produc1834551554reeRes: $tType ).
thf(func_def_3,type,
produc405342261i_name: $tType ).
thf(func_def_4,type,
produc629157763_pi_pi: $tType ).
thf(func_def_5,type,
produc1359399907ubject: $tType ).
thf(func_def_6,type,
produc355105483reeRes: $tType ).
thf(func_def_7,type,
produc214645451ubject: $tType ).
thf(func_def_8,type,
produc1357834675reeRes: $tType ).
thf(func_def_9,type,
produc1998742700t_name: $tType ).
thf(func_def_10,type,
produc2052722628s_name: $tType ).
thf(func_def_11,type,
produc865358760ubject: $tType ).
thf(func_def_12,type,
produc2008547984reeRes: $tType ).
thf(func_def_13,type,
produc140253050ect_pi: $tType ).
thf(func_def_14,type,
produc992857746Res_pi: $tType ).
thf(func_def_15,type,
set_Pr1834926343_pi_pi: $tType ).
thf(func_def_16,type,
product_prod_pi_pi: $tType ).
thf(func_def_17,type,
noption_Late_subject: $tType ).
thf(func_def_18,type,
noption_Late_freeRes: $tType ).
thf(func_def_19,type,
noption_name: $tType ).
thf(func_def_20,type,
noption_pi: $tType ).
thf(func_def_21,type,
late_residual: $tType ).
thf(func_def_22,type,
late_subject: $tType ).
thf(func_def_23,type,
late_freeRes: $tType ).
thf(func_def_24,type,
name: $tType ).
thf(func_def_25,type,
pi: $tType ).
thf(func_def_26,type,
bang: pi > pi ).
thf(func_def_27,type,
input: name > name > pi > pi ).
thf(func_def_28,type,
match: name > name > pi > pi ).
thf(func_def_29,type,
mismatch: name > name > pi > pi ).
thf(func_def_30,type,
output: name > name > pi > pi ).
thf(func_def_31,type,
par: pi > pi > pi ).
thf(func_def_32,type,
piNil: pi ).
thf(func_def_33,type,
res: name > pi > pi ).
thf(func_def_34,type,
sum: pi > pi > pi ).
thf(func_def_35,type,
tau: pi > pi ).
thf(func_def_36,type,
subs: pi > name > name > pi ).
thf(func_def_37,type,
subst_name: name > name > name > name ).
thf(func_def_38,type,
if_name: $o > name > name > name ).
thf(func_def_39,type,
late_OutputR: name > name > late_freeRes ).
thf(func_def_40,type,
late_TauR: late_freeRes ).
thf(func_def_41,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(func_def_42,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(func_def_43,type,
late_BoundOutputS: name > late_subject ).
thf(func_def_44,type,
late_InputS: name > late_subject ).
thf(func_def_45,type,
late_transitions: pi > late_residual > $o ).
thf(func_def_46,type,
abs_fun_name_name: name > name > name > noption_name ).
thf(func_def_47,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(func_def_48,type,
abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
thf(func_def_49,type,
abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject ).
thf(func_def_50,type,
fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
thf(func_def_51,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
thf(func_def_52,type,
fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
thf(func_def_53,type,
fresh_728038529ubject: name > ( name > noption_Late_subject ) > $o ).
thf(func_def_54,type,
fresh_name_name: name > name > $o ).
thf(func_def_55,type,
fresh_name_pi: name > pi > $o ).
thf(func_def_56,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(func_def_57,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(func_def_58,type,
fresh_717452603ubject: name > late_subject > $o ).
thf(func_def_59,type,
fresh_225680151ion_pi: name > produc1462499409ion_pi > $o ).
thf(func_def_60,type,
fresh_453496559i_name: name > produc405342261i_name > $o ).
thf(func_def_61,type,
fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o ).
thf(func_def_62,type,
fresh_1711070152reeRes: name > produc1834551554reeRes > $o ).
thf(func_def_63,type,
fresh_567880928ubject: name > produc691362330ubject > $o ).
thf(func_def_64,type,
fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
thf(func_def_65,type,
fresh_820177506ubject: name > produc865358760ubject > $o ).
thf(func_def_66,type,
fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
thf(func_def_67,type,
fresh_2007541374s_name: name > produc2052722628s_name > $o ).
thf(func_def_68,type,
fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
thf(func_def_69,type,
fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
thf(func_def_70,type,
fresh_1498103185ubject: name > produc214645451ubject > $o ).
thf(func_def_71,type,
fresh_1953561446t_name: name > produc1998742700t_name > $o ).
thf(func_def_72,type,
fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).
thf(func_def_73,type,
fresh_1638563217reeRes: name > produc355105483reeRes > $o ).
thf(func_def_74,type,
fresh_495373993ubject: name > produc1359399907ubject > $o ).
thf(func_def_75,type,
produc1342893193ion_pi: ( name > noption_pi ) > ( name > noption_pi ) > produc1462499409ion_pi ).
thf(func_def_76,type,
produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).
thf(func_def_77,type,
produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).
thf(func_def_78,type,
produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
thf(func_def_79,type,
produc581368530ubject: ( name > noption_pi ) > late_subject > produc691362330ubject ).
thf(func_def_80,type,
produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
thf(func_def_81,type,
produc607574050ubject: name > late_subject > produc865358760ubject ).
thf(func_def_82,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(func_def_83,type,
produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
thf(func_def_84,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(func_def_85,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(func_def_86,type,
produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
thf(func_def_87,type,
produc1647375838t_name: late_subject > name > produc1998742700t_name ).
thf(func_def_88,type,
produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
thf(func_def_89,type,
produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
thf(func_def_90,type,
produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
thf(func_def_91,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(func_def_92,type,
collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
thf(func_def_93,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(func_def_94,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(func_def_95,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(func_def_96,type,
p: pi ).
thf(func_def_97,type,
pqr: pi ).
thf(func_def_98,type,
q: pi ).
thf(func_def_99,type,
qr: pi ).
thf(func_def_100,type,
q2: pi ).
thf(func_def_101,type,
r: pi ).
thf(func_def_102,type,
rel: set_Pr1834926343_pi_pi ).
thf(func_def_103,type,
a: late_subject ).
thf(func_def_104,type,
x: name ).
thf(func_def_122,type,
sK0: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_123,type,
sK1: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_124,type,
sK2: product_prod_pi_pi > pi ).
thf(func_def_125,type,
sK3: product_prod_pi_pi > pi ).
thf(func_def_126,type,
sK4: ( late_residual > $o ) > late_freeRes ).
thf(func_def_127,type,
sK5: ( late_residual > $o ) > pi ).
thf(func_def_128,type,
sK6: ( late_residual > $o ) > name ).
thf(func_def_129,type,
sK7: ( late_residual > $o ) > late_subject ).
thf(func_def_130,type,
sK8: ( late_residual > $o ) > pi ).
thf(func_def_131,type,
sK9: set_Pr1834926343_pi_pi > pi ).
thf(func_def_132,type,
sK10: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_133,type,
sK11: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_134,type,
sK12: set_Pr1834926343_pi_pi > pi ).
thf(func_def_135,type,
sK13: set_Pr1834926343_pi_pi > name ).
thf(func_def_136,type,
sK14: set_Pr1834926343_pi_pi > pi ).
thf(func_def_137,type,
sK15: set_Pr1834926343_pi_pi > pi ).
thf(func_def_138,type,
sK16: set_Pr1834926343_pi_pi > pi ).
thf(func_def_139,type,
sK17: product_prod_pi_pi > pi ).
thf(func_def_140,type,
sK18: product_prod_pi_pi > pi ).
thf(func_def_141,type,
sK19: set_Pr1834926343_pi_pi > late_freeRes > pi > pi > pi ).
thf(func_def_142,type,
sK20: set_Pr1834926343_pi_pi > pi ).
thf(func_def_143,type,
sK21: name > late_subject > ( pi > $o ) > pi > pi > pi ).
thf(func_def_144,type,
sK22: name > late_subject > ( pi > $o ) > pi > pi > pi ).
thf(func_def_145,type,
sK23: pi > name ).
thf(func_def_146,type,
sK24: pi > pi > set_Pr1834926343_pi_pi > pi ).
thf(func_def_147,type,
sK25: pi > pi > set_Pr1834926343_pi_pi > name ).
thf(func_def_148,type,
sK26: pi > pi > set_Pr1834926343_pi_pi > late_subject ).
thf(func_def_149,type,
sK27: pi > pi > set_Pr1834926343_pi_pi > pi ).
thf(func_def_150,type,
sK28: pi > pi > set_Pr1834926343_pi_pi > late_freeRes ).
thf(func_def_151,type,
sK29: set_Pr1834926343_pi_pi > late_subject > pi > name > pi > pi ).
thf(func_def_153,type,
ph31:
!>[X0: $tType] : X0 ).
thf(f959,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f958,f916]) ).
thf(f916,plain,
( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f769]) ).
thf(f769,plain,
( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f768]) ).
thf(f768,plain,
late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ),
file('/export/starexec/sandbox/tmp/tmp.oMnfvnLLzL/DTF2THF_17066.p',fact_2__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_A_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_092_060close_062) ).
thf(f958,plain,
( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f955]) ).
thf(f955,plain,
( ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f875,f945]) ).
thf(f945,plain,
( ( strong2129052853vative @ ( par @ ( par @ p @ q2 ) @ r ) @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel )
= $true ),
inference(cnf_transformation,[status(thm)],[f387]) ).
thf(f387,plain,
( ( strong2129052853vative @ ( par @ ( par @ p @ q2 ) @ r ) @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel )
= $true ),
inference(fool_elimination,[status(thm)],[f386]) ).
thf(f386,plain,
strong2129052853vative @ ( par @ ( par @ p @ q2 ) @ r ) @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
strong2129052853vative @ ( par @ ( par @ p @ q2 ) @ r ) @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel,
file('/export/starexec/sandbox/tmp/tmp.oMnfvnLLzL/DTF2THF_17066.p',fact_0__092_060open_062derivative_A_I_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_J_A_IP_A_092_060parallel_062_AQ_H_A_092_060parallel_062_AR_J_Aa_Ax_ARel_092_060close_062) ).
thf(f875,plain,
! [X0: pi] :
( ( ( strong2129052853vative @ X0 @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel )
!= $true )
| ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f832]) ).
thf(f832,plain,
! [X0: pi] :
( ( ( strong2129052853vative @ X0 @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel )
!= $true )
| ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ X0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f757]) ).
thf(f757,plain,
~ ? [X0: pi] :
( ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ X0 ) )
= $true )
& ( ( strong2129052853vative @ X0 @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel )
= $true ) ),
inference(fool_elimination,[status(thm)],[f756]) ).
thf(f756,plain,
~ ? [X0: pi] :
( ( strong2129052853vative @ X0 @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel )
& ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ X0 ) ) ),
inference(rectify,[status(thm)],[f322]) ).
thf(f322,negated_conjecture,
~ ? [X59: pi] :
( ( strong2129052853vative @ X59 @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel )
& ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ X59 ) ) ),
inference(negated_conjecture,[status(cth)],[f321]) ).
thf(f321,conjecture,
? [X59: pi] :
( ( strong2129052853vative @ X59 @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel )
& ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ X59 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oMnfvnLLzL/DTF2THF_17066.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP184^1 : 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 : n006.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 08:29:00 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
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : ITP184^1 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.47 % Domain : Interactive Theorem Proving
% 0.19/0.47 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_470__3413054_1
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Des21]
% 0.19/0.47 % Names : Strong_Late_Sim_SC/prob_470__3413054_1 [Des21]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
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% 0.19/0.47
% 0.19/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 0.19/0.47 produc1647375838t_name: late_subject > name > produc1998742700t_name ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
% 0.19/0.47 produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 0.19/0.47 produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 0.19/0.47 produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 0.19/0.47 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.19/0.47 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.19/0.47 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.19/0.47 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.19/0.47 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_P,type,
% 0.19/0.47 p: pi ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_PQR____,type,
% 0.19/0.47 pqr: pi ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_Q,type,
% 0.19/0.47 q: pi ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_QR____,type,
% 0.19/0.47 qr: pi ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_Q_H____,type,
% 0.19/0.47 q2: pi ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_R,type,
% 0.19/0.47 r: pi ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_Rel,type,
% 0.19/0.47 rel: set_Pr1834926343_pi_pi ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_a____,type,
% 0.19/0.47 a: late_subject ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_x____,type,
% 0.19/0.47 x: name ).
% 0.19/0.47
% 0.19/0.47 % Relevant facts (317)
% 0.19/0.47 thf(fact_0__092_060open_062derivative_A_I_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_J_A_IP_A_092_060parallel_062_AQ_H_A_092_060parallel_062_AR_J_Aa_Ax_ARel_092_060close_062,axiom,
% 0.19/0.47 strong2129052853vative @ ( par @ ( par @ p @ q2 ) @ r ) @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel ).
% 0.19/0.47
% 0.19/0.47 % \<open>derivative ((P \<parallel> Q') \<parallel> R) (P \<parallel> Q' \<parallel> R) a x Rel\<close>
% 0.19/0.47 thf(fact_1_cPar1_Ohyps,axiom,
% 0.19/0.47 late_transitions @ q @ ( late_BoundR @ a @ x @ q2 ) ).
% 0.19/0.47
% 0.19/0.47 % cPar1.hyps
% 0.19/0.47 thf(fact_2__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_A_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_092_060close_062,axiom,
% 0.19/0.47 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ) ).
% 0.19/0.47
% 0.19/0.47 % \<open>(P \<parallel> Q) \<parallel> R \<longmapsto> a\<guillemotleft>x\<guillemotright> \<prec> (P \<parallel> Q') \<parallel> R\<close>
% 0.19/0.47 thf(fact_3_cPar2_Ohyps,axiom,
% 0.19/0.47 late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ a @ x @ qr ) ).
% 0.19/0.47
% 0.19/0.47 % cPar2.hyps
% 0.19/0.47 thf(fact_4_Bound_Ohyps_I1_J,axiom,
% 0.19/0.47 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_BoundR @ a @ x @ pqr ) ).
% 0.19/0.47
% 0.19/0.47 % Bound.hyps(1)
% 0.19/0.47 thf(fact_5__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062,axiom,
% 0.19/0.47 late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ a @ x @ ( par @ p @ q2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % \<open>P \<parallel> Q \<longmapsto> a\<guillemotleft>x\<guillemotright> \<prec> P \<parallel> Q'\<close>
% 0.19/0.47 thf(fact_6_Bound_Ohyps_I2_J,axiom,
% 0.19/0.47 fresh_name_pi @ x @ ( par @ ( par @ p @ q ) @ r ) ).
% 0.19/0.47
% 0.19/0.47 % Bound.hyps(2)
% 0.19/0.47 thf(fact_7__092_060open_062x_A_092_060sharp_062_AQ_A_092_060parallel_062_AR_092_060close_062,axiom,
% 0.19/0.47 fresh_name_pi @ x @ ( par @ q @ r ) ).
% 0.19/0.47
% 0.19/0.47 % \<open>x \<sharp> Q \<parallel> R\<close>
% 0.19/0.47 thf(fact_8__092_060open_062x_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.19/0.47 fresh_name_pi @ x @ q ).
% 0.19/0.47
% 0.19/0.47 % \<open>x \<sharp> Q\<close>
% 0.19/0.47 thf(fact_9__092_060open_062x_A_092_060sharp_062_AP_092_060close_062,axiom,
% 0.19/0.47 fresh_name_pi @ x @ p ).
% 0.19/0.47
% 0.19/0.47 % \<open>x \<sharp> P\<close>
% 0.19/0.47 thf(fact_10__092_060open_062x_A_092_060sharp_062_AR_092_060close_062,axiom,
% 0.19/0.47 fresh_name_pi @ x @ r ).
% 0.19/0.47
% 0.19/0.47 % \<open>x \<sharp> R\<close>
% 0.19/0.47 thf(fact_11_Ass,axiom,
% 0.19/0.47 ! [S: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S @ T ) @ U ) @ ( par @ S @ ( par @ T @ U ) ) ) @ rel ) ).
% 0.19/0.47
% 0.19/0.47 % Ass
% 0.19/0.47 thf(fact_12_pi_Oinject_I7_J,axiom,
% 0.19/0.47 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.19/0.47 ( ( ( par @ X2 @ X1 )
% 0.19/0.47 = ( par @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(7)
% 0.19/0.47 thf(fact_13_Late__Semantics_OPar1B,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Par1B
% 0.19/0.47 thf(fact_14_Late__Semantics_OPar2B,axiom,
% 0.19/0.47 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Par2B
% 0.19/0.47 thf(fact_15_parCasesB,axiom,
% 0.19/0.47 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 0.19/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ! [P3: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.19/0.47 => ( Prop @ ( par @ P3 @ Q ) ) )
% 0.19/0.47 => ( ! [Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 0.19/0.47 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.19/0.47 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % parCasesB
% 0.19/0.47 thf(fact_16_tauBoundTrans,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % tauBoundTrans
% 0.19/0.47 thf(fact_17_outputBoundTrans,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,C: late_subject,X: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C @ X @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputBoundTrans
% 0.19/0.47 thf(fact_18_Res,axiom,
% 0.19/0.47 ! [S: pi,T: pi,X: name] :
% 0.19/0.47 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S @ T ) @ rel )
% 0.19/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X @ S ) @ ( res @ X @ T ) ) @ rel ) ) ).
% 0.19/0.47
% 0.19/0.47 % Res
% 0.19/0.47 thf(fact_19_FreshExt_H,axiom,
% 0.19/0.47 ! [X: name,U: pi,S: pi,T: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ X @ U )
% 0.19/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X @ ( par @ S @ T ) ) @ U ) @ ( res @ X @ ( par @ S @ ( par @ T @ U ) ) ) ) @ rel ) ) ).
% 0.19/0.47
% 0.19/0.47 % FreshExt'
% 0.19/0.47 thf(fact_20_FreshExt,axiom,
% 0.19/0.47 ! [X: name,S: pi,T: pi,U: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ X @ S )
% 0.19/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X @ ( par @ ( par @ S @ T ) @ U ) ) @ ( par @ S @ ( res @ X @ ( par @ T @ U ) ) ) ) @ rel ) ) ).
% 0.19/0.47
% 0.19/0.47 % FreshExt
% 0.19/0.47 thf(fact_21_pi_Ofresh_I8_J,axiom,
% 0.19/0.47 ! [A: name,X2: pi,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_name_pi @ A @ X2 )
% 0.19/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(8)
% 0.19/0.47 thf(fact_22_pi_Ofresh_I3_J,axiom,
% 0.19/0.47 ! [A: name,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 0.19/0.47 = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(3)
% 0.19/0.47 thf(fact_23_pi_Oinject_I2_J,axiom,
% 0.19/0.47 ! [X1: pi,Y1: pi] :
% 0.19/0.47 ( ( ( tau @ X1 )
% 0.19/0.47 = ( tau @ Y1 ) )
% 0.19/0.47 = ( X1 = Y1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(2)
% 0.19/0.47 thf(fact_24_pi_Oinject_I1_J,axiom,
% 0.19/0.47 ! [X3: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 0.19/0.47 ( ( ( output @ X3 @ X2 @ X1 )
% 0.19/0.47 = ( output @ Y3 @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X3 = Y3 )
% 0.19/0.47 & ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(1)
% 0.19/0.47 thf(fact_25_pi_Odistinct_I45_J,axiom,
% 0.19/0.47 ! [Pi: pi,Name: name,Pi2: pi] :
% 0.19/0.47 ( ( tau @ Pi )
% 0.19/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(45)
% 0.19/0.47 thf(fact_26_pi_Odistinct_I31_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(31)
% 0.19/0.47 thf(fact_27_pi_Odistinct_I19_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( tau @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(19)
% 0.19/0.47 thf(fact_28_resTrans_I1_J,axiom,
% 0.19/0.47 ! [X: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % resTrans(1)
% 0.19/0.47 thf(fact_29_freshRes,axiom,
% 0.19/0.47 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshRes
% 0.19/0.47 thf(fact_30_name__exists__fresh,axiom,
% 0.19/0.47 ! [X: late_subject] :
% 0.19/0.47 ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_717452603ubject @ C2 @ X ) ).
% 0.19/0.47
% 0.19/0.47 % name_exists_fresh
% 0.19/0.47 thf(fact_31_name__exists__fresh,axiom,
% 0.19/0.47 ! [X: late_freeRes] :
% 0.19/0.47 ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_1641682979reeRes @ C2 @ X ) ).
% 0.19/0.47
% 0.19/0.47 % name_exists_fresh
% 0.19/0.47 thf(fact_32_name__exists__fresh,axiom,
% 0.19/0.47 ! [X: name] :
% 0.19/0.47 ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_name_name @ C2 @ X ) ).
% 0.19/0.47
% 0.19/0.47 % name_exists_fresh
% 0.19/0.47 thf(fact_33_name__exists__fresh,axiom,
% 0.19/0.47 ! [X: pi] :
% 0.19/0.47 ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_name_pi @ C2 @ X ) ).
% 0.19/0.47
% 0.19/0.47 % name_exists_fresh
% 0.19/0.47 thf(fact_34_pi_Odistinct_I85_J,axiom,
% 0.19/0.47 ! [Pi1: pi,Pi22: pi,Name: name,Pi2: pi] :
% 0.19/0.47 ( ( par @ Pi1 @ Pi22 )
% 0.19/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(85)
% 0.19/0.47 thf(fact_35_pi_Odistinct_I29_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(29)
% 0.19/0.47 thf(fact_36_pi_Odistinct_I43_J,axiom,
% 0.19/0.47 ! [Pi: pi,Pi12: pi,Pi23: pi] :
% 0.19/0.47 ( ( tau @ Pi )
% 0.19/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(43)
% 0.19/0.47 thf(fact_37_resTauBoundTrans,axiom,
% 0.19/0.47 ! [X: name,P: pi,A: late_subject,Y: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resTauBoundTrans
% 0.19/0.47 thf(fact_38_freshBoundDerivative_I2_J,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( ( Y != X )
% 0.19/0.47 => ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshBoundDerivative(2)
% 0.19/0.47 thf(fact_39_fresh__prod,axiom,
% 0.19/0.47 ! [A: name,X: late_subject,Y: late_subject] :
% 0.19/0.47 ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y ) )
% 0.19/0.47 = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prod
% 0.19/0.47 thf(fact_40_fresh__prod,axiom,
% 0.19/0.47 ! [A: name,X: late_subject,Y: late_freeRes] :
% 0.19/0.47 ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y ) )
% 0.19/0.47 = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prod
% 0.19/0.47 thf(fact_41_fresh__prod,axiom,
% 0.19/0.47 ! [A: name,X: late_subject,Y: name] :
% 0.19/0.47 ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y ) )
% 0.19/0.47 = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prod
% 0.19/0.47 thf(fact_42_fresh__prod,axiom,
% 0.19/0.47 ! [A: name,X: late_subject,Y: pi] :
% 0.19/0.47 ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y ) )
% 0.19/0.47 = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.47 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prod
% 0.19/0.47 thf(fact_43_fresh__prod,axiom,
% 0.19/0.47 ! [A: name,X: late_freeRes,Y: late_subject] :
% 0.19/0.47 ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y ) )
% 0.19/0.47 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prod
% 0.19/0.47 thf(fact_44_fresh__prod,axiom,
% 0.19/0.47 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 0.19/0.47 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
% 0.19/0.47 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prod
% 0.19/0.47 thf(fact_45_fresh__prod,axiom,
% 0.19/0.47 ! [A: name,X: late_freeRes,Y: name] :
% 0.19/0.47 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
% 0.19/0.47 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prod
% 0.19/0.47 thf(fact_46_fresh__prod,axiom,
% 0.19/0.47 ! [A: name,X: late_freeRes,Y: pi] :
% 0.19/0.47 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
% 0.19/0.47 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.47 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prod
% 0.19/0.47 thf(fact_47_fresh__prod,axiom,
% 0.19/0.47 ! [A: name,X: name,Y: late_subject] :
% 0.19/0.47 ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X )
% 0.19/0.47 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prod
% 0.19/0.47 thf(fact_48_fresh__prod,axiom,
% 0.19/0.47 ! [A: name,X: name,Y: late_freeRes] :
% 0.19/0.47 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X )
% 0.19/0.47 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prod
% 0.19/0.47 thf(fact_49_prod_Oinject,axiom,
% 0.19/0.47 ! [X1: name > noption_pi,X2: late_subject,Y1: name > noption_pi,Y2: late_subject] :
% 0.19/0.47 ( ( ( produc581368530ubject @ X1 @ X2 )
% 0.19/0.47 = ( produc581368530ubject @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( X1 = Y1 )
% 0.19/0.47 & ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod.inject
% 0.19/0.47 thf(fact_50_prod_Oinject,axiom,
% 0.19/0.47 ! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y2: late_freeRes] :
% 0.19/0.47 ( ( ( produc1505598906reeRes @ X1 @ X2 )
% 0.19/0.47 = ( produc1505598906reeRes @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( X1 = Y1 )
% 0.19/0.47 & ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod.inject
% 0.19/0.47 thf(fact_51_prod_Oinject,axiom,
% 0.19/0.47 ! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y2: name] :
% 0.19/0.47 ( ( ( produc540578151i_name @ X1 @ X2 )
% 0.19/0.47 = ( produc540578151i_name @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( X1 = Y1 )
% 0.19/0.47 & ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod.inject
% 0.19/0.47 thf(fact_52_prod_Oinject,axiom,
% 0.19/0.47 ! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y2: pi] :
% 0.19/0.47 ( ( ( produc1820286517_pi_pi @ X1 @ X2 )
% 0.19/0.47 = ( produc1820286517_pi_pi @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( X1 = Y1 )
% 0.19/0.47 & ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod.inject
% 0.19/0.47 thf(fact_53_prod_Oinject,axiom,
% 0.19/0.47 ! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y2: name > noption_pi] :
% 0.19/0.47 ( ( ( produc1342893193ion_pi @ X1 @ X2 )
% 0.19/0.47 = ( produc1342893193ion_pi @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( X1 = Y1 )
% 0.19/0.47 & ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod.inject
% 0.19/0.47 thf(fact_54_prod_Oinject,axiom,
% 0.19/0.47 ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 0.19/0.47 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 0.19/0.47 = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( X1 = Y1 )
% 0.19/0.47 & ( X2 = Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod.inject
% 0.19/0.47 thf(fact_55_old_Oprod_Oinject,axiom,
% 0.19/0.47 ! [A: name > noption_pi,B: late_subject,A2: name > noption_pi,B2: late_subject] :
% 0.19/0.47 ( ( ( produc581368530ubject @ A @ B )
% 0.19/0.47 = ( produc581368530ubject @ A2 @ B2 ) )
% 0.19/0.47 = ( ( A = A2 )
% 0.19/0.47 & ( B = B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inject
% 0.19/0.47 thf(fact_56_old_Oprod_Oinject,axiom,
% 0.19/0.47 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 0.19/0.47 ( ( ( produc1505598906reeRes @ A @ B )
% 0.19/0.47 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 0.19/0.47 = ( ( A = A2 )
% 0.19/0.47 & ( B = B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inject
% 0.19/0.47 thf(fact_57_old_Oprod_Oinject,axiom,
% 0.19/0.47 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 0.19/0.47 ( ( ( produc540578151i_name @ A @ B )
% 0.19/0.47 = ( produc540578151i_name @ A2 @ B2 ) )
% 0.19/0.47 = ( ( A = A2 )
% 0.19/0.47 & ( B = B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inject
% 0.19/0.47 thf(fact_58_old_Oprod_Oinject,axiom,
% 0.19/0.47 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 0.19/0.47 ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.19/0.47 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 0.19/0.47 = ( ( A = A2 )
% 0.19/0.47 & ( B = B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inject
% 0.19/0.47 thf(fact_59_old_Oprod_Oinject,axiom,
% 0.19/0.47 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 0.19/0.47 ( ( ( produc1342893193ion_pi @ A @ B )
% 0.19/0.47 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 0.19/0.47 = ( ( A = A2 )
% 0.19/0.47 & ( B = B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inject
% 0.19/0.47 thf(fact_60_old_Oprod_Oinject,axiom,
% 0.19/0.47 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.19/0.47 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.19/0.47 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.19/0.47 = ( ( A = A2 )
% 0.19/0.47 & ( B = B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inject
% 0.19/0.47 thf(fact_61_fresh__prodD_I2_J,axiom,
% 0.19/0.47 ! [A: name,X: name > noption_pi,Y: late_subject] :
% 0.19/0.47 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y ) )
% 0.19/0.47 => ( fresh_717452603ubject @ A @ Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(2)
% 0.19/0.47 thf(fact_62_fresh__prodD_I2_J,axiom,
% 0.19/0.47 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 0.19/0.47 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 0.19/0.47 => ( fresh_1641682979reeRes @ A @ Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(2)
% 0.19/0.47 thf(fact_63_fresh__prodD_I2_J,axiom,
% 0.19/0.47 ! [A: name,X: name > noption_pi,Y: name] :
% 0.19/0.47 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 0.19/0.47 => ( fresh_name_name @ A @ Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(2)
% 0.19/0.47 thf(fact_64_fresh__prodD_I2_J,axiom,
% 0.19/0.47 ! [A: name,X: name > noption_pi,Y: pi] :
% 0.19/0.47 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 0.19/0.47 => ( fresh_name_pi @ A @ Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(2)
% 0.19/0.47 thf(fact_65_fresh__prodD_I2_J,axiom,
% 0.19/0.47 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 0.19/0.47 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 0.19/0.47 => ( fresh_543891186ion_pi @ A @ Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(2)
% 0.19/0.47 thf(fact_66_fresh__prodD_I2_J,axiom,
% 0.19/0.47 ! [A: name,X: pi,Y: pi] :
% 0.19/0.47 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.19/0.47 => ( fresh_name_pi @ A @ Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(2)
% 0.19/0.47 thf(fact_67_fresh__prodD_I1_J,axiom,
% 0.19/0.47 ! [A: name,X: name > noption_pi,Y: late_subject] :
% 0.19/0.47 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y ) )
% 0.19/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(1)
% 0.19/0.47 thf(fact_68_fresh__prodD_I1_J,axiom,
% 0.19/0.47 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 0.19/0.47 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 0.19/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(1)
% 0.19/0.47 thf(fact_69_fresh__prodD_I1_J,axiom,
% 0.19/0.47 ! [A: name,X: name > noption_pi,Y: name] :
% 0.19/0.47 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 0.19/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(1)
% 0.19/0.47 thf(fact_70_fresh__prodD_I1_J,axiom,
% 0.19/0.47 ! [A: name,X: name > noption_pi,Y: pi] :
% 0.19/0.47 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 0.19/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(1)
% 0.19/0.47 thf(fact_71_fresh__prodD_I1_J,axiom,
% 0.19/0.47 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 0.19/0.47 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 0.19/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(1)
% 0.19/0.47 thf(fact_72_fresh__prodD_I1_J,axiom,
% 0.19/0.47 ! [A: name,X: pi,Y: pi] :
% 0.19/0.47 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.19/0.47 => ( fresh_name_pi @ A @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_prodD(1)
% 0.19/0.47 thf(fact_73_resOutputInputTrans,axiom,
% 0.19/0.47 ! [X: name,A: name,B: name,P: pi,C: name,Y: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resOutputInputTrans
% 0.19/0.47 thf(fact_74_transitions_OResB,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Y @ A )
% 0.19/0.47 => ( ( Y != X )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.19/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.ResB
% 0.19/0.47 thf(fact_75_transitions_OPar2B,axiom,
% 0.19/0.47 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Par2B
% 0.19/0.47 thf(fact_76_transitions_OPar1B,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Par1B
% 0.19/0.47 thf(fact_77_mem__Collect__eq,axiom,
% 0.19/0.47 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 0.19/0.47 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 0.19/0.47 = ( P @ A ) ) ).
% 0.19/0.47
% 0.19/0.47 % mem_Collect_eq
% 0.19/0.47 thf(fact_78_Collect__mem__eq,axiom,
% 0.19/0.47 ! [A3: set_Pr1834926343_pi_pi] :
% 0.19/0.47 ( ( collec1051790738_pi_pi
% 0.19/0.47 @ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A3 ) )
% 0.19/0.47 = A3 ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_mem_eq
% 0.19/0.47 thf(fact_79_Collect__cong,axiom,
% 0.19/0.47 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 0.19/0.47 ( ! [X5: product_prod_pi_pi] :
% 0.19/0.47 ( ( P @ X5 )
% 0.19/0.47 = ( Q @ X5 ) )
% 0.19/0.47 => ( ( collec1051790738_pi_pi @ P )
% 0.19/0.47 = ( collec1051790738_pi_pi @ Q ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_cong
% 0.19/0.47 thf(fact_80_parCasesB_H,axiom,
% 0.19/0.47 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.19/0.47 => ( ! [P4: pi,A4: late_subject,X5: name,P3: pi,Q4: pi] :
% 0.19/0.47 ( ( ( par @ P @ Q )
% 0.19/0.47 = ( par @ P4 @ Q4 ) )
% 0.19/0.47 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.19/0.47 = ( late_BoundR @ A4 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ Q4 )
% 0.19/0.47 => ~ ( fresh_717452603ubject @ X5 @ A4 ) ) ) ) ) )
% 0.19/0.47 => ~ ! [Q4: pi,A4: late_subject,X5: name,Q3: pi,P4: pi] :
% 0.19/0.47 ( ( ( par @ P @ Q )
% 0.19/0.47 = ( par @ P4 @ Q4 ) )
% 0.19/0.47 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.19/0.47 = ( late_BoundR @ A4 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 0.19/0.47 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ Q4 )
% 0.19/0.47 => ~ ( fresh_717452603ubject @ X5 @ A4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % parCasesB'
% 0.19/0.47 thf(fact_81_pi_Ofresh_I2_J,axiom,
% 0.19/0.47 ! [A: name,X3: name,X2: name,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( output @ X3 @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X3 )
% 0.19/0.47 & ( fresh_name_name @ A @ X2 )
% 0.19/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(2)
% 0.19/0.47 thf(fact_82_subject_Ofresh_I1_J,axiom,
% 0.19/0.47 ! [A: name,X1: name] :
% 0.19/0.47 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 0.19/0.47 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % subject.fresh(1)
% 0.19/0.47 thf(fact_83_freshResidual,axiom,
% 0.19/0.47 ! [P: pi,Rs: late_residual,X: name] :
% 0.19/0.47 ( ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshResidual
% 0.19/0.47 thf(fact_84_Late__Semantics_OResB,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Y @ A )
% 0.19/0.47 => ( ( Y != X )
% 0.19/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.ResB
% 0.19/0.47 thf(fact_85_freshBoundDerivative_I1_J,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshBoundDerivative(1)
% 0.19/0.47 thf(fact_86_old_Oprod_Oinducts,axiom,
% 0.19/0.47 ! [P: produc691362330ubject > $o,Prod: produc691362330ubject] :
% 0.19/0.47 ( ! [A4: name > noption_pi,B3: late_subject] : ( P @ ( produc581368530ubject @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ Prod ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inducts
% 0.19/0.47 thf(fact_87_old_Oprod_Oinducts,axiom,
% 0.19/0.47 ! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
% 0.19/0.47 ( ! [A4: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ Prod ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inducts
% 0.19/0.47 thf(fact_88_old_Oprod_Oinducts,axiom,
% 0.19/0.47 ! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
% 0.19/0.47 ( ! [A4: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ Prod ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inducts
% 0.19/0.47 thf(fact_89_old_Oprod_Oinducts,axiom,
% 0.19/0.47 ! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
% 0.19/0.47 ( ! [A4: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ Prod ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inducts
% 0.19/0.47 thf(fact_90_old_Oprod_Oinducts,axiom,
% 0.19/0.47 ! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
% 0.19/0.47 ( ! [A4: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ Prod ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inducts
% 0.19/0.47 thf(fact_91_old_Oprod_Oinducts,axiom,
% 0.19/0.47 ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 0.19/0.47 ( ! [A4: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ Prod ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.inducts
% 0.19/0.47 thf(fact_92_old_Oprod_Oexhaust,axiom,
% 0.19/0.47 ! [Y: produc691362330ubject] :
% 0.19/0.47 ~ ! [A4: name > noption_pi,B3: late_subject] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( produc581368530ubject @ A4 @ B3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.exhaust
% 0.19/0.47 thf(fact_93_old_Oprod_Oexhaust,axiom,
% 0.19/0.47 ! [Y: produc1834551554reeRes] :
% 0.19/0.47 ~ ! [A4: name > noption_pi,B3: late_freeRes] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( produc1505598906reeRes @ A4 @ B3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.exhaust
% 0.19/0.47 thf(fact_94_old_Oprod_Oexhaust,axiom,
% 0.19/0.47 ! [Y: produc405342261i_name] :
% 0.19/0.47 ~ ! [A4: name > noption_pi,B3: name] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( produc540578151i_name @ A4 @ B3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.exhaust
% 0.19/0.47 thf(fact_95_old_Oprod_Oexhaust,axiom,
% 0.19/0.47 ! [Y: produc629157763_pi_pi] :
% 0.19/0.47 ~ ! [A4: name > noption_pi,B3: pi] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( produc1820286517_pi_pi @ A4 @ B3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.exhaust
% 0.19/0.47 thf(fact_96_old_Oprod_Oexhaust,axiom,
% 0.19/0.47 ! [Y: produc1462499409ion_pi] :
% 0.19/0.47 ~ ! [A4: name > noption_pi,B3: name > noption_pi] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( produc1342893193ion_pi @ A4 @ B3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.exhaust
% 0.19/0.47 thf(fact_97_old_Oprod_Oexhaust,axiom,
% 0.19/0.47 ! [Y: product_prod_pi_pi] :
% 0.19/0.47 ~ ! [A4: pi,B3: pi] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( product_Pair_pi_pi @ A4 @ B3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.prod.exhaust
% 0.19/0.47 thf(fact_98_Pair__inject,axiom,
% 0.19/0.47 ! [A: name > noption_pi,B: late_subject,A2: name > noption_pi,B2: late_subject] :
% 0.19/0.47 ( ( ( produc581368530ubject @ A @ B )
% 0.19/0.47 = ( produc581368530ubject @ A2 @ B2 ) )
% 0.19/0.47 => ~ ( ( A = A2 )
% 0.19/0.47 => ( B != B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Pair_inject
% 0.19/0.47 thf(fact_99_Pair__inject,axiom,
% 0.19/0.47 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 0.19/0.47 ( ( ( produc1505598906reeRes @ A @ B )
% 0.19/0.47 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 0.19/0.47 => ~ ( ( A = A2 )
% 0.19/0.47 => ( B != B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Pair_inject
% 0.19/0.47 thf(fact_100_Pair__inject,axiom,
% 0.19/0.47 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 0.19/0.47 ( ( ( produc540578151i_name @ A @ B )
% 0.19/0.47 = ( produc540578151i_name @ A2 @ B2 ) )
% 0.19/0.47 => ~ ( ( A = A2 )
% 0.19/0.47 => ( B != B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Pair_inject
% 0.19/0.47 thf(fact_101_Pair__inject,axiom,
% 0.19/0.47 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 0.19/0.47 ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.19/0.47 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 0.19/0.47 => ~ ( ( A = A2 )
% 0.19/0.47 => ( B != B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Pair_inject
% 0.19/0.47 thf(fact_102_Pair__inject,axiom,
% 0.19/0.47 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 0.19/0.47 ( ( ( produc1342893193ion_pi @ A @ B )
% 0.19/0.47 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 0.19/0.47 => ~ ( ( A = A2 )
% 0.19/0.47 => ( B != B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Pair_inject
% 0.19/0.47 thf(fact_103_Pair__inject,axiom,
% 0.19/0.47 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.19/0.47 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.19/0.47 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.19/0.47 => ~ ( ( A = A2 )
% 0.19/0.47 => ( B != B2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Pair_inject
% 0.19/0.47 thf(fact_104_prod__cases,axiom,
% 0.19/0.47 ! [P: produc691362330ubject > $o,P5: produc691362330ubject] :
% 0.19/0.47 ( ! [A4: name > noption_pi,B3: late_subject] : ( P @ ( produc581368530ubject @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ P5 ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases
% 0.19/0.47 thf(fact_105_prod__cases,axiom,
% 0.19/0.47 ! [P: produc1834551554reeRes > $o,P5: produc1834551554reeRes] :
% 0.19/0.47 ( ! [A4: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ P5 ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases
% 0.19/0.47 thf(fact_106_prod__cases,axiom,
% 0.19/0.47 ! [P: produc405342261i_name > $o,P5: produc405342261i_name] :
% 0.19/0.47 ( ! [A4: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ P5 ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases
% 0.19/0.47 thf(fact_107_prod__cases,axiom,
% 0.19/0.47 ! [P: produc629157763_pi_pi > $o,P5: produc629157763_pi_pi] :
% 0.19/0.47 ( ! [A4: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ P5 ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases
% 0.19/0.47 thf(fact_108_prod__cases,axiom,
% 0.19/0.47 ! [P: produc1462499409ion_pi > $o,P5: produc1462499409ion_pi] :
% 0.19/0.47 ( ! [A4: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ P5 ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases
% 0.19/0.47 thf(fact_109_prod__cases,axiom,
% 0.19/0.47 ! [P: product_prod_pi_pi > $o,P5: product_prod_pi_pi] :
% 0.19/0.47 ( ! [A4: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A4 @ B3 ) )
% 0.19/0.47 => ( P @ P5 ) ) ).
% 0.19/0.47
% 0.19/0.47 % prod_cases
% 0.19/0.47 thf(fact_110_surj__pair,axiom,
% 0.19/0.47 ! [P5: produc691362330ubject] :
% 0.19/0.47 ? [X5: name > noption_pi,Y4: late_subject] :
% 0.19/0.47 ( P5
% 0.19/0.47 = ( produc581368530ubject @ X5 @ Y4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % surj_pair
% 0.19/0.47 thf(fact_111_surj__pair,axiom,
% 0.19/0.47 ! [P5: produc1834551554reeRes] :
% 0.19/0.47 ? [X5: name > noption_pi,Y4: late_freeRes] :
% 0.19/0.47 ( P5
% 0.19/0.47 = ( produc1505598906reeRes @ X5 @ Y4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % surj_pair
% 0.19/0.47 thf(fact_112_surj__pair,axiom,
% 0.19/0.47 ! [P5: produc405342261i_name] :
% 0.19/0.47 ? [X5: name > noption_pi,Y4: name] :
% 0.19/0.47 ( P5
% 0.19/0.47 = ( produc540578151i_name @ X5 @ Y4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % surj_pair
% 0.19/0.47 thf(fact_113_surj__pair,axiom,
% 0.19/0.47 ! [P5: produc629157763_pi_pi] :
% 0.19/0.47 ? [X5: name > noption_pi,Y4: pi] :
% 0.19/0.47 ( P5
% 0.19/0.47 = ( produc1820286517_pi_pi @ X5 @ Y4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % surj_pair
% 0.19/0.47 thf(fact_114_surj__pair,axiom,
% 0.19/0.47 ! [P5: produc1462499409ion_pi] :
% 0.19/0.47 ? [X5: name > noption_pi,Y4: name > noption_pi] :
% 0.19/0.47 ( P5
% 0.19/0.47 = ( produc1342893193ion_pi @ X5 @ Y4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % surj_pair
% 0.19/0.47 thf(fact_115_surj__pair,axiom,
% 0.19/0.47 ! [P5: product_prod_pi_pi] :
% 0.19/0.47 ? [X5: pi,Y4: pi] :
% 0.19/0.47 ( P5
% 0.19/0.47 = ( product_Pair_pi_pi @ X5 @ Y4 ) ) ).
% 0.19/0.47
% 0.19/0.47 % surj_pair
% 0.19/0.47 thf(fact_116_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.19/0.47 ! [X1: name,Y1: name] :
% 0.19/0.47 ( ( ( late_InputS @ X1 )
% 0.19/0.47 = ( late_InputS @ Y1 ) )
% 0.19/0.47 = ( X1 = Y1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics1.subject.inject(1)
% 0.19/0.47 thf(fact_117_parSym,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 0.19/0.47 ( ! [R: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R @ S2 ) @ ( par @ S2 @ R ) ) @ Rel )
% 0.19/0.47 => ( ! [R: pi,S2: pi,X5: name] :
% 0.19/0.47 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R @ S2 ) @ Rel )
% 0.19/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X5 @ R ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 0.19/0.47 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % parSym
% 0.19/0.47 thf(fact_118_inputIneqTrans,axiom,
% 0.19/0.47 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.19/0.47 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % inputIneqTrans
% 0.19/0.47 thf(fact_119_Late__Semantics_OInput,axiom,
% 0.19/0.47 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Input
% 0.19/0.47 thf(fact_120_transitions_OInput,axiom,
% 0.19/0.47 ! [X: name,A: name,P: pi] :
% 0.19/0.47 ( ( X != A )
% 0.19/0.47 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Input
% 0.19/0.47 thf(fact_121_name__fresh,axiom,
% 0.19/0.47 ( fresh_name_name
% 0.19/0.47 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % name_fresh
% 0.19/0.47 thf(fact_122_pi_Odistinct_I55_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.19/0.47 ( ( input @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(55)
% 0.19/0.47 thf(fact_123_pi_Odistinct_I57_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.19/0.47 ( ( input @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(57)
% 0.19/0.47 thf(fact_124_pi_Odistinct_I21_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(21)
% 0.19/0.47 thf(fact_125_pi_Odistinct_I35_J,axiom,
% 0.19/0.47 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( ( tau @ Pi )
% 0.19/0.47 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(35)
% 0.19/0.47 thf(fact_126_resTrans_I2_J,axiom,
% 0.19/0.47 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % resTrans(2)
% 0.19/0.47 thf(fact_127_simE_I1_J,axiom,
% 0.19/0.47 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 0.19/0.47 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ? [P3: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.19/0.47 & ( strong2129052853vative @ P3 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simE(1)
% 0.19/0.47 thf(fact_128_resInputBoundOutputTrans,axiom,
% 0.19/0.47 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resInputBoundOutputTrans
% 0.19/0.47 thf(fact_129_simulation__def,axiom,
% 0.19/0.47 ( strong743114133lation
% 0.19/0.47 = ( ^ [P6: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 0.19/0.47 ( ! [A5: late_subject,X4: name,Q6: pi] :
% 0.19/0.47 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 0.19/0.47 & ( fresh_name_pi @ X4 @ P6 ) )
% 0.19/0.47 => ? [P7: pi] :
% 0.19/0.47 ( ( late_transitions @ P6 @ ( late_BoundR @ A5 @ X4 @ P7 ) )
% 0.19/0.47 & ( strong2129052853vative @ P7 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 0.19/0.47 & ! [Alpha: late_freeRes,Q6: pi] :
% 0.19/0.47 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha @ Q6 ) )
% 0.19/0.47 => ? [P7: pi] :
% 0.19/0.47 ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha @ P7 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simulation_def
% 0.19/0.47 thf(fact_130_simCases,axiom,
% 0.19/0.47 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 0.19/0.47 ( ! [A4: late_subject,Y4: name,Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y4 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y4 @ P )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y4 @ P8 ) )
% 0.19/0.47 & ( strong2129052853vative @ P8 @ Q3 @ A4 @ Y4 @ Rel ) ) ) )
% 0.19/0.47 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 0.19/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simCases
% 0.19/0.47 thf(fact_131_residual_Ofresh_I1_J,axiom,
% 0.19/0.47 ! [A: name,X3: late_subject,X1: name,X2: pi] :
% 0.19/0.47 ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X3 @ X1 @ X2 ) )
% 0.19/0.47 = ( ( fresh_717452603ubject @ A @ X3 )
% 0.19/0.47 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.fresh(1)
% 0.19/0.47 thf(fact_132_inputCases_H,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ~ ! [X5: name,A4: name,P4: pi] :
% 0.19/0.47 ( ( ( A = A4 )
% 0.19/0.47 & ( ( abs_fun_name_pi @ B @ P )
% 0.19/0.47 = ( abs_fun_name_pi @ X5 @ P4 ) ) )
% 0.19/0.47 => ( ( Rs
% 0.19/0.47 = ( late_BoundR @ ( late_InputS @ A4 ) @ X5 @ P4 ) )
% 0.19/0.47 => ( X5 = A4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % inputCases'
% 0.19/0.47 thf(fact_133_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.19/0.47 ! [X2: name,Y2: name] :
% 0.19/0.47 ( ( ( late_BoundOutputS @ X2 )
% 0.19/0.47 = ( late_BoundOutputS @ Y2 ) )
% 0.19/0.47 = ( X2 = Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics1.subject.inject(2)
% 0.19/0.47 thf(fact_134_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.19/0.47 ! [X1: name,Y1: name] :
% 0.19/0.47 ( ( ( late_BoundOutputS @ X1 )
% 0.19/0.47 = ( late_BoundOutputS @ Y1 ) )
% 0.19/0.47 = ( X1 = Y1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.subject.inject(2)
% 0.19/0.47 thf(fact_135_subject_Ofresh_I2_J,axiom,
% 0.19/0.47 ! [A: name,X1: name] :
% 0.19/0.47 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 0.19/0.47 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % subject.fresh(2)
% 0.19/0.47 thf(fact_136_residual_Ofresh_I2_J,axiom,
% 0.19/0.47 ! [A: name,X2: late_freeRes,X1: pi] :
% 0.19/0.47 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 0.19/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.fresh(2)
% 0.19/0.47 thf(fact_137_pi_Ofresh_I9_J,axiom,
% 0.19/0.47 ! [A: name,X1: name,X2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 0.19/0.47 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(9)
% 0.19/0.47 thf(fact_138_pi_Ofresh_I4_J,axiom,
% 0.19/0.47 ! [A: name,X3: name,X1: name,X2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( input @ X3 @ X1 @ X2 ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X3 )
% 0.19/0.47 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(4)
% 0.19/0.47 thf(fact_139_residual_Oinject_I2_J,axiom,
% 0.19/0.47 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.19/0.47 ( ( ( late_FreeR @ X2 @ X1 )
% 0.19/0.47 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.inject(2)
% 0.19/0.47 thf(fact_140_abs__fun__eq1,axiom,
% 0.19/0.47 ! [A: name,X: name,Y: name] :
% 0.19/0.47 ( ( ( abs_fun_name_name @ A @ X )
% 0.19/0.47 = ( abs_fun_name_name @ A @ Y ) )
% 0.19/0.47 = ( X = Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fun_eq1
% 0.19/0.47 thf(fact_141_abs__fun__eq1,axiom,
% 0.19/0.47 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 0.19/0.47 ( ( ( abs_fu681348580reeRes @ A @ X )
% 0.19/0.47 = ( abs_fu681348580reeRes @ A @ Y ) )
% 0.19/0.47 = ( X = Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fun_eq1
% 0.19/0.47 thf(fact_142_abs__fun__eq1,axiom,
% 0.19/0.47 ! [A: name,X: late_subject,Y: late_subject] :
% 0.19/0.47 ( ( ( abs_fu1904601852ubject @ A @ X )
% 0.19/0.47 = ( abs_fu1904601852ubject @ A @ Y ) )
% 0.19/0.47 = ( X = Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fun_eq1
% 0.19/0.47 thf(fact_143_abs__fun__eq1,axiom,
% 0.19/0.47 ! [A: name,X: pi,Y: pi] :
% 0.19/0.47 ( ( ( abs_fun_name_pi @ A @ X )
% 0.19/0.47 = ( abs_fun_name_pi @ A @ Y ) )
% 0.19/0.47 = ( X = Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fun_eq1
% 0.19/0.47 thf(fact_144_pi_Oinject_I8_J,axiom,
% 0.19/0.47 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 0.19/0.47 ( ( ( res @ X1 @ X2 )
% 0.19/0.47 = ( res @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.19/0.47 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(8)
% 0.19/0.47 thf(fact_145_residual_Oinject_I1_J,axiom,
% 0.19/0.47 ! [X3: late_subject,X1: name,X2: pi,Y3: late_subject,Y1: name,Y2: pi] :
% 0.19/0.47 ( ( ( late_BoundR @ X3 @ X1 @ X2 )
% 0.19/0.47 = ( late_BoundR @ Y3 @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( X3 = Y3 )
% 0.19/0.47 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.19/0.47 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.inject(1)
% 0.19/0.47 thf(fact_146_residual_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [Subject: late_subject,Name3: name,Pi: pi,FreeRes: late_freeRes,Pi2: pi] :
% 0.19/0.47 ( ( late_BoundR @ Subject @ Name3 @ Pi )
% 0.19/0.47 != ( late_FreeR @ FreeRes @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.distinct(1)
% 0.19/0.47 thf(fact_147_residual_Oinducts,axiom,
% 0.19/0.47 ! [P: late_residual > $o,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) )
% 0.19/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.19/0.47 => ( P @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.inducts
% 0.19/0.47 thf(fact_148_name__fresh__abs,axiom,
% 0.19/0.47 ! [B: name,A: name,X: late_subject] :
% 0.19/0.47 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % name_fresh_abs
% 0.19/0.47 thf(fact_149_name__fresh__abs,axiom,
% 0.19/0.47 ! [B: name,A: name,X: late_freeRes] :
% 0.19/0.47 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % name_fresh_abs
% 0.19/0.47 thf(fact_150_name__fresh__abs,axiom,
% 0.19/0.47 ! [B: name,A: name,X: name] :
% 0.19/0.47 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % name_fresh_abs
% 0.19/0.47 thf(fact_151_name__fresh__abs,axiom,
% 0.19/0.47 ! [B: name,A: name,X: pi] :
% 0.19/0.47 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % name_fresh_abs
% 0.19/0.47 thf(fact_152_abs__fresh_I1_J,axiom,
% 0.19/0.47 ! [B: name,A: name,X: late_subject] :
% 0.19/0.47 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(1)
% 0.19/0.47 thf(fact_153_abs__fresh_I1_J,axiom,
% 0.19/0.47 ! [B: name,A: name,X: late_freeRes] :
% 0.19/0.47 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(1)
% 0.19/0.47 thf(fact_154_abs__fresh_I1_J,axiom,
% 0.19/0.47 ! [B: name,A: name,X: name] :
% 0.19/0.47 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(1)
% 0.19/0.47 thf(fact_155_abs__fresh_I1_J,axiom,
% 0.19/0.47 ! [B: name,A: name,X: pi] :
% 0.19/0.47 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(1)
% 0.19/0.47 thf(fact_156_pi_Oinject_I3_J,axiom,
% 0.19/0.47 ! [X3: name,X1: name,X2: pi,Y3: name,Y1: name,Y2: pi] :
% 0.19/0.47 ( ( ( input @ X3 @ X1 @ X2 )
% 0.19/0.47 = ( input @ Y3 @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( X3 = Y3 )
% 0.19/0.47 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.19/0.47 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(3)
% 0.19/0.47 thf(fact_157_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [Name3: name,Name: name] :
% 0.19/0.47 ( ( late_InputS @ Name3 )
% 0.19/0.47 != ( late_BoundOutputS @ Name ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.subject.distinct(1)
% 0.19/0.47 thf(fact_158_subject_Oinducts,axiom,
% 0.19/0.47 ! [P: late_subject > $o,Subject: late_subject] :
% 0.19/0.47 ( ! [Name4: name] : ( P @ ( late_InputS @ Name4 ) )
% 0.19/0.47 => ( ! [Name4: name] : ( P @ ( late_BoundOutputS @ Name4 ) )
% 0.19/0.47 => ( P @ Subject ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % subject.inducts
% 0.19/0.47 thf(fact_159_subject_Oexhaust,axiom,
% 0.19/0.47 ! [Y: late_subject] :
% 0.19/0.47 ( ! [X12: name] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( late_InputS @ X12 ) )
% 0.19/0.47 => ~ ! [X22: name] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % subject.exhaust
% 0.19/0.47 thf(fact_160_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [X1: name,X2: name] :
% 0.19/0.47 ( ( late_InputS @ X1 )
% 0.19/0.47 != ( late_BoundOutputS @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics1.subject.distinct(1)
% 0.19/0.47 thf(fact_161_Par1F,axiom,
% 0.19/0.47 ! [P: pi,Alpha3: late_freeRes,P2: pi,Q: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha3 @ ( par @ P2 @ Q ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Par1F
% 0.19/0.47 thf(fact_162_Par2F,axiom,
% 0.19/0.47 ! [Q: pi,Alpha3: late_freeRes,Q2: pi,P: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha3 @ Q2 ) )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha3 @ ( par @ P @ Q2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Par2F
% 0.19/0.47 thf(fact_163_ResF,axiom,
% 0.19/0.47 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ Y @ Alpha3 )
% 0.19/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha3 @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ResF
% 0.19/0.47 thf(fact_164_resCasesF_H,axiom,
% 0.19/0.47 ! [X: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.19/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y4: name] :
% 0.19/0.47 ( ( ( res @ X @ P )
% 0.19/0.47 = ( res @ Y4 @ P4 ) )
% 0.19/0.47 => ( ( ( late_FreeR @ Alpha3 @ P2 )
% 0.19/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y4 @ P3 ) ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.19/0.47 => ~ ( fresh_1641682979reeRes @ Y4 @ Alpha2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resCasesF'
% 0.19/0.47 thf(fact_165_resCasesF,axiom,
% 0.19/0.47 ! [X: name,P: pi,Alpha3: late_freeRes,XP: pi,F: pi > $o] :
% 0.19/0.47 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha3 @ XP ) )
% 0.19/0.47 => ( ! [P3: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P3 ) )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha3 )
% 0.19/0.47 => ( F @ ( res @ X @ P3 ) ) ) )
% 0.19/0.47 => ( F @ XP ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resCasesF
% 0.19/0.47 thf(fact_166_freshFreeDerivative_I1_J,axiom,
% 0.19/0.47 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( fresh_1641682979reeRes @ Y @ Alpha3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshFreeDerivative(1)
% 0.19/0.47 thf(fact_167_freshFreeDerivative_I2_J,axiom,
% 0.19/0.47 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( fresh_name_pi @ Y @ P2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshFreeDerivative(2)
% 0.19/0.47 thf(fact_168_inputFreeTrans,axiom,
% 0.19/0.47 ! [A: name,X: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % inputFreeTrans
% 0.19/0.47 thf(fact_169_outputFreshTrans,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.19/0.47 => ~ ( ( fresh_1641682979reeRes @ A @ Alpha3 )
% 0.19/0.47 | ( fresh_1641682979reeRes @ B @ Alpha3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputFreshTrans
% 0.19/0.47 thf(fact_170_simE_I2_J,axiom,
% 0.19/0.47 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha3: late_freeRes,Q2: pi] :
% 0.19/0.47 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha3 @ Q2 ) )
% 0.19/0.47 => ? [P3: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P3 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simE(2)
% 0.19/0.47 thf(fact_171_resInputFreeTrans,axiom,
% 0.19/0.47 ! [X: name,A: name,Y: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha3 @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resInputFreeTrans
% 0.19/0.47 thf(fact_172_residual_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ( fresh_717452603ubject @ Name4 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_inducts
% 0.19/0.47 thf(fact_173_residual_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_inducts
% 0.19/0.47 thf(fact_174_residual_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ( fresh_name_name @ Name4 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_inducts
% 0.19/0.47 thf(fact_175_residual_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_inducts
% 0.19/0.47 thf(fact_176_residual_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ( fresh_717452603ubject @ Name4 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_induct
% 0.19/0.47 thf(fact_177_residual_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_induct
% 0.19/0.47 thf(fact_178_residual_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ( fresh_name_name @ Name4 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_induct
% 0.19/0.47 thf(fact_179_residual_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_induct
% 0.19/0.47 thf(fact_180_inputBoundOutputTrans,axiom,
% 0.19/0.47 ! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % inputBoundOutputTrans
% 0.19/0.47 thf(fact_181_simCasesCont,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_subject] :
% 0.19/0.47 ( ( eqvt_pi @ Rel )
% 0.19/0.47 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ Q )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X5 @ A4 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X5 @ C3 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P8 ) )
% 0.19/0.47 & ( strong2129052853vative @ P8 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 0.19/0.47 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 0.19/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simCasesCont
% 0.19/0.47 thf(fact_182_simCasesCont,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_freeRes] :
% 0.19/0.47 ( ( eqvt_pi @ Rel )
% 0.19/0.47 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ Q )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X5 @ A4 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X5 @ C3 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P8 ) )
% 0.19/0.47 & ( strong2129052853vative @ P8 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 0.19/0.47 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 0.19/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simCasesCont
% 0.19/0.47 thf(fact_183_simCasesCont,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
% 0.19/0.47 ( ( eqvt_pi @ Rel )
% 0.19/0.47 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ Q )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X5 @ A4 )
% 0.19/0.47 => ( ( fresh_name_name @ X5 @ C3 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P8 ) )
% 0.19/0.47 & ( strong2129052853vative @ P8 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 0.19/0.47 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 0.19/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simCasesCont
% 0.19/0.47 thf(fact_184_simCasesCont,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
% 0.19/0.47 ( ( eqvt_pi @ Rel )
% 0.19/0.47 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ Q )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X5 @ A4 )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ C3 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P8 ) )
% 0.19/0.47 & ( strong2129052853vative @ P8 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 0.19/0.47 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 0.19/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simCasesCont
% 0.19/0.47 thf(fact_185_resCases_H,axiom,
% 0.19/0.47 ! [X: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 0.19/0.47 => ( ! [P4: pi,A4: name,B3: name] :
% 0.19/0.47 ( ( ( res @ X @ P )
% 0.19/0.47 = ( res @ B3 @ P4 ) )
% 0.19/0.47 => ! [P3: pi] :
% 0.19/0.47 ( ( Rs
% 0.19/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P3 ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P3 ) )
% 0.19/0.47 => ( A4 = B3 ) ) ) )
% 0.19/0.47 => ( ! [P4: pi,A4: late_subject,X5: name,P3: pi,Y4: name] :
% 0.19/0.47 ( ( ( res @ X @ P )
% 0.19/0.47 = ( res @ Y4 @ P4 ) )
% 0.19/0.47 => ( ( Rs
% 0.19/0.47 = ( late_BoundR @ A4 @ X5 @ ( res @ Y4 @ P3 ) ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Y4 @ A4 )
% 0.19/0.47 => ( ( Y4 != X5 )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.19/0.47 => ~ ( fresh_717452603ubject @ X5 @ A4 ) ) ) ) ) ) )
% 0.19/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y4: name] :
% 0.19/0.47 ( ( ( res @ X @ P )
% 0.19/0.47 = ( res @ Y4 @ P4 ) )
% 0.19/0.47 => ( ( Rs
% 0.19/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y4 @ P3 ) ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.19/0.47 => ~ ( fresh_1641682979reeRes @ Y4 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resCases'
% 0.19/0.47 thf(fact_186_resCasesB_H,axiom,
% 0.19/0.47 ! [X6: name,P: pi,A: late_subject,Y5: name,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A @ Y5 @ P2 ) )
% 0.19/0.47 => ( ! [P4: pi,A4: name,B3: name] :
% 0.19/0.47 ( ( ( res @ X6 @ P )
% 0.19/0.47 = ( res @ B3 @ P4 ) )
% 0.19/0.47 => ! [P3: pi] :
% 0.19/0.47 ( ( ( late_BoundR @ A @ Y5 @ P2 )
% 0.19/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P3 ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P3 ) )
% 0.19/0.47 => ( A4 = B3 ) ) ) )
% 0.19/0.47 => ~ ! [P4: pi,A4: late_subject,X5: name,P3: pi,Y4: name] :
% 0.19/0.47 ( ( ( res @ X6 @ P )
% 0.19/0.47 = ( res @ Y4 @ P4 ) )
% 0.19/0.47 => ( ( ( late_BoundR @ A @ Y5 @ P2 )
% 0.19/0.47 = ( late_BoundR @ A4 @ X5 @ ( res @ Y4 @ P3 ) ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Y4 @ A4 )
% 0.19/0.47 => ( ( Y4 != X5 )
% 0.19/0.47 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.19/0.47 => ~ ( fresh_717452603ubject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resCasesB'
% 0.19/0.47 thf(fact_187_resSimCases,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_subject] :
% 0.19/0.47 ( ( eqvt_pi @ Rel )
% 0.19/0.47 => ( ! [Q3: pi,A4: name] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X ) @ Q3 ) )
% 0.19/0.47 => ( ( A4 != X )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) ) )
% 0.19/0.47 => ( ! [Q3: pi,A4: late_subject,Y4: name] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y4 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X @ A4 )
% 0.19/0.47 => ( ( X != Y4 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Y4 @ C3 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y4 @ P8 ) )
% 0.19/0.47 & ( strong2129052853vative @ P8 @ ( res @ X @ Q3 ) @ A4 @ Y4 @ Rel ) ) ) ) ) )
% 0.19/0.47 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 0.19/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resSimCases
% 0.19/0.47 thf(fact_188_resSimCases,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_freeRes] :
% 0.19/0.47 ( ( eqvt_pi @ Rel )
% 0.19/0.47 => ( ! [Q3: pi,A4: name] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X ) @ Q3 ) )
% 0.19/0.47 => ( ( A4 != X )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) ) )
% 0.19/0.47 => ( ! [Q3: pi,A4: late_subject,Y4: name] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y4 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X @ A4 )
% 0.19/0.47 => ( ( X != Y4 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ Y4 @ C3 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y4 @ P8 ) )
% 0.19/0.47 & ( strong2129052853vative @ P8 @ ( res @ X @ Q3 ) @ A4 @ Y4 @ Rel ) ) ) ) ) )
% 0.19/0.47 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 0.19/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resSimCases
% 0.19/0.47 thf(fact_189_resSimCases,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
% 0.19/0.47 ( ( eqvt_pi @ Rel )
% 0.19/0.47 => ( ! [Q3: pi,A4: name] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X ) @ Q3 ) )
% 0.19/0.47 => ( ( A4 != X )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) ) )
% 0.19/0.47 => ( ! [Q3: pi,A4: late_subject,Y4: name] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y4 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X @ A4 )
% 0.19/0.47 => ( ( X != Y4 )
% 0.19/0.47 => ( ( fresh_name_name @ Y4 @ C3 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y4 @ P8 ) )
% 0.19/0.47 & ( strong2129052853vative @ P8 @ ( res @ X @ Q3 ) @ A4 @ Y4 @ Rel ) ) ) ) ) )
% 0.19/0.47 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 0.19/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resSimCases
% 0.19/0.47 thf(fact_190_resSimCases,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
% 0.19/0.47 ( ( eqvt_pi @ Rel )
% 0.19/0.47 => ( ! [Q3: pi,A4: name] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X ) @ Q3 ) )
% 0.19/0.47 => ( ( A4 != X )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) ) )
% 0.19/0.47 => ( ! [Q3: pi,A4: late_subject,Y4: name] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y4 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X @ A4 )
% 0.19/0.47 => ( ( X != Y4 )
% 0.19/0.47 => ( ( fresh_name_pi @ Y4 @ C3 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y4 @ P8 ) )
% 0.19/0.47 & ( strong2129052853vative @ P8 @ ( res @ X @ Q3 ) @ A4 @ Y4 @ Rel ) ) ) ) ) )
% 0.19/0.47 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.19/0.47 => ? [P8: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.19/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 0.19/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resSimCases
% 0.19/0.47 thf(fact_191_Open,axiom,
% 0.19/0.47 ! [P: pi,A: name,B: name,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.19/0.47 => ( ( A != B )
% 0.19/0.47 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Open
% 0.19/0.47 thf(fact_192_resOutputTauTrans,axiom,
% 0.19/0.47 ! [X: name,A: name,B: name,P: pi,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resOutputTauTrans
% 0.19/0.47 thf(fact_193_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.19/0.47 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.19/0.47 ( ( ( late_OutputR @ X2 @ X1 )
% 0.19/0.47 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.freeRes.inject
% 0.19/0.47 thf(fact_194_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.19/0.47 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.19/0.47 ( ( ( late_OutputR @ X11 @ X122 )
% 0.19/0.47 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.19/0.47 = ( ( X11 = Y11 )
% 0.19/0.47 & ( X122 = Y12 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics1.freeRes.inject
% 0.19/0.47 thf(fact_195_freeRes_Ofresh_I2_J,axiom,
% 0.19/0.47 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 0.19/0.47
% 0.19/0.47 % freeRes.fresh(2)
% 0.19/0.47 thf(fact_196_freeRes_Ofresh_I1_J,axiom,
% 0.19/0.47 ! [A: name,X2: name,X1: name] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X2 )
% 0.19/0.47 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freeRes.fresh(1)
% 0.19/0.47 thf(fact_197_freeRes_Oinducts,axiom,
% 0.19/0.47 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.19/0.47 ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.19/0.47 => ( ( P @ late_TauR )
% 0.19/0.47 => ( P @ FreeRes3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freeRes.inducts
% 0.19/0.47 thf(fact_198_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name] :
% 0.19/0.47 ( ( late_OutputR @ Name1 @ Name2 )
% 0.19/0.47 != late_TauR ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.freeRes.distinct(1)
% 0.19/0.47 thf(fact_199_freeRes_Oexhaust,axiom,
% 0.19/0.47 ! [Y: late_freeRes] :
% 0.19/0.47 ( ! [X112: name,X123: name] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( late_OutputR @ X112 @ X123 ) )
% 0.19/0.47 => ( Y = late_TauR ) ) ).
% 0.19/0.47
% 0.19/0.47 % freeRes.exhaust
% 0.19/0.47 thf(fact_200_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [X11: name,X122: name] :
% 0.19/0.47 ( ( late_OutputR @ X11 @ X122 )
% 0.19/0.47 != late_TauR ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics1.freeRes.distinct(1)
% 0.19/0.47 thf(fact_201_outputCases,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Alpha3: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.19/0.47 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.19/0.47 => ( ( ( Alpha3
% 0.19/0.47 = ( late_OutputR @ A @ B ) )
% 0.19/0.47 => ( ( P = P2 )
% 0.19/0.47 => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 0.19/0.47 => ( Prop @ Alpha3 @ P2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputCases
% 0.19/0.47 thf(fact_202_outputCases_H,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ~ ! [A4: name,B3: name,P4: pi] :
% 0.19/0.47 ( ( ( A = A4 )
% 0.19/0.47 & ( B = B3 )
% 0.19/0.47 & ( P = P4 ) )
% 0.19/0.47 => ( Rs
% 0.19/0.47 != ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputCases'
% 0.19/0.47 thf(fact_203_outputIneqTrans,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,C: name,D: name,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P2 ) )
% 0.19/0.47 => ~ ( ( A != C )
% 0.19/0.47 | ( B != D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputIneqTrans
% 0.19/0.47 thf(fact_204_Output,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % Output
% 0.19/0.47 thf(fact_205_tauOutputTrans,axiom,
% 0.19/0.47 ! [P: pi,A: name,B: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % tauOutputTrans
% 0.19/0.47 thf(fact_206_outputTauTrans,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputTauTrans
% 0.19/0.47 thf(fact_207_tauCases,axiom,
% 0.19/0.47 ! [P: pi,Alpha3: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.19/0.47 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 0.19/0.47 => ( ( ( Alpha3 = late_TauR )
% 0.19/0.47 => ( ( P = P2 )
% 0.19/0.47 => ( Prop @ late_TauR @ P ) ) )
% 0.19/0.47 => ( Prop @ Alpha3 @ P2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % tauCases
% 0.19/0.47 thf(fact_208_tauCases_H,axiom,
% 0.19/0.47 ! [P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.19/0.47 => ~ ! [P4: pi] :
% 0.19/0.47 ( ( ( tau @ P )
% 0.19/0.47 = ( tau @ P4 ) )
% 0.19/0.47 => ( Rs
% 0.19/0.47 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % tauCases'
% 0.19/0.47 thf(fact_209_Tau,axiom,
% 0.19/0.47 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % Tau
% 0.19/0.47 thf(fact_210_resOutputOutputTrans,axiom,
% 0.19/0.47 ! [X: name,A: name,P: pi,B: name,Y: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resOutputOutputTrans
% 0.19/0.47 thf(fact_211_resTauOutputTrans,axiom,
% 0.19/0.47 ! [X: name,P: pi,A: name,B: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resTauOutputTrans
% 0.19/0.47 thf(fact_212_Late__Semantics_OClose1,axiom,
% 0.19/0.47 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Close1
% 0.19/0.47 thf(fact_213_Late__Semantics_OClose2,axiom,
% 0.19/0.47 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ Q )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Close2
% 0.19/0.47 thf(fact_214_transitions_OClose1,axiom,
% 0.19/0.47 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ Q )
% 0.19/0.47 => ( ( X != A )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q2 )
% 0.19/0.47 => ( ( Y != A )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P2 )
% 0.19/0.47 => ( ( X != Y )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Close1
% 0.19/0.47 thf(fact_215_transitions_OClose2,axiom,
% 0.19/0.47 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ Q )
% 0.19/0.47 => ( ( X != A )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P2 )
% 0.19/0.47 => ( ( Y != A )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ Q2 )
% 0.19/0.47 => ( ( X != Y )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Close2
% 0.19/0.47 thf(fact_216_subst__identity,axiom,
% 0.19/0.47 ! [P: pi,A: name] :
% 0.19/0.47 ( ( subs @ P @ A @ A )
% 0.19/0.47 = P ) ).
% 0.19/0.47
% 0.19/0.47 % subst_identity
% 0.19/0.47 thf(fact_217_simps_I8_J,axiom,
% 0.19/0.47 ! [P: pi,Q: pi,C: name,D: name] :
% 0.19/0.47 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 0.19/0.47 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(8)
% 0.19/0.47 thf(fact_218_simps_I9_J,axiom,
% 0.19/0.47 ! [X: name,C: name,D: name,P: pi] :
% 0.19/0.47 ( ( X != C )
% 0.19/0.47 => ( ( X != D )
% 0.19/0.47 => ( ( subs @ ( res @ X @ P ) @ C @ D )
% 0.19/0.47 = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(9)
% 0.19/0.47 thf(fact_219_substTrans,axiom,
% 0.19/0.47 ! [B: name,P: pi,A: name,C: name] :
% 0.19/0.47 ( ( fresh_name_pi @ B @ P )
% 0.19/0.47 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
% 0.19/0.47 = ( subs @ P @ A @ C ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % substTrans
% 0.19/0.47 thf(fact_220_simps_I2_J,axiom,
% 0.19/0.47 ! [P: pi,C: name,D: name] :
% 0.19/0.47 ( ( subs @ ( tau @ P ) @ C @ D )
% 0.19/0.47 = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(2)
% 0.19/0.47 thf(fact_221_forget,axiom,
% 0.19/0.47 ! [A: name,P: pi,B: name] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ P )
% 0.19/0.47 => ( ( subs @ P @ A @ B )
% 0.19/0.47 = P ) ) ).
% 0.19/0.47
% 0.19/0.47 % forget
% 0.19/0.47 thf(fact_222_fresh__fact1,axiom,
% 0.19/0.47 ! [A: name,P: pi,C: name,B: name] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ P )
% 0.19/0.47 => ( ( A != C )
% 0.19/0.47 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_fact1
% 0.19/0.47 thf(fact_223_fresh__fact2,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi] :
% 0.19/0.47 ( ( A != B )
% 0.19/0.47 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_fact2
% 0.19/0.47 thf(fact_224_substRes3,axiom,
% 0.19/0.47 ! [B: name,P: pi,A: name] :
% 0.19/0.47 ( ( fresh_name_pi @ B @ P )
% 0.19/0.47 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 0.19/0.47 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % substRes3
% 0.19/0.47 thf(fact_225_substRes2,axiom,
% 0.19/0.47 ! [B: name,P: pi,A: name] :
% 0.19/0.47 ( ( fresh_name_pi @ B @ P )
% 0.19/0.47 => ( ( res @ A @ P )
% 0.19/0.47 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % substRes2
% 0.19/0.47 thf(fact_226_Late__Semantics_OComm1,axiom,
% 0.19/0.47 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Comm1
% 0.19/0.47 thf(fact_227_Late__Semantics_OComm2,axiom,
% 0.19/0.47 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Comm2
% 0.19/0.47 thf(fact_228_transitions_OComm2,axiom,
% 0.19/0.47 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( X != A )
% 0.19/0.47 => ( ( X != B )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P2 )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Comm2
% 0.19/0.47 thf(fact_229_transitions_OComm1,axiom,
% 0.19/0.47 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( X != A )
% 0.19/0.47 => ( ( X != B )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q2 )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Comm1
% 0.19/0.47 thf(fact_230_simps_I3_J,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.19/0.47 ( ( subs @ ( output @ A @ B @ P ) @ C @ D )
% 0.19/0.47 = ( output @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(3)
% 0.19/0.47 thf(fact_231_simps_I4_J,axiom,
% 0.19/0.47 ! [X: name,A: name,C: name,D: name,P: pi] :
% 0.19/0.47 ( ( X != A )
% 0.19/0.47 => ( ( X != C )
% 0.19/0.47 => ( ( X != D )
% 0.19/0.47 => ( ( subs @ ( input @ A @ X @ P ) @ C @ D )
% 0.19/0.47 = ( input @ ( subst_name @ A @ C @ D ) @ X @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(4)
% 0.19/0.47 thf(fact_232_substInput,axiom,
% 0.19/0.47 ! [X: name,B: name,C: name,A: name,P: pi] :
% 0.19/0.47 ( ( X != B )
% 0.19/0.47 => ( ( X != C )
% 0.19/0.47 => ( ( subs @ ( input @ A @ X @ P ) @ B @ C )
% 0.19/0.47 = ( input @ ( subst_name @ A @ B @ C ) @ X @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % substInput
% 0.19/0.47 thf(fact_233_subst__name__def,axiom,
% 0.19/0.47 ( subst_name
% 0.19/0.47 = ( ^ [A5: name,B4: name,C4: name] : ( if_name @ ( A5 = B4 ) @ C4 @ A5 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % subst_name_def
% 0.19/0.47 thf(fact_234_parZeroLeft,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.19/0.47 ( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
% 0.19/0.47 => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % parZeroLeft
% 0.19/0.47 thf(fact_235_parZeroRight,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.19/0.47 ( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
% 0.19/0.47 => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % parZeroRight
% 0.19/0.47 thf(fact_236_simps_I6_J,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.19/0.47 ( ( subs @ ( mismatch @ A @ B @ P ) @ C @ D )
% 0.19/0.47 = ( mismatch @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(6)
% 0.19/0.47 thf(fact_237_pi_Ofresh_I1_J,axiom,
% 0.19/0.47 ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(1)
% 0.19/0.47 thf(fact_238_simps_I1_J,axiom,
% 0.19/0.47 ! [C: name,D: name] :
% 0.19/0.47 ( ( subs @ piNil @ C @ D )
% 0.19/0.47 = piNil ) ).
% 0.19/0.47
% 0.19/0.47 % simps(1)
% 0.19/0.47 thf(fact_239_pi_Ofresh_I6_J,axiom,
% 0.19/0.47 ! [A: name,X3: name,X2: name,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( mismatch @ X3 @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X3 )
% 0.19/0.47 & ( fresh_name_name @ A @ X2 )
% 0.19/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(6)
% 0.19/0.47 thf(fact_240_mismatchNilLeft,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,A: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A @ A @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % mismatchNilLeft
% 0.19/0.47 thf(fact_241_pi_Oinject_I5_J,axiom,
% 0.19/0.47 ! [X3: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 0.19/0.47 ( ( ( mismatch @ X3 @ X2 @ X1 )
% 0.19/0.47 = ( mismatch @ Y3 @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X3 = Y3 )
% 0.19/0.47 & ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(5)
% 0.19/0.47 thf(fact_242_pi_Odistinct_I9_J,axiom,
% 0.19/0.47 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(9)
% 0.19/0.47 thf(fact_243_nilSimRight,axiom,
% 0.19/0.47 ! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.19/0.47
% 0.19/0.47 % nilSimRight
% 0.19/0.47 thf(fact_244_pi_Odistinct_I3_J,axiom,
% 0.19/0.47 ! [Pi2: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( tau @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(3)
% 0.19/0.47 thf(fact_245_pi_Odistinct_I39_J,axiom,
% 0.19/0.47 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( ( tau @ Pi )
% 0.19/0.47 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(39)
% 0.19/0.47 thf(fact_246_pi_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( output @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(1)
% 0.19/0.47 thf(fact_247_pi_Odistinct_I25_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(25)
% 0.19/0.47 thf(fact_248_pi_Odistinct_I5_J,axiom,
% 0.19/0.47 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(5)
% 0.19/0.47 thf(fact_249_pi_Odistinct_I51_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( ( input @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(51)
% 0.19/0.47 thf(fact_250_pi_Odistinct_I15_J,axiom,
% 0.19/0.47 ! [Name: name,Pi2: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(15)
% 0.19/0.47 thf(fact_251_pi_Odistinct_I75_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.19/0.47 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(75)
% 0.19/0.47 thf(fact_252_pi_Odistinct_I13_J,axiom,
% 0.19/0.47 ! [Pi12: pi,Pi23: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(13)
% 0.19/0.47 thf(fact_253_pi_Odistinct_I73_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.19/0.47 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(73)
% 0.19/0.47 thf(fact_254_zeroTrans,axiom,
% 0.19/0.47 ! [Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % zeroTrans
% 0.19/0.47 thf(fact_255_nilCases_H,axiom,
% 0.19/0.47 ! [Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % nilCases'
% 0.19/0.47 thf(fact_256_Mismatch,axiom,
% 0.19/0.47 ! [P: pi,Rs: late_residual,A: name,B: name] :
% 0.19/0.47 ( ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( ( A != B )
% 0.19/0.47 => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Mismatch
% 0.19/0.47 thf(fact_257_mismatchCases_H,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ~ ! [P4: pi,A4: name,B3: name] :
% 0.19/0.47 ( ( ( A = A4 )
% 0.19/0.47 & ( B = B3 )
% 0.19/0.47 & ( P = P4 ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ Rs )
% 0.19/0.47 => ( A4 = B3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % mismatchCases'
% 0.19/0.47 thf(fact_258_mismatchTrans,axiom,
% 0.19/0.47 ! [A: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % mismatchTrans
% 0.19/0.47 thf(fact_259_mismatchCases,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.19/0.47 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ( ( ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( ( A != B )
% 0.19/0.47 => ( F @ A @ B ) ) )
% 0.19/0.47 => ( F @ A @ B ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % mismatchCases
% 0.19/0.47 thf(fact_260_resZeroTrans,axiom,
% 0.19/0.47 ! [X: name,Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % resZeroTrans
% 0.19/0.47 thf(fact_261_nilSim_I2_J,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
% 0.19/0.47 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % nilSim(2)
% 0.19/0.47 thf(fact_262_nilSim_I3_J,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 0.19/0.47 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % nilSim(3)
% 0.19/0.47 thf(fact_263_nilSim_I1_J,axiom,
% 0.19/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.19/0.47 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % nilSim(1)
% 0.19/0.47 thf(fact_264_simps_I5_J,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.19/0.47 ( ( subs @ ( match @ A @ B @ P ) @ C @ D )
% 0.19/0.47 = ( match @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(5)
% 0.19/0.47 thf(fact_265_pi_Ofresh_I5_J,axiom,
% 0.19/0.47 ! [A: name,X3: name,X2: name,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( match @ X3 @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X3 )
% 0.19/0.47 & ( fresh_name_name @ A @ X2 )
% 0.19/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(5)
% 0.19/0.47 thf(fact_266_pi_Odistinct_I61_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( ( match @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(61)
% 0.19/0.47 thf(fact_267_pi_Odistinct_I7_J,axiom,
% 0.19/0.47 ! [Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(7)
% 0.19/0.47 thf(fact_268_matchCases,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.19/0.47 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ( ( ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( ( A = B )
% 0.19/0.47 => ( F @ A @ A ) ) )
% 0.19/0.47 => ( F @ A @ B ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % matchCases
% 0.19/0.47 thf(fact_269_matchTrans,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ( A = B ) ) ).
% 0.19/0.47
% 0.19/0.47 % matchTrans
% 0.19/0.47 thf(fact_270_matchCases_H,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ~ ! [P4: pi] :
% 0.19/0.47 ( ( ( B = A )
% 0.19/0.47 & ( P = P4 ) )
% 0.19/0.47 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % matchCases'
% 0.19/0.47 thf(fact_271_Match,axiom,
% 0.19/0.47 ! [P: pi,Rs: late_residual,B: name] :
% 0.19/0.47 ( ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 0.19/0.47
% 0.19/0.47 % Match
% 0.19/0.47 thf(fact_272_pi_Odistinct_I65_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.19/0.47 ( ( match @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(65)
% 0.19/0.47 thf(fact_273_pi_Odistinct_I67_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 0.19/0.47 ( ( match @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( res @ Name @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(67)
% 0.19/0.47 thf(fact_274_pi_Odistinct_I49_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( ( input @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(49)
% 0.19/0.47 thf(fact_275_pi_Odistinct_I23_J,axiom,
% 0.19/0.47 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name2 @ Pi )
% 0.19/0.47 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(23)
% 0.19/0.47 thf(fact_276_pi_Odistinct_I37_J,axiom,
% 0.19/0.47 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 0.19/0.47 ( ( tau @ Pi )
% 0.19/0.47 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(37)
% 0.19/0.47 thf(fact_277_pi_Oinject_I4_J,axiom,
% 0.19/0.47 ! [X3: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 0.19/0.47 ( ( ( match @ X3 @ X2 @ X1 )
% 0.19/0.47 = ( match @ Y3 @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X3 = Y3 )
% 0.19/0.47 & ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(4)
% 0.19/0.47 thf(fact_278_matchNilLeft,axiom,
% 0.19/0.47 ! [A: name,B: name,Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.19/0.47 ( ( A != B )
% 0.19/0.47 => ( strong743114133lation @ piNil @ Rel @ ( match @ A @ B @ P ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % matchNilLeft
% 0.19/0.47 thf(fact_279_pi_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: late_subject > pi > $o,Z: late_subject,Pi: pi] :
% 0.19/0.47 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 0.19/0.47 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
% 0.19/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
% 0.19/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.47 => ( ! [Name4: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ( fresh_717452603ubject @ Name4 @ Z2 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.47 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.strong_inducts
% 0.19/0.47 thf(fact_280_pi_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi: pi] :
% 0.19/0.47 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 0.19/0.47 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
% 0.19/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
% 0.19/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.47 => ( ! [Name4: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.47 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.strong_inducts
% 0.19/0.47 thf(fact_281_pi_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: name > pi > $o,Z: name,Pi: pi] :
% 0.19/0.47 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ( fresh_name_name @ Name23 @ Z2 )
% 0.19/0.47 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.19/0.47 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: name] : ( P @ Za @ Pi24 )
% 0.19/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: name] : ( P @ Za @ Pi24 )
% 0.19/0.48 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Name4: name,Pi3: pi,Z2: name] :
% 0.19/0.48 ( ( fresh_name_name @ Name4 @ Z2 )
% 0.19/0.48 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.19/0.48 => ( ! [Pi3: pi,Z2: name] :
% 0.19/0.48 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.48 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.strong_inducts
% 0.19/0.48 thf(fact_282_pi_Ostrong__inducts,axiom,
% 0.19/0.48 ! [P: pi > pi > $o,Z: pi,Pi: pi] :
% 0.19/0.48 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ( fresh_name_pi @ Name23 @ Z2 )
% 0.19/0.48 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.19/0.48 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.19/0.48 => ( ! [Za: pi] : ( P @ Za @ Pi24 )
% 0.19/0.48 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.19/0.48 => ( ! [Za: pi] : ( P @ Za @ Pi24 )
% 0.19/0.48 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Name4: name,Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.19/0.48 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.19/0.48 => ( ! [Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.48 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.strong_inducts
% 0.19/0.48 thf(fact_283_pi_Ostrong__induct,axiom,
% 0.19/0.48 ! [P: late_subject > pi > $o,Z: late_subject,Pi: pi] :
% 0.19/0.48 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.48 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi3: pi,Z2: late_subject] :
% 0.19/0.48 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.48 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 0.19/0.48 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.19/0.48 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.48 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.48 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
% 0.19/0.48 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.19/0.48 => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
% 0.19/0.48 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
% 0.19/0.48 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.19/0.48 => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
% 0.19/0.48 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Name4: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.48 ( ( fresh_717452603ubject @ Name4 @ Z2 )
% 0.19/0.48 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.19/0.48 => ( ! [Pi3: pi,Z2: late_subject] :
% 0.19/0.48 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.48 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.strong_induct
% 0.19/0.48 thf(fact_284_pi_Ostrong__induct,axiom,
% 0.19/0.48 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi: pi] :
% 0.19/0.48 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.48 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 0.19/0.48 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.48 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 0.19/0.48 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.19/0.48 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.48 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.48 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
% 0.19/0.48 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.19/0.48 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
% 0.19/0.48 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
% 0.19/0.48 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.19/0.48 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
% 0.19/0.48 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Name4: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.48 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 0.19/0.48 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.19/0.48 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 0.19/0.48 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.48 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.strong_induct
% 0.19/0.48 thf(fact_285_pi_Ostrong__induct,axiom,
% 0.19/0.48 ! [P: name > pi > $o,Z: name,Pi: pi] :
% 0.19/0.48 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.48 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi3: pi,Z2: name] :
% 0.19/0.48 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.48 ( ( fresh_name_name @ Name23 @ Z2 )
% 0.19/0.48 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.19/0.48 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.48 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.48 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
% 0.19/0.48 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.19/0.48 => ( ! [Za: name] : ( P @ Za @ Pi24 )
% 0.19/0.48 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
% 0.19/0.48 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.19/0.48 => ( ! [Za: name] : ( P @ Za @ Pi24 )
% 0.19/0.48 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Name4: name,Pi3: pi,Z2: name] :
% 0.19/0.48 ( ( fresh_name_name @ Name4 @ Z2 )
% 0.19/0.48 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.19/0.48 => ( ! [Pi3: pi,Z2: name] :
% 0.19/0.48 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.48 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.strong_induct
% 0.19/0.48 thf(fact_286_pi_Ostrong__induct,axiom,
% 0.19/0.48 ! [P: pi > pi > $o,Z: pi,Pi: pi] :
% 0.19/0.48 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ( fresh_name_pi @ Name23 @ Z2 )
% 0.19/0.48 => ( ( fresh_name_name @ Name23 @ Name13 )
% 0.19/0.48 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.19/0.48 => ( ! [Za: pi] : ( P @ Za @ Pi24 )
% 0.19/0.48 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.19/0.48 => ( ! [Za: pi] : ( P @ Za @ Pi24 )
% 0.19/0.48 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Name4: name,Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ( fresh_name_pi @ Name4 @ Z2 )
% 0.19/0.48 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 0.19/0.48 => ( ! [Pi3: pi,Z2: pi] :
% 0.19/0.48 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.48 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.48 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.strong_induct
% 0.19/0.48 thf(fact_287_pi_Ofresh_I10_J,axiom,
% 0.19/0.48 ! [A: name,X1: pi] :
% 0.19/0.48 ( ( fresh_name_pi @ A @ ( bang @ X1 ) )
% 0.19/0.48 = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.fresh(10)
% 0.19/0.48 thf(fact_288_pi_Ofresh_I7_J,axiom,
% 0.19/0.48 ! [A: name,X2: pi,X1: pi] :
% 0.19/0.48 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 0.19/0.48 = ( ( fresh_name_pi @ A @ X2 )
% 0.19/0.48 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.fresh(7)
% 0.19/0.48 thf(fact_289_simps_I10_J,axiom,
% 0.19/0.48 ! [P: pi,C: name,D: name] :
% 0.19/0.48 ( ( subs @ ( bang @ P ) @ C @ D )
% 0.19/0.48 = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % simps(10)
% 0.19/0.48 thf(fact_290_simps_I7_J,axiom,
% 0.19/0.48 ! [P: pi,Q: pi,C: name,D: name] :
% 0.19/0.48 ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 0.19/0.48 = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % simps(7)
% 0.19/0.48 thf(fact_291_pi_Odistinct_I63_J,axiom,
% 0.19/0.48 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.19/0.48 ( ( match @ Name1 @ Name2 @ Pi )
% 0.19/0.48 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(63)
% 0.19/0.48 thf(fact_292_pi_Odistinct_I69_J,axiom,
% 0.19/0.48 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.19/0.48 ( ( match @ Name1 @ Name2 @ Pi )
% 0.19/0.48 != ( bang @ Pi2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(69)
% 0.19/0.48 thf(fact_293_Bang,axiom,
% 0.19/0.48 ! [P: pi,Rs: late_residual] :
% 0.19/0.48 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 0.19/0.48 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 0.19/0.48
% 0.19/0.48 % Bang
% 0.19/0.48 thf(fact_294_bangCases,axiom,
% 0.19/0.48 ! [P: pi,Rs: late_residual] :
% 0.19/0.48 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 0.19/0.48 => ~ ! [P4: pi] :
% 0.19/0.48 ( ( ( bang @ P )
% 0.19/0.48 = ( bang @ P4 ) )
% 0.19/0.48 => ~ ( late_transitions @ ( par @ P4 @ ( bang @ P4 ) ) @ Rs ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % bangCases
% 0.19/0.48 thf(fact_295_pi_Odistinct_I87_J,axiom,
% 0.19/0.48 ! [Pi1: pi,Pi22: pi,Pi2: pi] :
% 0.19/0.48 ( ( par @ Pi1 @ Pi22 )
% 0.19/0.48 != ( bang @ Pi2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(87)
% 0.19/0.48 thf(fact_296_pi_Odistinct_I89_J,axiom,
% 0.19/0.48 ! [Name3: name,Pi: pi,Pi2: pi] :
% 0.19/0.48 ( ( res @ Name3 @ Pi )
% 0.19/0.48 != ( bang @ Pi2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(89)
% 0.19/0.48 thf(fact_297_pi_Odistinct_I59_J,axiom,
% 0.19/0.48 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.19/0.48 ( ( input @ Name1 @ Name2 @ Pi )
% 0.19/0.48 != ( bang @ Pi2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(59)
% 0.19/0.48 thf(fact_298_pi_Odistinct_I33_J,axiom,
% 0.19/0.48 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.19/0.48 ( ( output @ Name1 @ Name2 @ Pi )
% 0.19/0.48 != ( bang @ Pi2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(33)
% 0.19/0.48 thf(fact_299_Sum2,axiom,
% 0.19/0.48 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.19/0.48 ( ( late_transitions @ Q @ Rs )
% 0.19/0.48 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.19/0.48
% 0.19/0.48 % Sum2
% 0.19/0.48 thf(fact_300_Sum1,axiom,
% 0.19/0.48 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.19/0.48 ( ( late_transitions @ P @ Rs )
% 0.19/0.48 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.19/0.48
% 0.19/0.48 % Sum1
% 0.19/0.48 thf(fact_301_sumCases_H,axiom,
% 0.19/0.48 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.19/0.48 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.19/0.48 => ( ~ ( late_transitions @ P @ Rs )
% 0.19/0.48 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % sumCases'
% 0.19/0.48 thf(fact_302_sumCases,axiom,
% 0.19/0.48 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.19/0.48 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.19/0.48 => ( ~ ( late_transitions @ P @ Rs )
% 0.19/0.48 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % sumCases
% 0.19/0.48 thf(fact_303_pi_Odistinct_I47_J,axiom,
% 0.19/0.48 ! [Pi: pi,Pi2: pi] :
% 0.19/0.48 ( ( tau @ Pi )
% 0.19/0.48 != ( bang @ Pi2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(47)
% 0.19/0.48 thf(fact_304_pi_Odistinct_I79_J,axiom,
% 0.19/0.48 ! [Pi1: pi,Pi22: pi,Pi12: pi,Pi23: pi] :
% 0.19/0.48 ( ( sum @ Pi1 @ Pi22 )
% 0.19/0.48 != ( par @ Pi12 @ Pi23 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(79)
% 0.19/0.48 thf(fact_305_pi_Odistinct_I81_J,axiom,
% 0.19/0.48 ! [Pi1: pi,Pi22: pi,Name: name,Pi2: pi] :
% 0.19/0.48 ( ( sum @ Pi1 @ Pi22 )
% 0.19/0.48 != ( res @ Name @ Pi2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(81)
% 0.19/0.48 thf(fact_306_pi_Odistinct_I53_J,axiom,
% 0.19/0.48 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.19/0.48 ( ( input @ Name1 @ Name2 @ Pi )
% 0.19/0.48 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(53)
% 0.19/0.48 thf(fact_307_pi_Odistinct_I27_J,axiom,
% 0.19/0.48 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.19/0.48 ( ( output @ Name1 @ Name2 @ Pi )
% 0.19/0.48 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(27)
% 0.19/0.48 thf(fact_308_pi_Odistinct_I41_J,axiom,
% 0.19/0.48 ! [Pi: pi,Pi12: pi,Pi23: pi] :
% 0.19/0.48 ( ( tau @ Pi )
% 0.19/0.48 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(41)
% 0.19/0.48 thf(fact_309_pi_Oinject_I9_J,axiom,
% 0.19/0.48 ! [X1: pi,Y1: pi] :
% 0.19/0.48 ( ( ( bang @ X1 )
% 0.19/0.48 = ( bang @ Y1 ) )
% 0.19/0.48 = ( X1 = Y1 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.inject(9)
% 0.19/0.48 thf(fact_310_pi_Oinject_I6_J,axiom,
% 0.19/0.48 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.19/0.48 ( ( ( sum @ X2 @ X1 )
% 0.19/0.48 = ( sum @ Y2 @ Y1 ) )
% 0.19/0.48 = ( ( X2 = Y2 )
% 0.19/0.48 & ( X1 = Y1 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.inject(6)
% 0.19/0.48 thf(fact_311_pi_Odistinct_I83_J,axiom,
% 0.19/0.48 ! [Pi1: pi,Pi22: pi,Pi2: pi] :
% 0.19/0.48 ( ( sum @ Pi1 @ Pi22 )
% 0.19/0.48 != ( bang @ Pi2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(83)
% 0.19/0.48 thf(fact_312_pi_Odistinct_I11_J,axiom,
% 0.19/0.48 ! [Pi12: pi,Pi23: pi] :
% 0.19/0.48 ( piNil
% 0.19/0.48 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(11)
% 0.19/0.48 thf(fact_313_pi_Odistinct_I17_J,axiom,
% 0.19/0.48 ! [Pi2: pi] :
% 0.19/0.48 ( piNil
% 0.19/0.48 != ( bang @ Pi2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(17)
% 0.19/0.48 thf(fact_314_pi_Odistinct_I71_J,axiom,
% 0.19/0.48 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 0.19/0.48 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.19/0.48 != ( sum @ Pi12 @ Pi23 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(71)
% 0.19/0.48 thf(fact_315_pi_Odistinct_I77_J,axiom,
% 0.19/0.48 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 0.19/0.48 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 0.19/0.48 != ( bang @ Pi2 ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.distinct(77)
% 0.19/0.48 thf(fact_316_pi_Oinducts,axiom,
% 0.19/0.48 ! [P: pi > $o,Pi: pi] :
% 0.19/0.48 ( ( P @ piNil )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.19/0.48 ( ( P @ Pi3 )
% 0.19/0.48 => ( P @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi3: pi] :
% 0.19/0.48 ( ( P @ Pi3 )
% 0.19/0.48 => ( P @ ( tau @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.19/0.48 ( ( P @ Pi3 )
% 0.19/0.48 => ( P @ ( input @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.19/0.48 ( ( P @ Pi3 )
% 0.19/0.48 => ( P @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 0.19/0.48 ( ( P @ Pi3 )
% 0.19/0.48 => ( P @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi] :
% 0.19/0.48 ( ( P @ Pi13 )
% 0.19/0.48 => ( ( P @ Pi24 )
% 0.19/0.48 => ( P @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Pi13: pi,Pi24: pi] :
% 0.19/0.48 ( ( P @ Pi13 )
% 0.19/0.48 => ( ( P @ Pi24 )
% 0.19/0.48 => ( P @ ( par @ Pi13 @ Pi24 ) ) ) )
% 0.19/0.48 => ( ! [Name4: name,Pi3: pi] :
% 0.19/0.48 ( ( P @ Pi3 )
% 0.19/0.48 => ( P @ ( res @ Name4 @ Pi3 ) ) )
% 0.19/0.48 => ( ! [Pi3: pi] :
% 0.19/0.48 ( ( P @ Pi3 )
% 0.19/0.48 => ( P @ ( bang @ Pi3 ) ) )
% 0.19/0.48 => ( P @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.inducts
% 0.19/0.48
% 0.19/0.48 % Helper facts (3)
% 0.19/0.48 thf(help_If_3_1_If_001t__Agent__Oname_T,axiom,
% 0.19/0.48 ! [P: $o] :
% 0.19/0.48 ( ( P = $true )
% 0.19/0.48 | ( P = $false ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 0.19/0.48 ! [X: name,Y: name] :
% 0.19/0.48 ( ( if_name @ $false @ X @ Y )
% 0.19/0.48 = Y ) ).
% 0.19/0.48
% 0.19/0.48 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 0.19/0.48 ! [X: name,Y: name] :
% 0.19/0.48 ( ( if_name @ $true @ X @ Y )
% 0.19/0.48 = X ) ).
% 0.19/0.48
% 0.19/0.48 % Conjectures (1)
% 0.19/0.48 thf(conj_0,conjecture,
% 0.19/0.48 ? [P8: pi] :
% 0.19/0.48 ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ P8 ) )
% 0.19/0.48 & ( strong2129052853vative @ P8 @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 2.86/1.53 ---- Embedded in THF ---
% 2.86/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.86/1.53 %%% Generated on Tue Feb 24 08:29:01 EST 2026
% 2.86/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.86/1.53 %%% Logic specification used:
% 2.86/1.53 %%% thf(spec, logic, $$dhol).
% 2.86/1.53
% 2.86/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oMnfvnLLzL/DTF2DTF17066.p
% See solution above
% 2.86/1.53 ------------------------
% 2.86/1.56 ---- Cleaned THF ---
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 2.86/1.56 produc1462499409ion_pi: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__Osubject_J,type,
% 2.86/1.56 produc691362330ubject: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 2.86/1.56 produc1834551554reeRes: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 2.86/1.56 produc405342261i_name: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 2.86/1.56 produc629157763_pi_pi: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 2.86/1.56 produc1359399907ubject: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 2.86/1.56 produc355105483reeRes: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 2.86/1.56 produc214645451ubject: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 2.86/1.56 produc1357834675reeRes: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 2.86/1.56 produc1998742700t_name: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 2.86/1.56 produc2052722628s_name: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
% 2.86/1.56 produc865358760ubject: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 2.86/1.56 produc2008547984reeRes: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 2.86/1.56 produc140253050ect_pi: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 2.86/1.56 produc992857746Res_pi: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 2.86/1.56 set_Pr1834926343_pi_pi: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 2.86/1.56 product_prod_pi_pi: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__Osubject_J,type,
% 2.86/1.56 noption_Late_subject: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__OfreeRes_J,type,
% 2.86/1.56 noption_Late_freeRes: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Nominal__Onoption_It__Agent__Oname_J,type,
% 2.86/1.56 noption_name: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 2.86/1.56 noption_pi: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Late____Semantics__Oresidual,type,
% 2.86/1.56 late_residual: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Late____Semantics__Osubject,type,
% 2.86/1.56 late_subject: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 2.86/1.56 late_freeRes: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Agent__Oname,type,
% 2.86/1.56 name: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(ty_n_t__Agent__Opi,type,
% 2.86/1.56 pi: $tType ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Opi_OBang,type,
% 2.86/1.56 bang: pi > pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Opi_OInput,type,
% 2.86/1.56 input: name > name > pi > pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Opi_OMatch,type,
% 2.86/1.56 match: name > name > pi > pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Opi_OMismatch,type,
% 2.86/1.56 mismatch: name > name > pi > pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Opi_OOutput,type,
% 2.86/1.56 output: name > name > pi > pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Opi_OPar,type,
% 2.86/1.56 par: pi > pi > pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Opi_OPiNil,type,
% 2.86/1.56 piNil: pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Opi_ORes,type,
% 2.86/1.56 res: name > pi > pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Opi_OSum,type,
% 2.86/1.56 sum: pi > pi > pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Opi_OTau,type,
% 2.86/1.56 tau: pi > pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Osubs,type,
% 2.86/1.56 subs: pi > name > name > pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Agent_Osubst__name,type,
% 2.86/1.56 subst_name: name > name > name > name ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_If_001t__Agent__Oname,type,
% 2.86/1.56 if_name: $o > name > name > name ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 2.86/1.56 late_OutputR: name > name > late_freeRes ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 2.86/1.56 late_TauR: late_freeRes ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 2.86/1.56 late_BoundR: late_subject > name > pi > late_residual ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 2.86/1.56 late_FreeR: late_freeRes > pi > late_residual ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 2.86/1.56 late_BoundOutputS: name > late_subject ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 2.86/1.56 late_InputS: name > late_subject ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Late__Semantics_Otransitions,type,
% 2.86/1.56 late_transitions: pi > late_residual > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Oname,type,
% 2.86/1.56 abs_fun_name_name: name > name > name > noption_name ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Opi,type,
% 2.86/1.56 abs_fun_name_pi: name > pi > name > noption_pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 2.86/1.56 abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 2.86/1.56 abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J,type,
% 2.86/1.56 fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 2.86/1.56 fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J,type,
% 2.86/1.56 fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J,type,
% 2.86/1.56 fresh_728038529ubject: name > ( name > noption_Late_subject ) > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Oname,type,
% 2.86/1.56 fresh_name_name: name > name > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Opi,type,
% 2.86/1.56 fresh_name_pi: name > pi > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 2.86/1.56 fresh_1641682979reeRes: name > late_freeRes > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Oresidual,type,
% 2.86/1.56 fresh_81631222sidual: name > late_residual > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 2.86/1.56 fresh_717452603ubject: name > late_subject > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 2.86/1.56 fresh_225680151ion_pi: name > produc1462499409ion_pi > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 2.86/1.56 fresh_453496559i_name: name > produc405342261i_name > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 2.86/1.56 fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 2.86/1.56 fresh_1711070152reeRes: name > produc1834551554reeRes > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__Osubject_J,type,
% 2.86/1.56 fresh_567880928ubject: name > produc691362330ubject > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 2.86/1.56 fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
% 2.86/1.56 fresh_820177506ubject: name > produc865358760ubject > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 2.86/1.56 fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 2.86/1.56 fresh_2007541374s_name: name > produc2052722628s_name > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 2.86/1.56 fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 2.86/1.56 fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 2.86/1.56 fresh_1498103185ubject: name > produc214645451ubject > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 2.86/1.56 fresh_1953561446t_name: name > produc1998742700t_name > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 2.86/1.56 fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 2.86/1.56 fresh_1638563217reeRes: name > produc355105483reeRes > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 2.86/1.56 fresh_495373993ubject: name > produc1359399907ubject > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 2.86/1.56 produc1342893193ion_pi: ( name > noption_pi ) > ( name > noption_pi ) > produc1462499409ion_pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Oname,type,
% 2.86/1.56 produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Opi,type,
% 2.86/1.56 produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__OfreeRes,type,
% 2.86/1.56 produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__Osubject,type,
% 2.86/1.56 produc581368530ubject: ( name > noption_pi ) > late_subject > produc691362330ubject ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 2.86/1.56 produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 2.86/1.56 produc607574050ubject: name > late_subject > produc865358760ubject ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 2.86/1.56 product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 2.86/1.56 produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 2.86/1.56 produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 2.86/1.56 produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
% 2.86/1.56 produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 2.86/1.56 produc1647375838t_name: late_subject > name > produc1998742700t_name ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
% 2.86/1.56 produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 2.86/1.56 produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 2.86/1.56 produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 2.86/1.56 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 2.86/1.56 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 2.86/1.56 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 2.86/1.56 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 2.86/1.56 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 2.86/1.56
% 2.86/1.56 thf(sy_v_P,type,
% 2.86/1.56 p: pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_v_PQR____,type,
% 2.86/1.56 pqr: pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_v_Q,type,
% 2.86/1.56 q: pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_v_QR____,type,
% 2.86/1.56 qr: pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_v_Q_H____,type,
% 2.86/1.56 q2: pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_v_R,type,
% 2.86/1.56 r: pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_v_Rel,type,
% 2.86/1.56 rel: set_Pr1834926343_pi_pi ).
% 2.86/1.56
% 2.86/1.56 thf(sy_v_a____,type,
% 2.86/1.56 a: late_subject ).
% 2.86/1.56
% 2.86/1.56 thf(sy_v_x____,type,
% 2.86/1.56 x: name ).
% 2.86/1.56
% 2.86/1.56 thf(fact_0__092_060open_062derivative_A_I_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_J_A_IP_A_092_060parallel_062_AQ_H_A_092_060parallel_062_AR_J_Aa_Ax_ARel_092_060close_062,axiom,
% 2.86/1.56 strong2129052853vative @ ( par @ ( par @ p @ q2 ) @ r ) @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel ).
% 2.86/1.56
% 2.86/1.56 thf(fact_1_cPar1_Ohyps,axiom,
% 2.86/1.56 late_transitions @ q @ ( late_BoundR @ a @ x @ q2 ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_2__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_A_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_092_060close_062,axiom,
% 2.86/1.56 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ ( par @ ( par @ p @ q2 ) @ r ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_3_cPar2_Ohyps,axiom,
% 2.86/1.56 late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ a @ x @ qr ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_4_Bound_Ohyps_I1_J,axiom,
% 2.86/1.56 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_BoundR @ a @ x @ pqr ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_5__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062,axiom,
% 2.86/1.56 late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ a @ x @ ( par @ p @ q2 ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_6_Bound_Ohyps_I2_J,axiom,
% 2.86/1.56 fresh_name_pi @ x @ ( par @ ( par @ p @ q ) @ r ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_7__092_060open_062x_A_092_060sharp_062_AQ_A_092_060parallel_062_AR_092_060close_062,axiom,
% 2.86/1.56 fresh_name_pi @ x @ ( par @ q @ r ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_8__092_060open_062x_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 2.86/1.56 fresh_name_pi @ x @ q ).
% 2.86/1.56
% 2.86/1.56 thf(fact_9__092_060open_062x_A_092_060sharp_062_AP_092_060close_062,axiom,
% 2.86/1.56 fresh_name_pi @ x @ p ).
% 2.86/1.56
% 2.86/1.56 thf(fact_10__092_060open_062x_A_092_060sharp_062_AR_092_060close_062,axiom,
% 2.86/1.56 fresh_name_pi @ x @ r ).
% 2.86/1.56
% 2.86/1.56 thf(fact_11_Ass,axiom,
% 2.86/1.56 ! [S: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S @ T ) @ U ) @ ( par @ S @ ( par @ T @ U ) ) ) @ rel ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_12_pi_Oinject_I7_J,axiom,
% 2.86/1.56 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.86/1.56 ( ( ( par @ X2 @ X1 )
% 2.86/1.56 = ( par @ Y2 @ Y1 ) )
% 2.86/1.56 = ( ( X2 = Y2 )
% 2.86/1.56 & ( X1 = Y1 ) ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_13_Late__Semantics_OPar1B,axiom,
% 2.86/1.56 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 2.86/1.56 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.86/1.56 => ( ( fresh_name_pi @ X @ Q )
% 2.86/1.56 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_14_Late__Semantics_OPar2B,axiom,
% 2.86/1.56 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 2.86/1.56 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 2.86/1.56 => ( ( fresh_name_pi @ X @ P )
% 2.86/1.56 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_15_parCasesB,axiom,
% 2.86/1.56 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 2.86/1.56 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 2.86/1.56 => ( ( fresh_name_pi @ X @ P )
% 2.86/1.56 => ( ( fresh_name_pi @ X @ Q )
% 2.86/1.56 => ( ! [P3: pi] :
% 2.86/1.56 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 2.86/1.56 => ( Prop @ ( par @ P3 @ Q ) ) )
% 2.86/1.56 => ( ! [Q3: pi] :
% 2.86/1.56 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 2.86/1.56 => ( Prop @ ( par @ P @ Q3 ) ) )
% 2.86/1.56 => ( Prop @ PQ ) ) ) ) ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_16_tauBoundTrans,axiom,
% 2.86/1.56 ! [P: pi,A: late_subject,X: name,P2: pi] :
% 2.86/1.56 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P2 ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_17_outputBoundTrans,axiom,
% 2.86/1.56 ! [A: name,B: name,P: pi,C: late_subject,X: name,P2: pi] :
% 2.86/1.56 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C @ X @ P2 ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_18_Res,axiom,
% 2.86/1.56 ! [S: pi,T: pi,X: name] :
% 2.86/1.56 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S @ T ) @ rel )
% 2.86/1.56 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X @ S ) @ ( res @ X @ T ) ) @ rel ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_19_FreshExt_H,axiom,
% 2.86/1.56 ! [X: name,U: pi,S: pi,T: pi] :
% 2.86/1.56 ( ( fresh_name_pi @ X @ U )
% 2.86/1.56 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X @ ( par @ S @ T ) ) @ U ) @ ( res @ X @ ( par @ S @ ( par @ T @ U ) ) ) ) @ rel ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_20_FreshExt,axiom,
% 2.86/1.56 ! [X: name,S: pi,T: pi,U: pi] :
% 2.86/1.56 ( ( fresh_name_pi @ X @ S )
% 2.86/1.56 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X @ ( par @ ( par @ S @ T ) @ U ) ) @ ( par @ S @ ( res @ X @ ( par @ T @ U ) ) ) ) @ rel ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_21_pi_Ofresh_I8_J,axiom,
% 2.86/1.56 ! [A: name,X2: pi,X1: pi] :
% 2.86/1.56 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 2.86/1.56 = ( ( fresh_name_pi @ A @ X2 )
% 2.86/1.56 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_22_pi_Ofresh_I3_J,axiom,
% 2.86/1.56 ! [A: name,X1: pi] :
% 2.86/1.56 ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 2.86/1.56 = ( fresh_name_pi @ A @ X1 ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_23_pi_Oinject_I2_J,axiom,
% 2.86/1.56 ! [X1: pi,Y1: pi] :
% 2.86/1.56 ( ( ( tau @ X1 )
% 2.86/1.56 = ( tau @ Y1 ) )
% 2.86/1.56 = ( X1 = Y1 ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_24_pi_Oinject_I1_J,axiom,
% 2.86/1.56 ! [X3: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 2.86/1.56 ( ( ( output @ X3 @ X2 @ X1 )
% 2.86/1.56 = ( output @ Y3 @ Y2 @ Y1 ) )
% 2.86/1.56 = ( ( X3 = Y3 )
% 2.86/1.56 & ( X2 = Y2 )
% 2.86/1.56 & ( X1 = Y1 ) ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_25_pi_Odistinct_I45_J,axiom,
% 2.86/1.56 ! [Pi: pi,Name: name,Pi2: pi] :
% 2.86/1.56 ( ( tau @ Pi )
% 2.86/1.56 != ( res @ Name @ Pi2 ) ) ).
% 2.86/1.56
% 2.86/1.56 thf(fact_26_pi_Odistinct_I31_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 2.86/1.57 ( ( output @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( res @ Name @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_27_pi_Odistinct_I19_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 2.86/1.57 ( ( output @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( tau @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_28_resTrans_I1_J,axiom,
% 2.86/1.57 ! [X: name,B: name,P: pi,Rs: late_residual] :
% 2.86/1.57 ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_29_freshRes,axiom,
% 2.86/1.57 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_30_name__exists__fresh,axiom,
% 2.86/1.57 ! [X: late_subject] :
% 2.86/1.57 ~ ! [C2: name] :
% 2.86/1.57 ~ ( fresh_717452603ubject @ C2 @ X ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_31_name__exists__fresh,axiom,
% 2.86/1.57 ! [X: late_freeRes] :
% 2.86/1.57 ~ ! [C2: name] :
% 2.86/1.57 ~ ( fresh_1641682979reeRes @ C2 @ X ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_32_name__exists__fresh,axiom,
% 2.86/1.57 ! [X: name] :
% 2.86/1.57 ~ ! [C2: name] :
% 2.86/1.57 ~ ( fresh_name_name @ C2 @ X ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_33_name__exists__fresh,axiom,
% 2.86/1.57 ! [X: pi] :
% 2.86/1.57 ~ ! [C2: name] :
% 2.86/1.57 ~ ( fresh_name_pi @ C2 @ X ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_34_pi_Odistinct_I85_J,axiom,
% 2.86/1.57 ! [Pi1: pi,Pi22: pi,Name: name,Pi2: pi] :
% 2.86/1.57 ( ( par @ Pi1 @ Pi22 )
% 2.86/1.57 != ( res @ Name @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_35_pi_Odistinct_I29_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( ( output @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( par @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_36_pi_Odistinct_I43_J,axiom,
% 2.86/1.57 ! [Pi: pi,Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( ( tau @ Pi )
% 2.86/1.57 != ( par @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_37_resTauBoundTrans,axiom,
% 2.86/1.57 ! [X: name,P: pi,A: late_subject,Y: name,P2: pi] :
% 2.86/1.57 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_38_freshBoundDerivative_I2_J,axiom,
% 2.86/1.57 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ P )
% 2.86/1.57 => ( ( Y != X )
% 2.86/1.57 => ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_39_fresh__prod,axiom,
% 2.86/1.57 ! [A: name,X: late_subject,Y: late_subject] :
% 2.86/1.57 ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y ) )
% 2.86/1.57 = ( ( fresh_717452603ubject @ A @ X )
% 2.86/1.57 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_40_fresh__prod,axiom,
% 2.86/1.57 ! [A: name,X: late_subject,Y: late_freeRes] :
% 2.86/1.57 ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y ) )
% 2.86/1.57 = ( ( fresh_717452603ubject @ A @ X )
% 2.86/1.57 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_41_fresh__prod,axiom,
% 2.86/1.57 ! [A: name,X: late_subject,Y: name] :
% 2.86/1.57 ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y ) )
% 2.86/1.57 = ( ( fresh_717452603ubject @ A @ X )
% 2.86/1.57 & ( fresh_name_name @ A @ Y ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_42_fresh__prod,axiom,
% 2.86/1.57 ! [A: name,X: late_subject,Y: pi] :
% 2.86/1.57 ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y ) )
% 2.86/1.57 = ( ( fresh_717452603ubject @ A @ X )
% 2.86/1.57 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_43_fresh__prod,axiom,
% 2.86/1.57 ! [A: name,X: late_freeRes,Y: late_subject] :
% 2.86/1.57 ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y ) )
% 2.86/1.57 = ( ( fresh_1641682979reeRes @ A @ X )
% 2.86/1.57 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_44_fresh__prod,axiom,
% 2.86/1.57 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 2.86/1.57 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
% 2.86/1.57 = ( ( fresh_1641682979reeRes @ A @ X )
% 2.86/1.57 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_45_fresh__prod,axiom,
% 2.86/1.57 ! [A: name,X: late_freeRes,Y: name] :
% 2.86/1.57 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
% 2.86/1.57 = ( ( fresh_1641682979reeRes @ A @ X )
% 2.86/1.57 & ( fresh_name_name @ A @ Y ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_46_fresh__prod,axiom,
% 2.86/1.57 ! [A: name,X: late_freeRes,Y: pi] :
% 2.86/1.57 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
% 2.86/1.57 = ( ( fresh_1641682979reeRes @ A @ X )
% 2.86/1.57 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_47_fresh__prod,axiom,
% 2.86/1.57 ! [A: name,X: name,Y: late_subject] :
% 2.86/1.57 ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y ) )
% 2.86/1.57 = ( ( fresh_name_name @ A @ X )
% 2.86/1.57 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_48_fresh__prod,axiom,
% 2.86/1.57 ! [A: name,X: name,Y: late_freeRes] :
% 2.86/1.57 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
% 2.86/1.57 = ( ( fresh_name_name @ A @ X )
% 2.86/1.57 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_49_prod_Oinject,axiom,
% 2.86/1.57 ! [X1: name > noption_pi,X2: late_subject,Y1: name > noption_pi,Y2: late_subject] :
% 2.86/1.57 ( ( ( produc581368530ubject @ X1 @ X2 )
% 2.86/1.57 = ( produc581368530ubject @ Y1 @ Y2 ) )
% 2.86/1.57 = ( ( X1 = Y1 )
% 2.86/1.57 & ( X2 = Y2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_50_prod_Oinject,axiom,
% 2.86/1.57 ! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y2: late_freeRes] :
% 2.86/1.57 ( ( ( produc1505598906reeRes @ X1 @ X2 )
% 2.86/1.57 = ( produc1505598906reeRes @ Y1 @ Y2 ) )
% 2.86/1.57 = ( ( X1 = Y1 )
% 2.86/1.57 & ( X2 = Y2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_51_prod_Oinject,axiom,
% 2.86/1.57 ! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y2: name] :
% 2.86/1.57 ( ( ( produc540578151i_name @ X1 @ X2 )
% 2.86/1.57 = ( produc540578151i_name @ Y1 @ Y2 ) )
% 2.86/1.57 = ( ( X1 = Y1 )
% 2.86/1.57 & ( X2 = Y2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_52_prod_Oinject,axiom,
% 2.86/1.57 ! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y2: pi] :
% 2.86/1.57 ( ( ( produc1820286517_pi_pi @ X1 @ X2 )
% 2.86/1.57 = ( produc1820286517_pi_pi @ Y1 @ Y2 ) )
% 2.86/1.57 = ( ( X1 = Y1 )
% 2.86/1.57 & ( X2 = Y2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_53_prod_Oinject,axiom,
% 2.86/1.57 ! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y2: name > noption_pi] :
% 2.86/1.57 ( ( ( produc1342893193ion_pi @ X1 @ X2 )
% 2.86/1.57 = ( produc1342893193ion_pi @ Y1 @ Y2 ) )
% 2.86/1.57 = ( ( X1 = Y1 )
% 2.86/1.57 & ( X2 = Y2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_54_prod_Oinject,axiom,
% 2.86/1.57 ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 2.86/1.57 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 2.86/1.57 = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 2.86/1.57 = ( ( X1 = Y1 )
% 2.86/1.57 & ( X2 = Y2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_55_old_Oprod_Oinject,axiom,
% 2.86/1.57 ! [A: name > noption_pi,B: late_subject,A2: name > noption_pi,B2: late_subject] :
% 2.86/1.57 ( ( ( produc581368530ubject @ A @ B )
% 2.86/1.57 = ( produc581368530ubject @ A2 @ B2 ) )
% 2.86/1.57 = ( ( A = A2 )
% 2.86/1.57 & ( B = B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_56_old_Oprod_Oinject,axiom,
% 2.86/1.57 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 2.86/1.57 ( ( ( produc1505598906reeRes @ A @ B )
% 2.86/1.57 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 2.86/1.57 = ( ( A = A2 )
% 2.86/1.57 & ( B = B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_57_old_Oprod_Oinject,axiom,
% 2.86/1.57 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 2.86/1.57 ( ( ( produc540578151i_name @ A @ B )
% 2.86/1.57 = ( produc540578151i_name @ A2 @ B2 ) )
% 2.86/1.57 = ( ( A = A2 )
% 2.86/1.57 & ( B = B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_58_old_Oprod_Oinject,axiom,
% 2.86/1.57 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 2.86/1.57 ( ( ( produc1820286517_pi_pi @ A @ B )
% 2.86/1.57 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 2.86/1.57 = ( ( A = A2 )
% 2.86/1.57 & ( B = B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_59_old_Oprod_Oinject,axiom,
% 2.86/1.57 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 2.86/1.57 ( ( ( produc1342893193ion_pi @ A @ B )
% 2.86/1.57 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 2.86/1.57 = ( ( A = A2 )
% 2.86/1.57 & ( B = B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_60_old_Oprod_Oinject,axiom,
% 2.86/1.57 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 2.86/1.57 ( ( ( product_Pair_pi_pi @ A @ B )
% 2.86/1.57 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 2.86/1.57 = ( ( A = A2 )
% 2.86/1.57 & ( B = B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_61_fresh__prodD_I2_J,axiom,
% 2.86/1.57 ! [A: name,X: name > noption_pi,Y: late_subject] :
% 2.86/1.57 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y ) )
% 2.86/1.57 => ( fresh_717452603ubject @ A @ Y ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_62_fresh__prodD_I2_J,axiom,
% 2.86/1.57 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 2.86/1.57 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 2.86/1.57 => ( fresh_1641682979reeRes @ A @ Y ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_63_fresh__prodD_I2_J,axiom,
% 2.86/1.57 ! [A: name,X: name > noption_pi,Y: name] :
% 2.86/1.57 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 2.86/1.57 => ( fresh_name_name @ A @ Y ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_64_fresh__prodD_I2_J,axiom,
% 2.86/1.57 ! [A: name,X: name > noption_pi,Y: pi] :
% 2.86/1.57 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 2.86/1.57 => ( fresh_name_pi @ A @ Y ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_65_fresh__prodD_I2_J,axiom,
% 2.86/1.57 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 2.86/1.57 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 2.86/1.57 => ( fresh_543891186ion_pi @ A @ Y ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_66_fresh__prodD_I2_J,axiom,
% 2.86/1.57 ! [A: name,X: pi,Y: pi] :
% 2.86/1.57 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 2.86/1.57 => ( fresh_name_pi @ A @ Y ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_67_fresh__prodD_I1_J,axiom,
% 2.86/1.57 ! [A: name,X: name > noption_pi,Y: late_subject] :
% 2.86/1.57 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y ) )
% 2.86/1.57 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_68_fresh__prodD_I1_J,axiom,
% 2.86/1.57 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 2.86/1.57 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 2.86/1.57 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_69_fresh__prodD_I1_J,axiom,
% 2.86/1.57 ! [A: name,X: name > noption_pi,Y: name] :
% 2.86/1.57 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 2.86/1.57 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_70_fresh__prodD_I1_J,axiom,
% 2.86/1.57 ! [A: name,X: name > noption_pi,Y: pi] :
% 2.86/1.57 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 2.86/1.57 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_71_fresh__prodD_I1_J,axiom,
% 2.86/1.57 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 2.86/1.57 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 2.86/1.57 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_72_fresh__prodD_I1_J,axiom,
% 2.86/1.57 ! [A: name,X: pi,Y: pi] :
% 2.86/1.57 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 2.86/1.57 => ( fresh_name_pi @ A @ X ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_73_resOutputInputTrans,axiom,
% 2.86/1.57 ! [X: name,A: name,B: name,P: pi,C: name,Y: name,P2: pi] :
% 2.86/1.57 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_74_transitions_OResB,axiom,
% 2.86/1.57 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Y @ A )
% 2.86/1.57 => ( ( Y != X )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ P )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X @ A )
% 2.86/1.57 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_75_transitions_OPar2B,axiom,
% 2.86/1.57 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ Q )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X @ A )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_76_transitions_OPar1B,axiom,
% 2.86/1.57 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ Q )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X @ A )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_77_mem__Collect__eq,axiom,
% 2.86/1.57 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 2.86/1.57 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 2.86/1.57 = ( P @ A ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_78_Collect__mem__eq,axiom,
% 2.86/1.57 ! [A3: set_Pr1834926343_pi_pi] :
% 2.86/1.57 ( ( collec1051790738_pi_pi
% 2.86/1.57 @ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A3 ) )
% 2.86/1.57 = A3 ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_79_Collect__cong,axiom,
% 2.86/1.57 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 2.86/1.57 ( ! [X5: product_prod_pi_pi] :
% 2.86/1.57 ( ( P @ X5 )
% 2.86/1.57 = ( Q @ X5 ) )
% 2.86/1.57 => ( ( collec1051790738_pi_pi @ P )
% 2.86/1.57 = ( collec1051790738_pi_pi @ Q ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_80_parCasesB_H,axiom,
% 2.86/1.57 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 2.86/1.57 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 2.86/1.57 => ( ! [P4: pi,A4: late_subject,X5: name,P3: pi,Q4: pi] :
% 2.86/1.57 ( ( ( par @ P @ Q )
% 2.86/1.57 = ( par @ P4 @ Q4 ) )
% 2.86/1.57 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 2.86/1.57 = ( late_BoundR @ A4 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 2.86/1.57 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ P4 )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ Q4 )
% 2.86/1.57 => ~ ( fresh_717452603ubject @ X5 @ A4 ) ) ) ) ) )
% 2.86/1.57 => ~ ! [Q4: pi,A4: late_subject,X5: name,Q3: pi,P4: pi] :
% 2.86/1.57 ( ( ( par @ P @ Q )
% 2.86/1.57 = ( par @ P4 @ Q4 ) )
% 2.86/1.57 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 2.86/1.57 = ( late_BoundR @ A4 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 2.86/1.57 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ P4 )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ Q4 )
% 2.86/1.57 => ~ ( fresh_717452603ubject @ X5 @ A4 ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_81_pi_Ofresh_I2_J,axiom,
% 2.86/1.57 ! [A: name,X3: name,X2: name,X1: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ A @ ( output @ X3 @ X2 @ X1 ) )
% 2.86/1.57 = ( ( fresh_name_name @ A @ X3 )
% 2.86/1.57 & ( fresh_name_name @ A @ X2 )
% 2.86/1.57 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_82_subject_Ofresh_I1_J,axiom,
% 2.86/1.57 ! [A: name,X1: name] :
% 2.86/1.57 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 2.86/1.57 = ( fresh_name_name @ A @ X1 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_83_freshResidual,axiom,
% 2.86/1.57 ! [P: pi,Rs: late_residual,X: name] :
% 2.86/1.57 ( ( late_transitions @ P @ Rs )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ P )
% 2.86/1.57 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_84_Late__Semantics_OResB,axiom,
% 2.86/1.57 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Y @ A )
% 2.86/1.57 => ( ( Y != X )
% 2.86/1.57 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_85_freshBoundDerivative_I1_J,axiom,
% 2.86/1.57 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ P )
% 2.86/1.57 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_86_old_Oprod_Oinducts,axiom,
% 2.86/1.57 ! [P: produc691362330ubject > $o,Prod: produc691362330ubject] :
% 2.86/1.57 ( ! [A4: name > noption_pi,B3: late_subject] : ( P @ ( produc581368530ubject @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ Prod ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_87_old_Oprod_Oinducts,axiom,
% 2.86/1.57 ! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
% 2.86/1.57 ( ! [A4: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ Prod ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_88_old_Oprod_Oinducts,axiom,
% 2.86/1.57 ! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
% 2.86/1.57 ( ! [A4: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ Prod ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_89_old_Oprod_Oinducts,axiom,
% 2.86/1.57 ! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
% 2.86/1.57 ( ! [A4: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ Prod ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_90_old_Oprod_Oinducts,axiom,
% 2.86/1.57 ! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
% 2.86/1.57 ( ! [A4: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ Prod ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_91_old_Oprod_Oinducts,axiom,
% 2.86/1.57 ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 2.86/1.57 ( ! [A4: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ Prod ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_92_old_Oprod_Oexhaust,axiom,
% 2.86/1.57 ! [Y: produc691362330ubject] :
% 2.86/1.57 ~ ! [A4: name > noption_pi,B3: late_subject] :
% 2.86/1.57 ( Y
% 2.86/1.57 != ( produc581368530ubject @ A4 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_93_old_Oprod_Oexhaust,axiom,
% 2.86/1.57 ! [Y: produc1834551554reeRes] :
% 2.86/1.57 ~ ! [A4: name > noption_pi,B3: late_freeRes] :
% 2.86/1.57 ( Y
% 2.86/1.57 != ( produc1505598906reeRes @ A4 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_94_old_Oprod_Oexhaust,axiom,
% 2.86/1.57 ! [Y: produc405342261i_name] :
% 2.86/1.57 ~ ! [A4: name > noption_pi,B3: name] :
% 2.86/1.57 ( Y
% 2.86/1.57 != ( produc540578151i_name @ A4 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_95_old_Oprod_Oexhaust,axiom,
% 2.86/1.57 ! [Y: produc629157763_pi_pi] :
% 2.86/1.57 ~ ! [A4: name > noption_pi,B3: pi] :
% 2.86/1.57 ( Y
% 2.86/1.57 != ( produc1820286517_pi_pi @ A4 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_96_old_Oprod_Oexhaust,axiom,
% 2.86/1.57 ! [Y: produc1462499409ion_pi] :
% 2.86/1.57 ~ ! [A4: name > noption_pi,B3: name > noption_pi] :
% 2.86/1.57 ( Y
% 2.86/1.57 != ( produc1342893193ion_pi @ A4 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_97_old_Oprod_Oexhaust,axiom,
% 2.86/1.57 ! [Y: product_prod_pi_pi] :
% 2.86/1.57 ~ ! [A4: pi,B3: pi] :
% 2.86/1.57 ( Y
% 2.86/1.57 != ( product_Pair_pi_pi @ A4 @ B3 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_98_Pair__inject,axiom,
% 2.86/1.57 ! [A: name > noption_pi,B: late_subject,A2: name > noption_pi,B2: late_subject] :
% 2.86/1.57 ( ( ( produc581368530ubject @ A @ B )
% 2.86/1.57 = ( produc581368530ubject @ A2 @ B2 ) )
% 2.86/1.57 => ~ ( ( A = A2 )
% 2.86/1.57 => ( B != B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_99_Pair__inject,axiom,
% 2.86/1.57 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 2.86/1.57 ( ( ( produc1505598906reeRes @ A @ B )
% 2.86/1.57 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 2.86/1.57 => ~ ( ( A = A2 )
% 2.86/1.57 => ( B != B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_100_Pair__inject,axiom,
% 2.86/1.57 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 2.86/1.57 ( ( ( produc540578151i_name @ A @ B )
% 2.86/1.57 = ( produc540578151i_name @ A2 @ B2 ) )
% 2.86/1.57 => ~ ( ( A = A2 )
% 2.86/1.57 => ( B != B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_101_Pair__inject,axiom,
% 2.86/1.57 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 2.86/1.57 ( ( ( produc1820286517_pi_pi @ A @ B )
% 2.86/1.57 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 2.86/1.57 => ~ ( ( A = A2 )
% 2.86/1.57 => ( B != B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_102_Pair__inject,axiom,
% 2.86/1.57 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 2.86/1.57 ( ( ( produc1342893193ion_pi @ A @ B )
% 2.86/1.57 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 2.86/1.57 => ~ ( ( A = A2 )
% 2.86/1.57 => ( B != B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_103_Pair__inject,axiom,
% 2.86/1.57 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 2.86/1.57 ( ( ( product_Pair_pi_pi @ A @ B )
% 2.86/1.57 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 2.86/1.57 => ~ ( ( A = A2 )
% 2.86/1.57 => ( B != B2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_104_prod__cases,axiom,
% 2.86/1.57 ! [P: produc691362330ubject > $o,P5: produc691362330ubject] :
% 2.86/1.57 ( ! [A4: name > noption_pi,B3: late_subject] : ( P @ ( produc581368530ubject @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ P5 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_105_prod__cases,axiom,
% 2.86/1.57 ! [P: produc1834551554reeRes > $o,P5: produc1834551554reeRes] :
% 2.86/1.57 ( ! [A4: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ P5 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_106_prod__cases,axiom,
% 2.86/1.57 ! [P: produc405342261i_name > $o,P5: produc405342261i_name] :
% 2.86/1.57 ( ! [A4: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ P5 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_107_prod__cases,axiom,
% 2.86/1.57 ! [P: produc629157763_pi_pi > $o,P5: produc629157763_pi_pi] :
% 2.86/1.57 ( ! [A4: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ P5 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_108_prod__cases,axiom,
% 2.86/1.57 ! [P: produc1462499409ion_pi > $o,P5: produc1462499409ion_pi] :
% 2.86/1.57 ( ! [A4: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ P5 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_109_prod__cases,axiom,
% 2.86/1.57 ! [P: product_prod_pi_pi > $o,P5: product_prod_pi_pi] :
% 2.86/1.57 ( ! [A4: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A4 @ B3 ) )
% 2.86/1.57 => ( P @ P5 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_110_surj__pair,axiom,
% 2.86/1.57 ! [P5: produc691362330ubject] :
% 2.86/1.57 ? [X5: name > noption_pi,Y4: late_subject] :
% 2.86/1.57 ( P5
% 2.86/1.57 = ( produc581368530ubject @ X5 @ Y4 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_111_surj__pair,axiom,
% 2.86/1.57 ! [P5: produc1834551554reeRes] :
% 2.86/1.57 ? [X5: name > noption_pi,Y4: late_freeRes] :
% 2.86/1.57 ( P5
% 2.86/1.57 = ( produc1505598906reeRes @ X5 @ Y4 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_112_surj__pair,axiom,
% 2.86/1.57 ! [P5: produc405342261i_name] :
% 2.86/1.57 ? [X5: name > noption_pi,Y4: name] :
% 2.86/1.57 ( P5
% 2.86/1.57 = ( produc540578151i_name @ X5 @ Y4 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_113_surj__pair,axiom,
% 2.86/1.57 ! [P5: produc629157763_pi_pi] :
% 2.86/1.57 ? [X5: name > noption_pi,Y4: pi] :
% 2.86/1.57 ( P5
% 2.86/1.57 = ( produc1820286517_pi_pi @ X5 @ Y4 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_114_surj__pair,axiom,
% 2.86/1.57 ! [P5: produc1462499409ion_pi] :
% 2.86/1.57 ? [X5: name > noption_pi,Y4: name > noption_pi] :
% 2.86/1.57 ( P5
% 2.86/1.57 = ( produc1342893193ion_pi @ X5 @ Y4 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_115_surj__pair,axiom,
% 2.86/1.57 ! [P5: product_prod_pi_pi] :
% 2.86/1.57 ? [X5: pi,Y4: pi] :
% 2.86/1.57 ( P5
% 2.86/1.57 = ( product_Pair_pi_pi @ X5 @ Y4 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_116_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 2.86/1.57 ! [X1: name,Y1: name] :
% 2.86/1.57 ( ( ( late_InputS @ X1 )
% 2.86/1.57 = ( late_InputS @ Y1 ) )
% 2.86/1.57 = ( X1 = Y1 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_117_parSym,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 2.86/1.57 ( ! [R: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R @ S2 ) @ ( par @ S2 @ R ) ) @ Rel )
% 2.86/1.57 => ( ! [R: pi,S2: pi,X5: name] :
% 2.86/1.57 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R @ S2 ) @ Rel )
% 2.86/1.57 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X5 @ R ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 2.86/1.57 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_118_inputIneqTrans,axiom,
% 2.86/1.57 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 2.86/1.57 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 2.86/1.57 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_119_Late__Semantics_OInput,axiom,
% 2.86/1.57 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_120_transitions_OInput,axiom,
% 2.86/1.57 ! [X: name,A: name,P: pi] :
% 2.86/1.57 ( ( X != A )
% 2.86/1.57 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_121_name__fresh,axiom,
% 2.86/1.57 ( fresh_name_name
% 2.86/1.57 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_122_pi_Odistinct_I55_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( ( input @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( par @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_123_pi_Odistinct_I57_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 2.86/1.57 ( ( input @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( res @ Name @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_124_pi_Odistinct_I21_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( ( output @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_125_pi_Odistinct_I35_J,axiom,
% 2.86/1.57 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( ( tau @ Pi )
% 2.86/1.57 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_126_resTrans_I2_J,axiom,
% 2.86/1.57 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 2.86/1.57 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_127_simE_I1_J,axiom,
% 2.86/1.57 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 2.86/1.57 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.86/1.57 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ P )
% 2.86/1.57 => ? [P3: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 2.86/1.57 & ( strong2129052853vative @ P3 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_128_resInputBoundOutputTrans,axiom,
% 2.86/1.57 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 2.86/1.57 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_129_simulation__def,axiom,
% 2.86/1.57 ( strong743114133lation
% 2.86/1.57 = ( ^ [P6: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 2.86/1.57 ( ! [A5: late_subject,X4: name,Q6: pi] :
% 2.86/1.57 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 2.86/1.57 & ( fresh_name_pi @ X4 @ P6 ) )
% 2.86/1.57 => ? [P7: pi] :
% 2.86/1.57 ( ( late_transitions @ P6 @ ( late_BoundR @ A5 @ X4 @ P7 ) )
% 2.86/1.57 & ( strong2129052853vative @ P7 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 2.86/1.57 & ! [Alpha: late_freeRes,Q6: pi] :
% 2.86/1.57 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha @ Q6 ) )
% 2.86/1.57 => ? [P7: pi] :
% 2.86/1.57 ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha @ P7 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_130_simCases,axiom,
% 2.86/1.57 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 2.86/1.57 ( ! [A4: late_subject,Y4: name,Q3: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y4 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ Y4 @ P )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y4 @ P8 ) )
% 2.86/1.57 & ( strong2129052853vative @ P8 @ Q3 @ A4 @ Y4 @ Rel ) ) ) )
% 2.86/1.57 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 2.86/1.57 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_131_residual_Ofresh_I1_J,axiom,
% 2.86/1.57 ! [A: name,X3: late_subject,X1: name,X2: pi] :
% 2.86/1.57 ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X3 @ X1 @ X2 ) )
% 2.86/1.57 = ( ( fresh_717452603ubject @ A @ X3 )
% 2.86/1.57 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_132_inputCases_H,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 2.86/1.57 ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 2.86/1.57 => ~ ! [X5: name,A4: name,P4: pi] :
% 2.86/1.57 ( ( ( A = A4 )
% 2.86/1.57 & ( ( abs_fun_name_pi @ B @ P )
% 2.86/1.57 = ( abs_fun_name_pi @ X5 @ P4 ) ) )
% 2.86/1.57 => ( ( Rs
% 2.86/1.57 = ( late_BoundR @ ( late_InputS @ A4 ) @ X5 @ P4 ) )
% 2.86/1.57 => ( X5 = A4 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_133_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 2.86/1.57 ! [X2: name,Y2: name] :
% 2.86/1.57 ( ( ( late_BoundOutputS @ X2 )
% 2.86/1.57 = ( late_BoundOutputS @ Y2 ) )
% 2.86/1.57 = ( X2 = Y2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_134_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 2.86/1.57 ! [X1: name,Y1: name] :
% 2.86/1.57 ( ( ( late_BoundOutputS @ X1 )
% 2.86/1.57 = ( late_BoundOutputS @ Y1 ) )
% 2.86/1.57 = ( X1 = Y1 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_135_subject_Ofresh_I2_J,axiom,
% 2.86/1.57 ! [A: name,X1: name] :
% 2.86/1.57 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 2.86/1.57 = ( fresh_name_name @ A @ X1 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_136_residual_Ofresh_I2_J,axiom,
% 2.86/1.57 ! [A: name,X2: late_freeRes,X1: pi] :
% 2.86/1.57 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 2.86/1.57 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 2.86/1.57 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_137_pi_Ofresh_I9_J,axiom,
% 2.86/1.57 ! [A: name,X1: name,X2: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 2.86/1.57 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_138_pi_Ofresh_I4_J,axiom,
% 2.86/1.57 ! [A: name,X3: name,X1: name,X2: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ A @ ( input @ X3 @ X1 @ X2 ) )
% 2.86/1.57 = ( ( fresh_name_name @ A @ X3 )
% 2.86/1.57 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_139_residual_Oinject_I2_J,axiom,
% 2.86/1.57 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 2.86/1.57 ( ( ( late_FreeR @ X2 @ X1 )
% 2.86/1.57 = ( late_FreeR @ Y2 @ Y1 ) )
% 2.86/1.57 = ( ( X2 = Y2 )
% 2.86/1.57 & ( X1 = Y1 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_140_abs__fun__eq1,axiom,
% 2.86/1.57 ! [A: name,X: name,Y: name] :
% 2.86/1.57 ( ( ( abs_fun_name_name @ A @ X )
% 2.86/1.57 = ( abs_fun_name_name @ A @ Y ) )
% 2.86/1.57 = ( X = Y ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_141_abs__fun__eq1,axiom,
% 2.86/1.57 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 2.86/1.57 ( ( ( abs_fu681348580reeRes @ A @ X )
% 2.86/1.57 = ( abs_fu681348580reeRes @ A @ Y ) )
% 2.86/1.57 = ( X = Y ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_142_abs__fun__eq1,axiom,
% 2.86/1.57 ! [A: name,X: late_subject,Y: late_subject] :
% 2.86/1.57 ( ( ( abs_fu1904601852ubject @ A @ X )
% 2.86/1.57 = ( abs_fu1904601852ubject @ A @ Y ) )
% 2.86/1.57 = ( X = Y ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_143_abs__fun__eq1,axiom,
% 2.86/1.57 ! [A: name,X: pi,Y: pi] :
% 2.86/1.57 ( ( ( abs_fun_name_pi @ A @ X )
% 2.86/1.57 = ( abs_fun_name_pi @ A @ Y ) )
% 2.86/1.57 = ( X = Y ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_144_pi_Oinject_I8_J,axiom,
% 2.86/1.57 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 2.86/1.57 ( ( ( res @ X1 @ X2 )
% 2.86/1.57 = ( res @ Y1 @ Y2 ) )
% 2.86/1.57 = ( ( abs_fun_name_pi @ X1 @ X2 )
% 2.86/1.57 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_145_residual_Oinject_I1_J,axiom,
% 2.86/1.57 ! [X3: late_subject,X1: name,X2: pi,Y3: late_subject,Y1: name,Y2: pi] :
% 2.86/1.57 ( ( ( late_BoundR @ X3 @ X1 @ X2 )
% 2.86/1.57 = ( late_BoundR @ Y3 @ Y1 @ Y2 ) )
% 2.86/1.57 = ( ( X3 = Y3 )
% 2.86/1.57 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 2.86/1.57 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_146_residual_Odistinct_I1_J,axiom,
% 2.86/1.57 ! [Subject: late_subject,Name3: name,Pi: pi,FreeRes: late_freeRes,Pi2: pi] :
% 2.86/1.57 ( ( late_BoundR @ Subject @ Name3 @ Pi )
% 2.86/1.57 != ( late_FreeR @ FreeRes @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_147_residual_Oinducts,axiom,
% 2.86/1.57 ! [P: late_residual > $o,Residual: late_residual] :
% 2.86/1.57 ( ! [Subject2: late_subject,Name4: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) )
% 2.86/1.57 => ( ! [FreeRes2: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 2.86/1.57 => ( P @ Residual ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_148_name__fresh__abs,axiom,
% 2.86/1.57 ! [B: name,A: name,X: late_subject] :
% 2.86/1.57 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 2.86/1.57 = ( ( B = A )
% 2.86/1.57 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_149_name__fresh__abs,axiom,
% 2.86/1.57 ! [B: name,A: name,X: late_freeRes] :
% 2.86/1.57 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 2.86/1.57 = ( ( B = A )
% 2.86/1.57 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_150_name__fresh__abs,axiom,
% 2.86/1.57 ! [B: name,A: name,X: name] :
% 2.86/1.57 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 2.86/1.57 = ( ( B = A )
% 2.86/1.57 | ( fresh_name_name @ B @ X ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_151_name__fresh__abs,axiom,
% 2.86/1.57 ! [B: name,A: name,X: pi] :
% 2.86/1.57 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 2.86/1.57 = ( ( B = A )
% 2.86/1.57 | ( fresh_name_pi @ B @ X ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_152_abs__fresh_I1_J,axiom,
% 2.86/1.57 ! [B: name,A: name,X: late_subject] :
% 2.86/1.57 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 2.86/1.57 = ( ( B = A )
% 2.86/1.57 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_153_abs__fresh_I1_J,axiom,
% 2.86/1.57 ! [B: name,A: name,X: late_freeRes] :
% 2.86/1.57 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 2.86/1.57 = ( ( B = A )
% 2.86/1.57 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_154_abs__fresh_I1_J,axiom,
% 2.86/1.57 ! [B: name,A: name,X: name] :
% 2.86/1.57 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 2.86/1.57 = ( ( B = A )
% 2.86/1.57 | ( fresh_name_name @ B @ X ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_155_abs__fresh_I1_J,axiom,
% 2.86/1.57 ! [B: name,A: name,X: pi] :
% 2.86/1.57 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 2.86/1.57 = ( ( B = A )
% 2.86/1.57 | ( fresh_name_pi @ B @ X ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_156_pi_Oinject_I3_J,axiom,
% 2.86/1.57 ! [X3: name,X1: name,X2: pi,Y3: name,Y1: name,Y2: pi] :
% 2.86/1.57 ( ( ( input @ X3 @ X1 @ X2 )
% 2.86/1.57 = ( input @ Y3 @ Y1 @ Y2 ) )
% 2.86/1.57 = ( ( X3 = Y3 )
% 2.86/1.57 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 2.86/1.57 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_157_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 2.86/1.57 ! [Name3: name,Name: name] :
% 2.86/1.57 ( ( late_InputS @ Name3 )
% 2.86/1.57 != ( late_BoundOutputS @ Name ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_158_subject_Oinducts,axiom,
% 2.86/1.57 ! [P: late_subject > $o,Subject: late_subject] :
% 2.86/1.57 ( ! [Name4: name] : ( P @ ( late_InputS @ Name4 ) )
% 2.86/1.57 => ( ! [Name4: name] : ( P @ ( late_BoundOutputS @ Name4 ) )
% 2.86/1.57 => ( P @ Subject ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_159_subject_Oexhaust,axiom,
% 2.86/1.57 ! [Y: late_subject] :
% 2.86/1.57 ( ! [X12: name] :
% 2.86/1.57 ( Y
% 2.86/1.57 != ( late_InputS @ X12 ) )
% 2.86/1.57 => ~ ! [X22: name] :
% 2.86/1.57 ( Y
% 2.86/1.57 != ( late_BoundOutputS @ X22 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_160_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 2.86/1.57 ! [X1: name,X2: name] :
% 2.86/1.57 ( ( late_InputS @ X1 )
% 2.86/1.57 != ( late_BoundOutputS @ X2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_161_Par1F,axiom,
% 2.86/1.57 ! [P: pi,Alpha3: late_freeRes,P2: pi,Q: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha3 @ ( par @ P2 @ Q ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_162_Par2F,axiom,
% 2.86/1.57 ! [Q: pi,Alpha3: late_freeRes,Q2: pi,P: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha3 @ Q2 ) )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha3 @ ( par @ P @ Q2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_163_ResF,axiom,
% 2.86/1.57 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 2.86/1.57 => ( ( fresh_1641682979reeRes @ Y @ Alpha3 )
% 2.86/1.57 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha3 @ ( res @ Y @ P2 ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_164_resCasesF_H,axiom,
% 2.86/1.57 ! [X: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 2.86/1.57 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 2.86/1.57 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y4: name] :
% 2.86/1.57 ( ( ( res @ X @ P )
% 2.86/1.57 = ( res @ Y4 @ P4 ) )
% 2.86/1.57 => ( ( ( late_FreeR @ Alpha3 @ P2 )
% 2.86/1.57 = ( late_FreeR @ Alpha2 @ ( res @ Y4 @ P3 ) ) )
% 2.86/1.57 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 2.86/1.57 => ~ ( fresh_1641682979reeRes @ Y4 @ Alpha2 ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_165_resCasesF,axiom,
% 2.86/1.57 ! [X: name,P: pi,Alpha3: late_freeRes,XP: pi,F: pi > $o] :
% 2.86/1.57 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha3 @ XP ) )
% 2.86/1.57 => ( ! [P3: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P3 ) )
% 2.86/1.57 => ( ( fresh_1641682979reeRes @ X @ Alpha3 )
% 2.86/1.57 => ( F @ ( res @ X @ P3 ) ) ) )
% 2.86/1.57 => ( F @ XP ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_166_freshFreeDerivative_I1_J,axiom,
% 2.86/1.57 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ P )
% 2.86/1.57 => ( fresh_1641682979reeRes @ Y @ Alpha3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_167_freshFreeDerivative_I2_J,axiom,
% 2.86/1.57 ! [P: pi,Alpha3: late_freeRes,P2: pi,Y: name] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ P )
% 2.86/1.57 => ( fresh_name_pi @ Y @ P2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_168_inputFreeTrans,axiom,
% 2.86/1.57 ! [A: name,X: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 2.86/1.57 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_169_outputFreshTrans,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 2.86/1.57 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 2.86/1.57 => ~ ( ( fresh_1641682979reeRes @ A @ Alpha3 )
% 2.86/1.57 | ( fresh_1641682979reeRes @ B @ Alpha3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_170_simE_I2_J,axiom,
% 2.86/1.57 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha3: late_freeRes,Q2: pi] :
% 2.86/1.57 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.86/1.57 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha3 @ Q2 ) )
% 2.86/1.57 => ? [P3: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha3 @ P3 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_171_resInputFreeTrans,axiom,
% 2.86/1.57 ! [X: name,A: name,Y: name,P: pi,Alpha3: late_freeRes,P2: pi] :
% 2.86/1.57 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha3 @ P2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_172_residual_Ostrong__inducts,axiom,
% 2.86/1.57 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 2.86/1.57 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ( fresh_717452603ubject @ Name4 @ Z2 )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 2.86/1.57 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 2.86/1.57 => ( P @ Z @ Residual ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_173_residual_Ostrong__inducts,axiom,
% 2.86/1.57 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 2.86/1.57 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 2.86/1.57 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 2.86/1.57 => ( P @ Z @ Residual ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_174_residual_Ostrong__inducts,axiom,
% 2.86/1.57 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 2.86/1.57 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ( fresh_name_name @ Name4 @ Z2 )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 2.86/1.57 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 2.86/1.57 => ( P @ Z @ Residual ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_175_residual_Ostrong__inducts,axiom,
% 2.86/1.57 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 2.86/1.57 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ Name4 @ Z2 )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 2.86/1.57 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 2.86/1.57 => ( P @ Z @ Residual ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_176_residual_Ostrong__induct,axiom,
% 2.86/1.57 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 2.86/1.57 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ( fresh_717452603ubject @ Name4 @ Z2 )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 2.86/1.57 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 2.86/1.57 => ( P @ Z @ Residual ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_177_residual_Ostrong__induct,axiom,
% 2.86/1.57 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 2.86/1.57 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 2.86/1.57 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 2.86/1.57 => ( P @ Z @ Residual ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_178_residual_Ostrong__induct,axiom,
% 2.86/1.57 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 2.86/1.57 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ( fresh_name_name @ Name4 @ Z2 )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 2.86/1.57 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 2.86/1.57 => ( P @ Z @ Residual ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_179_residual_Ostrong__induct,axiom,
% 2.86/1.57 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 2.86/1.57 ( ! [Subject2: late_subject,Name4: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ Name4 @ Z2 )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Name4 @ Subject2 )
% 2.86/1.57 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [FreeRes2: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi3 ) )
% 2.86/1.57 => ( P @ Z @ Residual ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_180_inputBoundOutputTrans,axiom,
% 2.86/1.57 ! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
% 2.86/1.57 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_181_simCasesCont,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_subject] :
% 2.86/1.57 ( ( eqvt_pi @ Rel )
% 2.86/1.57 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ Q )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X5 @ A4 )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X5 @ C3 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P8 ) )
% 2.86/1.57 & ( strong2129052853vative @ P8 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 2.86/1.57 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 2.86/1.57 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_182_simCasesCont,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_freeRes] :
% 2.86/1.57 ( ( eqvt_pi @ Rel )
% 2.86/1.57 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ Q )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X5 @ A4 )
% 2.86/1.57 => ( ( fresh_1641682979reeRes @ X5 @ C3 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P8 ) )
% 2.86/1.57 & ( strong2129052853vative @ P8 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 2.86/1.57 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 2.86/1.57 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_183_simCasesCont,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
% 2.86/1.57 ( ( eqvt_pi @ Rel )
% 2.86/1.57 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ Q )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X5 @ A4 )
% 2.86/1.57 => ( ( fresh_name_name @ X5 @ C3 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P8 ) )
% 2.86/1.57 & ( strong2129052853vative @ P8 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 2.86/1.57 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 2.86/1.57 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_184_simCasesCont,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
% 2.86/1.57 ( ( eqvt_pi @ Rel )
% 2.86/1.57 => ( ! [A4: late_subject,X5: name,Q3: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ X5 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ Q )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X5 @ A4 )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ C3 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ X5 @ P8 ) )
% 2.86/1.57 & ( strong2129052853vative @ P8 @ Q3 @ A4 @ X5 @ Rel ) ) ) ) ) ) )
% 2.86/1.57 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 2.86/1.57 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_185_resCases_H,axiom,
% 2.86/1.57 ! [X: name,P: pi,Rs: late_residual] :
% 2.86/1.57 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 2.86/1.57 => ( ! [P4: pi,A4: name,B3: name] :
% 2.86/1.57 ( ( ( res @ X @ P )
% 2.86/1.57 = ( res @ B3 @ P4 ) )
% 2.86/1.57 => ! [P3: pi] :
% 2.86/1.57 ( ( Rs
% 2.86/1.57 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P3 ) )
% 2.86/1.57 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P3 ) )
% 2.86/1.57 => ( A4 = B3 ) ) ) )
% 2.86/1.57 => ( ! [P4: pi,A4: late_subject,X5: name,P3: pi,Y4: name] :
% 2.86/1.57 ( ( ( res @ X @ P )
% 2.86/1.57 = ( res @ Y4 @ P4 ) )
% 2.86/1.57 => ( ( Rs
% 2.86/1.57 = ( late_BoundR @ A4 @ X5 @ ( res @ Y4 @ P3 ) ) )
% 2.86/1.57 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Y4 @ A4 )
% 2.86/1.57 => ( ( Y4 != X5 )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ P4 )
% 2.86/1.57 => ~ ( fresh_717452603ubject @ X5 @ A4 ) ) ) ) ) ) )
% 2.86/1.57 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y4: name] :
% 2.86/1.57 ( ( ( res @ X @ P )
% 2.86/1.57 = ( res @ Y4 @ P4 ) )
% 2.86/1.57 => ( ( Rs
% 2.86/1.57 = ( late_FreeR @ Alpha2 @ ( res @ Y4 @ P3 ) ) )
% 2.86/1.57 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 2.86/1.57 => ~ ( fresh_1641682979reeRes @ Y4 @ Alpha2 ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_186_resCasesB_H,axiom,
% 2.86/1.57 ! [X6: name,P: pi,A: late_subject,Y5: name,P2: pi] :
% 2.86/1.57 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A @ Y5 @ P2 ) )
% 2.86/1.57 => ( ! [P4: pi,A4: name,B3: name] :
% 2.86/1.57 ( ( ( res @ X6 @ P )
% 2.86/1.57 = ( res @ B3 @ P4 ) )
% 2.86/1.57 => ! [P3: pi] :
% 2.86/1.57 ( ( ( late_BoundR @ A @ Y5 @ P2 )
% 2.86/1.57 = ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ B3 @ P3 ) )
% 2.86/1.57 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P3 ) )
% 2.86/1.57 => ( A4 = B3 ) ) ) )
% 2.86/1.57 => ~ ! [P4: pi,A4: late_subject,X5: name,P3: pi,Y4: name] :
% 2.86/1.57 ( ( ( res @ X6 @ P )
% 2.86/1.57 = ( res @ Y4 @ P4 ) )
% 2.86/1.57 => ( ( ( late_BoundR @ A @ Y5 @ P2 )
% 2.86/1.57 = ( late_BoundR @ A4 @ X5 @ ( res @ Y4 @ P3 ) ) )
% 2.86/1.57 => ( ( late_transitions @ P4 @ ( late_BoundR @ A4 @ X5 @ P3 ) )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Y4 @ A4 )
% 2.86/1.57 => ( ( Y4 != X5 )
% 2.86/1.57 => ( ( fresh_name_pi @ X5 @ P4 )
% 2.86/1.57 => ~ ( fresh_717452603ubject @ X5 @ A4 ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_187_resSimCases,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_subject] :
% 2.86/1.57 ( ( eqvt_pi @ Rel )
% 2.86/1.57 => ( ! [Q3: pi,A4: name] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X ) @ Q3 ) )
% 2.86/1.57 => ( ( A4 != X )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) ) )
% 2.86/1.57 => ( ! [Q3: pi,A4: late_subject,Y4: name] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y4 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X @ A4 )
% 2.86/1.57 => ( ( X != Y4 )
% 2.86/1.57 => ( ( fresh_717452603ubject @ Y4 @ C3 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y4 @ P8 ) )
% 2.86/1.57 & ( strong2129052853vative @ P8 @ ( res @ X @ Q3 ) @ A4 @ Y4 @ Rel ) ) ) ) ) )
% 2.86/1.57 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 2.86/1.57 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_188_resSimCases,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_freeRes] :
% 2.86/1.57 ( ( eqvt_pi @ Rel )
% 2.86/1.57 => ( ! [Q3: pi,A4: name] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X ) @ Q3 ) )
% 2.86/1.57 => ( ( A4 != X )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) ) )
% 2.86/1.57 => ( ! [Q3: pi,A4: late_subject,Y4: name] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y4 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X @ A4 )
% 2.86/1.57 => ( ( X != Y4 )
% 2.86/1.57 => ( ( fresh_1641682979reeRes @ Y4 @ C3 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y4 @ P8 ) )
% 2.86/1.57 & ( strong2129052853vative @ P8 @ ( res @ X @ Q3 ) @ A4 @ Y4 @ Rel ) ) ) ) ) )
% 2.86/1.57 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 2.86/1.57 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_189_resSimCases,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
% 2.86/1.57 ( ( eqvt_pi @ Rel )
% 2.86/1.57 => ( ! [Q3: pi,A4: name] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X ) @ Q3 ) )
% 2.86/1.57 => ( ( A4 != X )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) ) )
% 2.86/1.57 => ( ! [Q3: pi,A4: late_subject,Y4: name] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y4 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X @ A4 )
% 2.86/1.57 => ( ( X != Y4 )
% 2.86/1.57 => ( ( fresh_name_name @ Y4 @ C3 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y4 @ P8 ) )
% 2.86/1.57 & ( strong2129052853vative @ P8 @ ( res @ X @ Q3 ) @ A4 @ Y4 @ Rel ) ) ) ) ) )
% 2.86/1.57 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 2.86/1.57 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_190_resSimCases,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
% 2.86/1.57 ( ( eqvt_pi @ Rel )
% 2.86/1.57 => ( ! [Q3: pi,A4: name] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A4 @ X ) @ Q3 ) )
% 2.86/1.57 => ( ( A4 != X )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A4 ) @ X @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) ) )
% 2.86/1.57 => ( ! [Q3: pi,A4: late_subject,Y4: name] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_BoundR @ A4 @ Y4 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_717452603ubject @ X @ A4 )
% 2.86/1.57 => ( ( X != Y4 )
% 2.86/1.57 => ( ( fresh_name_pi @ Y4 @ C3 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ A4 @ Y4 @ P8 ) )
% 2.86/1.57 & ( strong2129052853vative @ P8 @ ( res @ X @ Q3 ) @ A4 @ Y4 @ Rel ) ) ) ) ) )
% 2.86/1.57 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 2.86/1.57 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 2.86/1.57 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.86/1.57 => ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 2.86/1.57 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 2.86/1.57 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_191_Open,axiom,
% 2.86/1.57 ! [P: pi,A: name,B: name,P2: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 2.86/1.57 => ( ( A != B )
% 2.86/1.57 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_192_resOutputTauTrans,axiom,
% 2.86/1.57 ! [X: name,A: name,B: name,P: pi,P2: pi] :
% 2.86/1.57 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_193_Late__Semantics_OfreeRes_Oinject,axiom,
% 2.86/1.57 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 2.86/1.57 ( ( ( late_OutputR @ X2 @ X1 )
% 2.86/1.57 = ( late_OutputR @ Y2 @ Y1 ) )
% 2.86/1.57 = ( ( X2 = Y2 )
% 2.86/1.57 & ( X1 = Y1 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_194_Late__Semantics1_OfreeRes_Oinject,axiom,
% 2.86/1.57 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 2.86/1.57 ( ( ( late_OutputR @ X11 @ X122 )
% 2.86/1.57 = ( late_OutputR @ Y11 @ Y12 ) )
% 2.86/1.57 = ( ( X11 = Y11 )
% 2.86/1.57 & ( X122 = Y12 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_195_freeRes_Ofresh_I2_J,axiom,
% 2.86/1.57 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_196_freeRes_Ofresh_I1_J,axiom,
% 2.86/1.57 ! [A: name,X2: name,X1: name] :
% 2.86/1.57 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 2.86/1.57 = ( ( fresh_name_name @ A @ X2 )
% 2.86/1.57 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_197_freeRes_Oinducts,axiom,
% 2.86/1.57 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 2.86/1.57 ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 2.86/1.57 => ( ( P @ late_TauR )
% 2.86/1.57 => ( P @ FreeRes3 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_198_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name] :
% 2.86/1.57 ( ( late_OutputR @ Name1 @ Name2 )
% 2.86/1.57 != late_TauR ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_199_freeRes_Oexhaust,axiom,
% 2.86/1.57 ! [Y: late_freeRes] :
% 2.86/1.57 ( ! [X112: name,X123: name] :
% 2.86/1.57 ( Y
% 2.86/1.57 != ( late_OutputR @ X112 @ X123 ) )
% 2.86/1.57 => ( Y = late_TauR ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_200_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 2.86/1.57 ! [X11: name,X122: name] :
% 2.86/1.57 ( ( late_OutputR @ X11 @ X122 )
% 2.86/1.57 != late_TauR ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_201_outputCases,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,Alpha3: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.86/1.57 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 2.86/1.57 => ( ( ( Alpha3
% 2.86/1.57 = ( late_OutputR @ A @ B ) )
% 2.86/1.57 => ( ( P = P2 )
% 2.86/1.57 => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 2.86/1.57 => ( Prop @ Alpha3 @ P2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_202_outputCases_H,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 2.86/1.57 ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 2.86/1.57 => ~ ! [A4: name,B3: name,P4: pi] :
% 2.86/1.57 ( ( ( A = A4 )
% 2.86/1.57 & ( B = B3 )
% 2.86/1.57 & ( P = P4 ) )
% 2.86/1.57 => ( Rs
% 2.86/1.57 != ( late_FreeR @ ( late_OutputR @ A4 @ B3 ) @ P4 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_203_outputIneqTrans,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,C: name,D: name,P2: pi] :
% 2.86/1.57 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P2 ) )
% 2.86/1.57 => ~ ( ( A != C )
% 2.86/1.57 | ( B != D ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_204_Output,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_205_tauOutputTrans,axiom,
% 2.86/1.57 ! [P: pi,A: name,B: name,P2: pi] :
% 2.86/1.57 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_206_outputTauTrans,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,P2: pi] :
% 2.86/1.57 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_207_tauCases,axiom,
% 2.86/1.57 ! [P: pi,Alpha3: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.86/1.57 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha3 @ P2 ) )
% 2.86/1.57 => ( ( ( Alpha3 = late_TauR )
% 2.86/1.57 => ( ( P = P2 )
% 2.86/1.57 => ( Prop @ late_TauR @ P ) ) )
% 2.86/1.57 => ( Prop @ Alpha3 @ P2 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_208_tauCases_H,axiom,
% 2.86/1.57 ! [P: pi,Rs: late_residual] :
% 2.86/1.57 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 2.86/1.57 => ~ ! [P4: pi] :
% 2.86/1.57 ( ( ( tau @ P )
% 2.86/1.57 = ( tau @ P4 ) )
% 2.86/1.57 => ( Rs
% 2.86/1.57 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_209_Tau,axiom,
% 2.86/1.57 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_210_resOutputOutputTrans,axiom,
% 2.86/1.57 ! [X: name,A: name,P: pi,B: name,Y: name,P2: pi] :
% 2.86/1.57 ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_211_resTauOutputTrans,axiom,
% 2.86/1.57 ! [X: name,P: pi,A: name,B: name,P2: pi] :
% 2.86/1.57 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_212_Late__Semantics_OClose1,axiom,
% 2.86/1.57 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 2.86/1.57 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ P )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_213_Late__Semantics_OClose2,axiom,
% 2.86/1.57 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 2.86/1.57 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ Q )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_214_transitions_OClose1,axiom,
% 2.86/1.57 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 2.86/1.57 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ Q )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ Q )
% 2.86/1.57 => ( ( X != A )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ Q2 )
% 2.86/1.57 => ( ( Y != A )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ P2 )
% 2.86/1.57 => ( ( X != Y )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_215_transitions_OClose2,axiom,
% 2.86/1.57 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 2.86/1.57 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ Q )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ Q )
% 2.86/1.57 => ( ( X != A )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ P2 )
% 2.86/1.57 => ( ( Y != A )
% 2.86/1.57 => ( ( fresh_name_pi @ Y @ Q2 )
% 2.86/1.57 => ( ( X != Y )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_216_subst__identity,axiom,
% 2.86/1.57 ! [P: pi,A: name] :
% 2.86/1.57 ( ( subs @ P @ A @ A )
% 2.86/1.57 = P ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_217_simps_I8_J,axiom,
% 2.86/1.57 ! [P: pi,Q: pi,C: name,D: name] :
% 2.86/1.57 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 2.86/1.57 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_218_simps_I9_J,axiom,
% 2.86/1.57 ! [X: name,C: name,D: name,P: pi] :
% 2.86/1.57 ( ( X != C )
% 2.86/1.57 => ( ( X != D )
% 2.86/1.57 => ( ( subs @ ( res @ X @ P ) @ C @ D )
% 2.86/1.57 = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_219_substTrans,axiom,
% 2.86/1.57 ! [B: name,P: pi,A: name,C: name] :
% 2.86/1.57 ( ( fresh_name_pi @ B @ P )
% 2.86/1.57 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
% 2.86/1.57 = ( subs @ P @ A @ C ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_220_simps_I2_J,axiom,
% 2.86/1.57 ! [P: pi,C: name,D: name] :
% 2.86/1.57 ( ( subs @ ( tau @ P ) @ C @ D )
% 2.86/1.57 = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_221_forget,axiom,
% 2.86/1.57 ! [A: name,P: pi,B: name] :
% 2.86/1.57 ( ( fresh_name_pi @ A @ P )
% 2.86/1.57 => ( ( subs @ P @ A @ B )
% 2.86/1.57 = P ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_222_fresh__fact1,axiom,
% 2.86/1.57 ! [A: name,P: pi,C: name,B: name] :
% 2.86/1.57 ( ( fresh_name_pi @ A @ P )
% 2.86/1.57 => ( ( A != C )
% 2.86/1.57 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_223_fresh__fact2,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi] :
% 2.86/1.57 ( ( A != B )
% 2.86/1.57 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_224_substRes3,axiom,
% 2.86/1.57 ! [B: name,P: pi,A: name] :
% 2.86/1.57 ( ( fresh_name_pi @ B @ P )
% 2.86/1.57 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 2.86/1.57 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_225_substRes2,axiom,
% 2.86/1.57 ! [B: name,P: pi,A: name] :
% 2.86/1.57 ( ( fresh_name_pi @ B @ P )
% 2.86/1.57 => ( ( res @ A @ P )
% 2.86/1.57 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_226_Late__Semantics_OComm1,axiom,
% 2.86/1.57 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 2.86/1.57 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_227_Late__Semantics_OComm2,axiom,
% 2.86/1.57 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 2.86/1.57 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_228_transitions_OComm2,axiom,
% 2.86/1.57 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 2.86/1.57 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ Q )
% 2.86/1.57 => ( ( X != A )
% 2.86/1.57 => ( ( X != B )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ P2 )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_229_transitions_OComm1,axiom,
% 2.86/1.57 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 2.86/1.57 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ P )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ Q )
% 2.86/1.57 => ( ( X != A )
% 2.86/1.57 => ( ( X != B )
% 2.86/1.57 => ( ( fresh_name_pi @ X @ Q2 )
% 2.86/1.57 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_230_simps_I3_J,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,C: name,D: name] :
% 2.86/1.57 ( ( subs @ ( output @ A @ B @ P ) @ C @ D )
% 2.86/1.57 = ( output @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_231_simps_I4_J,axiom,
% 2.86/1.57 ! [X: name,A: name,C: name,D: name,P: pi] :
% 2.86/1.57 ( ( X != A )
% 2.86/1.57 => ( ( X != C )
% 2.86/1.57 => ( ( X != D )
% 2.86/1.57 => ( ( subs @ ( input @ A @ X @ P ) @ C @ D )
% 2.86/1.57 = ( input @ ( subst_name @ A @ C @ D ) @ X @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_232_substInput,axiom,
% 2.86/1.57 ! [X: name,B: name,C: name,A: name,P: pi] :
% 2.86/1.57 ( ( X != B )
% 2.86/1.57 => ( ( X != C )
% 2.86/1.57 => ( ( subs @ ( input @ A @ X @ P ) @ B @ C )
% 2.86/1.57 = ( input @ ( subst_name @ A @ B @ C ) @ X @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_233_subst__name__def,axiom,
% 2.86/1.57 ( subst_name
% 2.86/1.57 = ( ^ [A5: name,B4: name,C4: name] : ( if_name @ ( A5 = B4 ) @ C4 @ A5 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_234_parZeroLeft,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 2.86/1.57 ( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
% 2.86/1.57 => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_235_parZeroRight,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 2.86/1.57 ( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
% 2.86/1.57 => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_236_simps_I6_J,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,C: name,D: name] :
% 2.86/1.57 ( ( subs @ ( mismatch @ A @ B @ P ) @ C @ D )
% 2.86/1.57 = ( mismatch @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_237_pi_Ofresh_I1_J,axiom,
% 2.86/1.57 ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_238_simps_I1_J,axiom,
% 2.86/1.57 ! [C: name,D: name] :
% 2.86/1.57 ( ( subs @ piNil @ C @ D )
% 2.86/1.57 = piNil ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_239_pi_Ofresh_I6_J,axiom,
% 2.86/1.57 ! [A: name,X3: name,X2: name,X1: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ A @ ( mismatch @ X3 @ X2 @ X1 ) )
% 2.86/1.57 = ( ( fresh_name_name @ A @ X3 )
% 2.86/1.57 & ( fresh_name_name @ A @ X2 )
% 2.86/1.57 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_240_mismatchNilLeft,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,A: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A @ A @ P ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_241_pi_Oinject_I5_J,axiom,
% 2.86/1.57 ! [X3: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 2.86/1.57 ( ( ( mismatch @ X3 @ X2 @ X1 )
% 2.86/1.57 = ( mismatch @ Y3 @ Y2 @ Y1 ) )
% 2.86/1.57 = ( ( X3 = Y3 )
% 2.86/1.57 & ( X2 = Y2 )
% 2.86/1.57 & ( X1 = Y1 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_242_pi_Odistinct_I9_J,axiom,
% 2.86/1.57 ! [Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( piNil
% 2.86/1.57 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_243_nilSimRight,axiom,
% 2.86/1.57 ! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_244_pi_Odistinct_I3_J,axiom,
% 2.86/1.57 ! [Pi2: pi] :
% 2.86/1.57 ( piNil
% 2.86/1.57 != ( tau @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_245_pi_Odistinct_I39_J,axiom,
% 2.86/1.57 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( ( tau @ Pi )
% 2.86/1.57 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_246_pi_Odistinct_I1_J,axiom,
% 2.86/1.57 ! [Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( piNil
% 2.86/1.57 != ( output @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_247_pi_Odistinct_I25_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( ( output @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_248_pi_Odistinct_I5_J,axiom,
% 2.86/1.57 ! [Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( piNil
% 2.86/1.57 != ( input @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_249_pi_Odistinct_I51_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( ( input @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_250_pi_Odistinct_I15_J,axiom,
% 2.86/1.57 ! [Name: name,Pi2: pi] :
% 2.86/1.57 ( piNil
% 2.86/1.57 != ( res @ Name @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_251_pi_Odistinct_I75_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 2.86/1.57 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( res @ Name @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_252_pi_Odistinct_I13_J,axiom,
% 2.86/1.57 ! [Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( piNil
% 2.86/1.57 != ( par @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_253_pi_Odistinct_I73_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( par @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_254_zeroTrans,axiom,
% 2.86/1.57 ! [Rs: late_residual] :
% 2.86/1.57 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_255_nilCases_H,axiom,
% 2.86/1.57 ! [Rs: late_residual] :
% 2.86/1.57 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_256_Mismatch,axiom,
% 2.86/1.57 ! [P: pi,Rs: late_residual,A: name,B: name] :
% 2.86/1.57 ( ( late_transitions @ P @ Rs )
% 2.86/1.57 => ( ( A != B )
% 2.86/1.57 => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_257_mismatchCases_H,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 2.86/1.57 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 2.86/1.57 => ~ ! [P4: pi,A4: name,B3: name] :
% 2.86/1.57 ( ( ( A = A4 )
% 2.86/1.57 & ( B = B3 )
% 2.86/1.57 & ( P = P4 ) )
% 2.86/1.57 => ( ( late_transitions @ P4 @ Rs )
% 2.86/1.57 => ( A4 = B3 ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_258_mismatchTrans,axiom,
% 2.86/1.57 ! [A: name,P: pi,Rs: late_residual] :
% 2.86/1.57 ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_259_mismatchCases,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 2.86/1.57 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 2.86/1.57 => ( ( ( late_transitions @ P @ Rs )
% 2.86/1.57 => ( ( A != B )
% 2.86/1.57 => ( F @ A @ B ) ) )
% 2.86/1.57 => ( F @ A @ B ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_260_resZeroTrans,axiom,
% 2.86/1.57 ! [X: name,Rs: late_residual] :
% 2.86/1.57 ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_261_nilSim_I2_J,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
% 2.86/1.57 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_262_nilSim_I3_J,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 2.86/1.57 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_263_nilSim_I1_J,axiom,
% 2.86/1.57 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 2.86/1.57 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_264_simps_I5_J,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,C: name,D: name] :
% 2.86/1.57 ( ( subs @ ( match @ A @ B @ P ) @ C @ D )
% 2.86/1.57 = ( match @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_265_pi_Ofresh_I5_J,axiom,
% 2.86/1.57 ! [A: name,X3: name,X2: name,X1: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ A @ ( match @ X3 @ X2 @ X1 ) )
% 2.86/1.57 = ( ( fresh_name_name @ A @ X3 )
% 2.86/1.57 & ( fresh_name_name @ A @ X2 )
% 2.86/1.57 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_266_pi_Odistinct_I61_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( ( match @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( mismatch @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_267_pi_Odistinct_I7_J,axiom,
% 2.86/1.57 ! [Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( piNil
% 2.86/1.57 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_268_matchCases,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 2.86/1.57 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 2.86/1.57 => ( ( ( late_transitions @ P @ Rs )
% 2.86/1.57 => ( ( A = B )
% 2.86/1.57 => ( F @ A @ A ) ) )
% 2.86/1.57 => ( F @ A @ B ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_269_matchTrans,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 2.86/1.57 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 2.86/1.57 => ( A = B ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_270_matchCases_H,axiom,
% 2.86/1.57 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 2.86/1.57 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 2.86/1.57 => ~ ! [P4: pi] :
% 2.86/1.57 ( ( ( B = A )
% 2.86/1.57 & ( P = P4 ) )
% 2.86/1.57 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_271_Match,axiom,
% 2.86/1.57 ! [P: pi,Rs: late_residual,B: name] :
% 2.86/1.57 ( ( late_transitions @ P @ Rs )
% 2.86/1.57 => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_272_pi_Odistinct_I65_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( ( match @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( par @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_273_pi_Odistinct_I67_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Name: name,Pi2: pi] :
% 2.86/1.57 ( ( match @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( res @ Name @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_274_pi_Odistinct_I49_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( ( input @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_275_pi_Odistinct_I23_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( ( output @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_276_pi_Odistinct_I37_J,axiom,
% 2.86/1.57 ! [Pi: pi,Name12: name,Name22: name,Pi2: pi] :
% 2.86/1.57 ( ( tau @ Pi )
% 2.86/1.57 != ( match @ Name12 @ Name22 @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_277_pi_Oinject_I4_J,axiom,
% 2.86/1.57 ! [X3: name,X2: name,X1: pi,Y3: name,Y2: name,Y1: pi] :
% 2.86/1.57 ( ( ( match @ X3 @ X2 @ X1 )
% 2.86/1.57 = ( match @ Y3 @ Y2 @ Y1 ) )
% 2.86/1.57 = ( ( X3 = Y3 )
% 2.86/1.57 & ( X2 = Y2 )
% 2.86/1.57 & ( X1 = Y1 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_278_matchNilLeft,axiom,
% 2.86/1.57 ! [A: name,B: name,Rel: set_Pr1834926343_pi_pi,P: pi] :
% 2.86/1.57 ( ( A != B )
% 2.86/1.57 => ( strong743114133lation @ piNil @ Rel @ ( match @ A @ B @ P ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_279_pi_Ostrong__inducts,axiom,
% 2.86/1.57 ! [P: late_subject > pi > $o,Z: late_subject,Pi: pi] :
% 2.86/1.57 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 2.86/1.57 => ( ( fresh_name_name @ Name23 @ Name13 )
% 2.86/1.57 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Name4: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ( fresh_717452603ubject @ Name4 @ Z2 )
% 2.86/1.57 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 2.86/1.57 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_280_pi_Ostrong__inducts,axiom,
% 2.86/1.57 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi: pi] :
% 2.86/1.57 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 2.86/1.57 => ( ( fresh_name_name @ Name23 @ Name13 )
% 2.86/1.57 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Name4: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 2.86/1.57 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 2.86/1.57 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_281_pi_Ostrong__inducts,axiom,
% 2.86/1.57 ! [P: name > pi > $o,Z: name,Pi: pi] :
% 2.86/1.57 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ( fresh_name_name @ Name23 @ Z2 )
% 2.86/1.57 => ( ( fresh_name_name @ Name23 @ Name13 )
% 2.86/1.57 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: name] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: name] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Name4: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ( fresh_name_name @ Name4 @ Z2 )
% 2.86/1.57 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 2.86/1.57 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_282_pi_Ostrong__inducts,axiom,
% 2.86/1.57 ! [P: pi > pi > $o,Z: pi,Pi: pi] :
% 2.86/1.57 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ Name23 @ Z2 )
% 2.86/1.57 => ( ( fresh_name_name @ Name23 @ Name13 )
% 2.86/1.57 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: pi] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: pi] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Name4: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ Name4 @ Z2 )
% 2.86/1.57 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 2.86/1.57 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_283_pi_Ostrong__induct,axiom,
% 2.86/1.57 ! [P: late_subject > pi > $o,Z: late_subject,Pi: pi] :
% 2.86/1.57 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 2.86/1.57 => ( ( fresh_name_name @ Name23 @ Name13 )
% 2.86/1.57 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: late_subject] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Name4: name,Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ( fresh_717452603ubject @ Name4 @ Z2 )
% 2.86/1.57 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: late_subject] :
% 2.86/1.57 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 2.86/1.57 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_284_pi_Ostrong__induct,axiom,
% 2.86/1.57 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi: pi] :
% 2.86/1.57 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 2.86/1.57 => ( ( fresh_name_name @ Name23 @ Name13 )
% 2.86/1.57 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Name4: name,Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ( fresh_1641682979reeRes @ Name4 @ Z2 )
% 2.86/1.57 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 2.86/1.57 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 2.86/1.57 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_285_pi_Ostrong__induct,axiom,
% 2.86/1.57 ! [P: name > pi > $o,Z: name,Pi: pi] :
% 2.86/1.57 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ( fresh_name_name @ Name23 @ Z2 )
% 2.86/1.57 => ( ( fresh_name_name @ Name23 @ Name13 )
% 2.86/1.57 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: name] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: name] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Name4: name,Pi3: pi,Z2: name] :
% 2.86/1.57 ( ( fresh_name_name @ Name4 @ Z2 )
% 2.86/1.57 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: name] :
% 2.86/1.57 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 2.86/1.57 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_286_pi_Ostrong__induct,axiom,
% 2.86/1.57 ! [P: pi > pi > $o,Z: pi,Pi: pi] :
% 2.86/1.57 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ Name23 @ Z2 )
% 2.86/1.57 => ( ( fresh_name_name @ Name23 @ Name13 )
% 2.86/1.57 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( input @ Name13 @ Name23 @ Pi3 ) ) ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: pi] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 2.86/1.57 => ( ! [Za: pi] : ( P @ Za @ Pi24 )
% 2.86/1.57 => ( P @ Z2 @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Name4: name,Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ Name4 @ Z2 )
% 2.86/1.57 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( res @ Name4 @ Pi3 ) ) ) )
% 2.86/1.57 => ( ! [Pi3: pi,Z2: pi] :
% 2.86/1.57 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 2.86/1.57 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 2.86/1.57 => ( P @ Z @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_287_pi_Ofresh_I10_J,axiom,
% 2.86/1.57 ! [A: name,X1: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ A @ ( bang @ X1 ) )
% 2.86/1.57 = ( fresh_name_pi @ A @ X1 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_288_pi_Ofresh_I7_J,axiom,
% 2.86/1.57 ! [A: name,X2: pi,X1: pi] :
% 2.86/1.57 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 2.86/1.57 = ( ( fresh_name_pi @ A @ X2 )
% 2.86/1.57 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_289_simps_I10_J,axiom,
% 2.86/1.57 ! [P: pi,C: name,D: name] :
% 2.86/1.57 ( ( subs @ ( bang @ P ) @ C @ D )
% 2.86/1.57 = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_290_simps_I7_J,axiom,
% 2.86/1.57 ! [P: pi,Q: pi,C: name,D: name] :
% 2.86/1.57 ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 2.86/1.57 = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_291_pi_Odistinct_I63_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( ( match @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( sum @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_292_pi_Odistinct_I69_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 2.86/1.57 ( ( match @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( bang @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_293_Bang,axiom,
% 2.86/1.57 ! [P: pi,Rs: late_residual] :
% 2.86/1.57 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 2.86/1.57 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_294_bangCases,axiom,
% 2.86/1.57 ! [P: pi,Rs: late_residual] :
% 2.86/1.57 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 2.86/1.57 => ~ ! [P4: pi] :
% 2.86/1.57 ( ( ( bang @ P )
% 2.86/1.57 = ( bang @ P4 ) )
% 2.86/1.57 => ~ ( late_transitions @ ( par @ P4 @ ( bang @ P4 ) ) @ Rs ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_295_pi_Odistinct_I87_J,axiom,
% 2.86/1.57 ! [Pi1: pi,Pi22: pi,Pi2: pi] :
% 2.86/1.57 ( ( par @ Pi1 @ Pi22 )
% 2.86/1.57 != ( bang @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_296_pi_Odistinct_I89_J,axiom,
% 2.86/1.57 ! [Name3: name,Pi: pi,Pi2: pi] :
% 2.86/1.57 ( ( res @ Name3 @ Pi )
% 2.86/1.57 != ( bang @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_297_pi_Odistinct_I59_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 2.86/1.57 ( ( input @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( bang @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_298_pi_Odistinct_I33_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 2.86/1.57 ( ( output @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( bang @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_299_Sum2,axiom,
% 2.86/1.57 ! [Q: pi,Rs: late_residual,P: pi] :
% 2.86/1.57 ( ( late_transitions @ Q @ Rs )
% 2.86/1.57 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_300_Sum1,axiom,
% 2.86/1.57 ! [P: pi,Rs: late_residual,Q: pi] :
% 2.86/1.57 ( ( late_transitions @ P @ Rs )
% 2.86/1.57 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_301_sumCases_H,axiom,
% 2.86/1.57 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.86/1.57 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.86/1.57 => ( ~ ( late_transitions @ P @ Rs )
% 2.86/1.57 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_302_sumCases,axiom,
% 2.86/1.57 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.86/1.57 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.86/1.57 => ( ~ ( late_transitions @ P @ Rs )
% 2.86/1.57 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_303_pi_Odistinct_I47_J,axiom,
% 2.86/1.57 ! [Pi: pi,Pi2: pi] :
% 2.86/1.57 ( ( tau @ Pi )
% 2.86/1.57 != ( bang @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_304_pi_Odistinct_I79_J,axiom,
% 2.86/1.57 ! [Pi1: pi,Pi22: pi,Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( ( sum @ Pi1 @ Pi22 )
% 2.86/1.57 != ( par @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_305_pi_Odistinct_I81_J,axiom,
% 2.86/1.57 ! [Pi1: pi,Pi22: pi,Name: name,Pi2: pi] :
% 2.86/1.57 ( ( sum @ Pi1 @ Pi22 )
% 2.86/1.57 != ( res @ Name @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_306_pi_Odistinct_I53_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( ( input @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( sum @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_307_pi_Odistinct_I27_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( ( output @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( sum @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_308_pi_Odistinct_I41_J,axiom,
% 2.86/1.57 ! [Pi: pi,Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( ( tau @ Pi )
% 2.86/1.57 != ( sum @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_309_pi_Oinject_I9_J,axiom,
% 2.86/1.57 ! [X1: pi,Y1: pi] :
% 2.86/1.57 ( ( ( bang @ X1 )
% 2.86/1.57 = ( bang @ Y1 ) )
% 2.86/1.57 = ( X1 = Y1 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_310_pi_Oinject_I6_J,axiom,
% 2.86/1.57 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.86/1.57 ( ( ( sum @ X2 @ X1 )
% 2.86/1.57 = ( sum @ Y2 @ Y1 ) )
% 2.86/1.57 = ( ( X2 = Y2 )
% 2.86/1.57 & ( X1 = Y1 ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_311_pi_Odistinct_I83_J,axiom,
% 2.86/1.57 ! [Pi1: pi,Pi22: pi,Pi2: pi] :
% 2.86/1.57 ( ( sum @ Pi1 @ Pi22 )
% 2.86/1.57 != ( bang @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_312_pi_Odistinct_I11_J,axiom,
% 2.86/1.57 ! [Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( piNil
% 2.86/1.57 != ( sum @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_313_pi_Odistinct_I17_J,axiom,
% 2.86/1.57 ! [Pi2: pi] :
% 2.86/1.57 ( piNil
% 2.86/1.57 != ( bang @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_314_pi_Odistinct_I71_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi12: pi,Pi23: pi] :
% 2.86/1.57 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( sum @ Pi12 @ Pi23 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_315_pi_Odistinct_I77_J,axiom,
% 2.86/1.57 ! [Name1: name,Name2: name,Pi: pi,Pi2: pi] :
% 2.86/1.57 ( ( mismatch @ Name1 @ Name2 @ Pi )
% 2.86/1.57 != ( bang @ Pi2 ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(fact_316_pi_Oinducts,axiom,
% 2.86/1.57 ! [P: pi > $o,Pi: pi] :
% 2.86/1.57 ( ( P @ piNil )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 2.86/1.57 ( ( P @ Pi3 )
% 2.86/1.57 => ( P @ ( output @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi3: pi] :
% 2.86/1.57 ( ( P @ Pi3 )
% 2.86/1.57 => ( P @ ( tau @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 2.86/1.57 ( ( P @ Pi3 )
% 2.86/1.57 => ( P @ ( input @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 2.86/1.57 ( ( P @ Pi3 )
% 2.86/1.57 => ( P @ ( match @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Name13: name,Name23: name,Pi3: pi] :
% 2.86/1.57 ( ( P @ Pi3 )
% 2.86/1.57 => ( P @ ( mismatch @ Name13 @ Name23 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi] :
% 2.86/1.57 ( ( P @ Pi13 )
% 2.86/1.57 => ( ( P @ Pi24 )
% 2.86/1.57 => ( P @ ( sum @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Pi13: pi,Pi24: pi] :
% 2.86/1.57 ( ( P @ Pi13 )
% 2.86/1.57 => ( ( P @ Pi24 )
% 2.86/1.57 => ( P @ ( par @ Pi13 @ Pi24 ) ) ) )
% 2.86/1.57 => ( ! [Name4: name,Pi3: pi] :
% 2.86/1.57 ( ( P @ Pi3 )
% 2.86/1.57 => ( P @ ( res @ Name4 @ Pi3 ) ) )
% 2.86/1.57 => ( ! [Pi3: pi] :
% 2.86/1.57 ( ( P @ Pi3 )
% 2.86/1.57 => ( P @ ( bang @ Pi3 ) ) )
% 2.86/1.57 => ( P @ Pi ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(help_If_3_1_If_001t__Agent__Oname_T,axiom,
% 2.86/1.57 ! [P: $o] :
% 2.86/1.57 ( ( P = $true )
% 2.86/1.57 | ( P = $false ) ) ).
% 2.86/1.57
% 2.86/1.57 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 2.86/1.57 ! [X: name,Y: name] :
% 2.86/1.57 ( ( if_name @ $false @ X @ Y )
% 2.86/1.57 = Y ) ).
% 2.86/1.57
% 2.86/1.57 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 2.86/1.57 ! [X: name,Y: name] :
% 2.86/1.57 ( ( if_name @ $true @ X @ Y )
% 2.86/1.57 = X ) ).
% 2.86/1.57
% 2.86/1.57 thf(conj_0,conjecture,
% 2.86/1.57 ? [P8: pi] :
% 2.86/1.57 ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_BoundR @ a @ x @ P8 ) )
% 2.86/1.57 & ( strong2129052853vative @ P8 @ ( par @ p @ ( par @ q2 @ r ) ) @ a @ x @ rel ) ) ).
% 2.86/1.57 ------------------------
% 2.92/1.60 % (17263)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_17066 for (2999ds/2Mi)
% 2.92/1.60 % (17264)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_17066 for (2999ds/275Mi)
% 2.92/1.60 % (17263)Instruction limit reached!
% 2.92/1.60 % (17263)------------------------------
% 2.92/1.60 % (17263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.60 % (17263)Termination reason: Unknown
% 2.92/1.60 % (17263)Termination phase: shuffling
% 2.92/1.60
% 2.92/1.60 % (17263)Memory used [KB]: 1535
% 2.92/1.60 % (17263)Time elapsed: 0.002 s
% 2.92/1.60 % (17263)Instructions burned: 2 (million)
% 2.92/1.60 % (17263)------------------------------
% 2.92/1.60 % (17263)------------------------------
% 2.92/1.60 % (17265)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17066 for (2999ds/18Mi)
% 2.92/1.60 % (17261)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_17066 for (2999ds/27Mi)
% 2.92/1.60 % (17262)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17066 for (2999ds/2Mi)
% 2.92/1.60 % (17259)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17066 for (2999ds/183Mi)
% 2.92/1.61 % (17262)Instruction limit reached!
% 2.92/1.61 % (17262)------------------------------
% 2.92/1.61 % (17262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (17262)Termination reason: Unknown
% 2.92/1.61 % (17262)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (17262)Memory used [KB]: 1535
% 2.92/1.61 % (17262)Time elapsed: 0.003 s
% 2.92/1.61 % (17262)Instructions burned: 2 (million)
% 2.92/1.61 % (17262)------------------------------
% 2.92/1.61 % (17262)------------------------------
% 2.92/1.61 % (17266)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17066 for (2999ds/3Mi)
% 2.92/1.61 % (17265)Instruction limit reached!
% 2.92/1.61 % (17265)------------------------------
% 2.92/1.61 % (17265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (17265)Termination reason: Unknown
% 2.92/1.61 % (17265)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (17265)Memory used [KB]: 1918
% 2.92/1.61 % (17265)Time elapsed: 0.011 s
% 2.92/1.61 % (17265)Instructions burned: 19 (million)
% 2.92/1.61 % (17265)------------------------------
% 2.92/1.61 % (17265)------------------------------
% 2.92/1.61 % (17266)Instruction limit reached!
% 2.92/1.61 % (17266)------------------------------
% 2.92/1.61 % (17266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (17266)Termination reason: Unknown
% 2.92/1.61 % (17266)Termination phase: shuffling
% 2.92/1.61 % (17260)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_17066 for (2999ds/4Mi)
% 2.92/1.61
% 2.92/1.61 % (17266)Memory used [KB]: 1535
% 2.92/1.61 % (17266)Time elapsed: 0.003 s
% 2.92/1.61 % (17266)Instructions burned: 5 (million)
% 2.92/1.61 % (17266)------------------------------
% 2.92/1.61 % (17266)------------------------------
% 2.92/1.61 % (17260)Instruction limit reached!
% 2.92/1.61 % (17260)------------------------------
% 2.92/1.61 % (17260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (17260)Termination reason: Unknown
% 2.92/1.61 % (17260)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (17260)Memory used [KB]: 1663
% 2.92/1.61 % (17260)Time elapsed: 0.004 s
% 2.92/1.61 % (17260)Instructions burned: 4 (million)
% 2.92/1.61 % (17260)------------------------------
% 2.92/1.61 % (17260)------------------------------
% 2.92/1.61 % (17261)Instruction limit reached!
% 2.92/1.61 % (17261)------------------------------
% 2.92/1.61 % (17261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.61 % (17261)Termination reason: Unknown
% 2.92/1.61 % (17261)Termination phase: shuffling
% 2.92/1.61
% 2.92/1.61 % (17261)Memory used [KB]: 2046
% 2.92/1.61 % (17261)Time elapsed: 0.016 s
% 2.92/1.61 % (17261)Instructions burned: 28 (million)
% 2.92/1.61 % (17261)------------------------------
% 2.92/1.61 % (17261)------------------------------
% 2.92/1.62 % (17269)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_17066 for (2999ds/3Mi)
% 2.92/1.62 % (17268)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_17066 for (2999ds/15Mi)
% 2.92/1.62 % (17269)Instruction limit reached!
% 2.92/1.62 % (17269)------------------------------
% 2.92/1.62 % (17269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.62 % (17269)Termination reason: Unknown
% 2.92/1.62 % (17269)Termination phase: shuffling
% 2.92/1.62
% 2.92/1.62 % (17269)Memory used [KB]: 1535
% 2.92/1.62 % (17269)Time elapsed: 0.003 s
% 2.92/1.62 % (17269)Instructions burned: 5 (million)
% 2.92/1.62 % (17269)------------------------------
% 2.92/1.62 % (17269)------------------------------
% 2.92/1.62 % (17267)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_17066 for (2999ds/37Mi)
% 2.92/1.62 % (17264)First to succeed.
% 2.92/1.63 % (17268)Instruction limit reached!
% 2.92/1.63 % (17268)------------------------------
% 2.92/1.63 % (17268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (17268)Termination reason: Unknown
% 2.92/1.63 % (17268)Termination phase: shuffling
% 2.92/1.63
% 2.92/1.63 % (17268)Memory used [KB]: 1791
% 2.92/1.63 % (17268)Time elapsed: 0.008 s
% 2.92/1.63 % (17268)Instructions burned: 17 (million)
% 2.92/1.63 % (17268)------------------------------
% 2.92/1.63 % (17268)------------------------------
% 2.92/1.63 % (17264)Refutation found. Thanks to Tanya!
% 2.92/1.63 % SZS status Theorem for DTF2THF_17066
% 2.92/1.63 % SZS output start Proof for DTF2THF_17066
% 2.92/1.63 thf(type_def_5, type, pi: $tType).
% 2.92/1.63 thf(type_def_7, type, name: $tType).
% 2.92/1.63 thf(type_def_8, type, late_freeRes: $tType).
% 2.92/1.63 thf(type_def_9, type, late_subject: $tType).
% 2.92/1.63 thf(type_def_10, type, late_residual: $tType).
% 2.92/1.63 thf(type_def_11, type, noption_name: $tType).
% 2.92/1.63 thf(type_def_12, type, noption_pi: $tType).
% 2.92/1.63 thf(type_def_13, type, noption_Late_freeRes: $tType).
% 2.92/1.63 thf(type_def_14, type, noption_Late_subject: $tType).
% 2.92/1.63 thf(type_def_15, type, produc1462499409ion_pi: $tType).
% 2.92/1.63 thf(type_def_16, type, produc405342261i_name: $tType).
% 2.92/1.63 thf(type_def_17, type, produc629157763_pi_pi: $tType).
% 2.92/1.63 thf(type_def_18, type, produc1834551554reeRes: $tType).
% 2.92/1.63 thf(type_def_19, type, produc691362330ubject: $tType).
% 2.92/1.63 thf(type_def_20, type, produc2008547984reeRes: $tType).
% 2.92/1.63 thf(type_def_21, type, produc865358760ubject: $tType).
% 2.92/1.63 thf(type_def_22, type, product_prod_pi_pi: $tType).
% 2.92/1.63 thf(type_def_23, type, produc2052722628s_name: $tType).
% 2.92/1.63 thf(type_def_24, type, produc992857746Res_pi: $tType).
% 2.92/1.63 thf(type_def_25, type, produc1357834675reeRes: $tType).
% 2.92/1.63 thf(type_def_26, type, produc214645451ubject: $tType).
% 2.92/1.63 thf(type_def_27, type, produc1998742700t_name: $tType).
% 2.92/1.63 thf(type_def_28, type, produc140253050ect_pi: $tType).
% 2.92/1.63 thf(type_def_29, type, produc355105483reeRes: $tType).
% 2.92/1.63 thf(type_def_30, type, produc1359399907ubject: $tType).
% 2.92/1.63 thf(type_def_31, type, set_Pr1834926343_pi_pi: $tType).
% 2.92/1.63 thf(func_def_0, type, produc1462499409ion_pi: $tType).
% 2.92/1.63 thf(func_def_1, type, produc691362330ubject: $tType).
% 2.92/1.63 thf(func_def_2, type, produc1834551554reeRes: $tType).
% 2.92/1.63 thf(func_def_3, type, produc405342261i_name: $tType).
% 2.92/1.63 thf(func_def_4, type, produc629157763_pi_pi: $tType).
% 2.92/1.63 thf(func_def_5, type, produc1359399907ubject: $tType).
% 2.92/1.63 thf(func_def_6, type, produc355105483reeRes: $tType).
% 2.92/1.63 thf(func_def_7, type, produc214645451ubject: $tType).
% 2.92/1.63 thf(func_def_8, type, produc1357834675reeRes: $tType).
% 2.92/1.63 thf(func_def_9, type, produc1998742700t_name: $tType).
% 2.92/1.63 thf(func_def_10, type, produc2052722628s_name: $tType).
% 2.92/1.63 thf(func_def_11, type, produc865358760ubject: $tType).
% 2.92/1.63 thf(func_def_12, type, produc2008547984reeRes: $tType).
% 2.92/1.63 thf(func_def_13, type, produc140253050ect_pi: $tType).
% 2.92/1.63 thf(func_def_14, type, produc992857746Res_pi: $tType).
% 2.92/1.63 thf(func_def_15, type, set_Pr1834926343_pi_pi: $tType).
% 2.92/1.63 thf(func_def_16, type, product_prod_pi_pi: $tType).
% 2.92/1.63 thf(func_def_17, type, noption_Late_subject: $tType).
% 2.92/1.63 thf(func_def_18, type, noption_Late_freeRes: $tType).
% 2.92/1.63 thf(func_def_19, type, noption_name: $tType).
% 2.92/1.63 thf(func_def_20, type, noption_pi: $tType).
% 2.92/1.63 thf(func_def_21, type, late_residual: $tType).
% 2.92/1.63 thf(func_def_22, type, late_subject: $tType).
% 2.92/1.63 thf(func_def_23, type, late_freeRes: $tType).
% 2.92/1.63 thf(func_def_24, type, name: $tType).
% 2.92/1.63 thf(func_def_25, type, pi: $tType).
% 2.92/1.63 thf(func_def_26, type, bang: pi > pi).
% 2.92/1.63 thf(func_def_27, type, input: name > name > pi > pi).
% 2.92/1.63 thf(func_def_28, type, match: name > name > pi > pi).
% 2.92/1.63 thf(func_def_29, type, mismatch: name > name > pi > pi).
% 2.92/1.63 thf(func_def_30, type, output: name > name > pi > pi).
% 2.92/1.63 thf(func_def_31, type, par: pi > pi > pi).
% 2.92/1.63 thf(func_def_32, type, piNil: pi).
% 2.92/1.63 thf(func_def_33, type, res: name > pi > pi).
% 2.92/1.63 thf(func_def_34, type, sum: pi > pi > pi).
% 2.92/1.63 thf(func_def_35, type, tau: pi > pi).
% 2.92/1.63 thf(func_def_36, type, subs: pi > name > name > pi).
% 2.92/1.63 thf(func_def_37, type, subst_name: name > name > name > name).
% 2.92/1.63 thf(func_def_38, type, if_name: $o > name > name > name).
% 2.92/1.63 thf(func_def_39, type, late_OutputR: name > name > late_freeRes).
% 2.92/1.63 thf(func_def_40, type, late_TauR: late_freeRes).
% 2.92/1.63 thf(func_def_41, type, late_BoundR: late_subject > name > pi > late_residual).
% 2.92/1.63 thf(func_def_42, type, late_FreeR: late_freeRes > pi > late_residual).
% 2.92/1.63 thf(func_def_43, type, late_BoundOutputS: name > late_subject).
% 2.92/1.63 thf(func_def_44, type, late_InputS: name > late_subject).
% 2.92/1.63 thf(func_def_45, type, late_transitions: pi > late_residual > $o).
% 2.92/1.63 thf(func_def_46, type, abs_fun_name_name: name > name > name > noption_name).
% 2.92/1.63 thf(func_def_47, type, abs_fun_name_pi: name > pi > name > noption_pi).
% 2.92/1.63 thf(func_def_48, type, abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes).
% 2.92/1.63 thf(func_def_49, type, abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject).
% 2.92/1.63 thf(func_def_50, type, fresh_1093033124n_name: name > (name > noption_name) > $o).
% 2.92/1.63 thf(func_def_51, type, fresh_543891186ion_pi: name > (name > noption_pi) > $o).
% 2.92/1.63 thf(func_def_52, type, fresh_785364841reeRes: name > (name > noption_Late_freeRes) > $o).
% 2.92/1.63 thf(func_def_53, type, fresh_728038529ubject: name > (name > noption_Late_subject) > $o).
% 2.92/1.63 thf(func_def_54, type, fresh_name_name: name > name > $o).
% 2.92/1.63 thf(func_def_55, type, fresh_name_pi: name > pi > $o).
% 2.92/1.63 thf(func_def_56, type, fresh_1641682979reeRes: name > late_freeRes > $o).
% 2.92/1.63 thf(func_def_57, type, fresh_81631222sidual: name > late_residual > $o).
% 2.92/1.63 thf(func_def_58, type, fresh_717452603ubject: name > late_subject > $o).
% 2.92/1.63 thf(func_def_59, type, fresh_225680151ion_pi: name > produc1462499409ion_pi > $o).
% 2.92/1.63 thf(func_def_60, type, fresh_453496559i_name: name > produc405342261i_name > $o).
% 2.92/1.63 thf(func_def_61, type, fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o).
% 2.92/1.63 thf(func_def_62, type, fresh_1711070152reeRes: name > produc1834551554reeRes > $o).
% 2.92/1.63 thf(func_def_63, type, fresh_567880928ubject: name > produc691362330ubject > $o).
% 2.92/1.63 thf(func_def_64, type, fresh_1963366730reeRes: name > produc2008547984reeRes > $o).
% 2.92/1.63 thf(func_def_65, type, fresh_820177506ubject: name > produc865358760ubject > $o).
% 2.92/1.63 thf(func_def_66, type, fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o).
% 2.92/1.63 thf(func_def_67, type, fresh_2007541374s_name: name > produc2052722628s_name > $o).
% 2.92/1.63 thf(func_def_68, type, fresh_1847501388Res_pi: name > produc992857746Res_pi > $o).
% 2.92/1.63 thf(func_def_69, type, fresh_493808761reeRes: name > produc1357834675reeRes > $o).
% 2.92/1.63 thf(func_def_70, type, fresh_1498103185ubject: name > produc214645451ubject > $o).
% 2.92/1.63 thf(func_def_71, type, fresh_1953561446t_name: name > produc1998742700t_name > $o).
% 2.92/1.63 thf(func_def_72, type, fresh_994896692ect_pi: name > produc140253050ect_pi > $o).
% 2.92/1.63 thf(func_def_73, type, fresh_1638563217reeRes: name > produc355105483reeRes > $o).
% 2.92/1.63 thf(func_def_74, type, fresh_495373993ubject: name > produc1359399907ubject > $o).
% 2.92/1.63 thf(func_def_75, type, produc1342893193ion_pi: (name > noption_pi) > (name > noption_pi) > produc1462499409ion_pi).
% 2.92/1.63 thf(func_def_76, type, produc540578151i_name: (name > noption_pi) > name > produc405342261i_name).
% 2.92/1.63 thf(func_def_77, type, produc1820286517_pi_pi: (name > noption_pi) > pi > produc629157763_pi_pi).
% 2.92/1.63 thf(func_def_78, type, produc1505598906reeRes: (name > noption_pi) > late_freeRes > produc1834551554reeRes).
% 2.92/1.63 thf(func_def_79, type, produc581368530ubject: (name > noption_pi) > late_subject > produc691362330ubject).
% 2.92/1.63 thf(func_def_80, type, produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes).
% 2.92/1.63 thf(func_def_81, type, produc607574050ubject: name > late_subject > produc865358760ubject).
% 2.92/1.63 thf(func_def_82, type, product_Pair_pi_pi: pi > pi > product_prod_pi_pi).
% 2.92/1.63 thf(func_def_83, type, produc1701355766s_name: late_freeRes > name > produc2052722628s_name).
% 2.92/1.63 thf(func_def_84, type, produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi).
% 2.92/1.63 thf(func_def_85, type, produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes).
% 2.92/1.63 thf(func_def_86, type, produc320590723ubject: late_freeRes > late_subject > produc214645451ubject).
% 2.92/1.63 thf(func_def_87, type, produc1647375838t_name: late_subject > name > produc1998742700t_name).
% 2.92/1.63 thf(func_def_88, type, produc324947500ect_pi: late_subject > pi > produc140253050ect_pi).
% 2.92/1.63 thf(func_def_89, type, produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes).
% 2.92/1.63 thf(func_def_90, type, produc1465345179ubject: late_subject > late_subject > produc1359399907ubject).
% 2.92/1.63 thf(func_def_91, type, eqvt_pi: set_Pr1834926343_pi_pi > $o).
% 2.92/1.63 thf(func_def_92, type, collec1051790738_pi_pi: (product_prod_pi_pi > $o) > set_Pr1834926343_pi_pi).
% 2.92/1.63 thf(func_def_93, type, strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o).
% 2.92/1.63 thf(func_def_94, type, strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o).
% 2.92/1.63 thf(func_def_95, type, member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o).
% 2.92/1.63 thf(func_def_96, type, p: pi).
% 2.92/1.63 thf(func_def_97, type, pqr: pi).
% 2.92/1.63 thf(func_def_98, type, q: pi).
% 2.92/1.63 thf(func_def_99, type, qr: pi).
% 2.92/1.63 thf(func_def_100, type, q2: pi).
% 2.92/1.63 thf(func_def_101, type, r: pi).
% 2.92/1.63 thf(func_def_102, type, rel: set_Pr1834926343_pi_pi).
% 2.92/1.63 thf(func_def_103, type, a: late_subject).
% 2.92/1.63 thf(func_def_104, type, x: name).
% 2.92/1.63 thf(func_def_122, type, sK0: (product_prod_pi_pi > $o) > pi).
% 2.92/1.63 thf(func_def_123, type, sK1: (product_prod_pi_pi > $o) > pi).
% 2.92/1.63 thf(func_def_124, type, sK2: product_prod_pi_pi > pi).
% 2.92/1.63 thf(func_def_125, type, sK3: product_prod_pi_pi > pi).
% 2.92/1.63 thf(func_def_126, type, sK4: (late_residual > $o) > late_freeRes).
% 2.92/1.63 thf(func_def_127, type, sK5: (late_residual > $o) > pi).
% 2.92/1.63 thf(func_def_128, type, sK6: (late_residual > $o) > name).
% 2.92/1.63 thf(func_def_129, type, sK7: (late_residual > $o) > late_subject).
% 2.92/1.63 thf(func_def_130, type, sK8: (late_residual > $o) > pi).
% 2.92/1.63 thf(func_def_131, type, sK9: set_Pr1834926343_pi_pi > pi).
% 2.92/1.63 thf(func_def_132, type, sK10: (product_prod_pi_pi > $o) > pi).
% 2.92/1.63 thf(func_def_133, type, sK11: (product_prod_pi_pi > $o) > pi).
% 2.92/1.63 thf(func_def_134, type, sK12: set_Pr1834926343_pi_pi > pi).
% 2.92/1.63 thf(func_def_135, type, sK13: set_Pr1834926343_pi_pi > name).
% 2.92/1.63 thf(func_def_136, type, sK14: set_Pr1834926343_pi_pi > pi).
% 2.92/1.63 thf(func_def_137, type, sK15: set_Pr1834926343_pi_pi > pi).
% 2.92/1.63 thf(func_def_138, type, sK16: set_Pr1834926343_pi_pi > pi).
% 2.92/1.63 thf(func_def_139, type, sK17: product_prod_pi_pi > pi).
% 2.92/1.63 thf(func_def_140, type, sK18: product_prod_pi_pi > pi).
% 2.92/1.63 thf(func_def_141, type, sK19: set_Pr1834926343_pi_pi > late_freeRes > pi > pi > pi).
% 2.92/1.63 thf(func_def_142, type, sK20: set_Pr1834926343_pi_pi > pi).
% 2.92/1.63 thf(func_def_143, type, sK21: name > late_subject > (pi > $o) > pi > pi > pi).
% 2.92/1.63 thf(func_def_144, type, sK22: name > late_subject > (pi > $o) > pi > pi > pi).
% 2.92/1.63 thf(func_def_145, type, sK23: pi > name).
% 2.92/1.63 thf(func_def_146, type, sK24: pi > pi > set_Pr1834926343_pi_pi > pi).
% 2.92/1.63 thf(func_def_147, type, sK25: pi > pi > set_Pr1834926343_pi_pi > name).
% 2.92/1.63 thf(func_def_148, type, sK26: pi > pi > set_Pr1834926343_pi_pi > late_subject).
% 2.92/1.63 thf(func_def_149, type, sK27: pi > pi > set_Pr1834926343_pi_pi > pi).
% 2.92/1.63 thf(func_def_150, type, sK28: pi > pi > set_Pr1834926343_pi_pi > late_freeRes).
% 2.92/1.63 thf(func_def_151, type, sK29: set_Pr1834926343_pi_pi > late_subject > pi > name > pi > pi).
% 2.92/1.63 thf(func_def_153, type, ph31: !>[X0: $tType]:(X0)).
% 2.92/1.63 thf(f959,plain,(
% 2.92/1.63 $false),
% 2.92/1.63 inference(subsumption_resolution,[status(thm)],[f958,f916])).
% 2.92/1.63 thf(f916,plain,(
% 2.92/1.63 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r))) = $true)),
% 2.92/1.63 inference(cnf_transformation,[status(thm)],[f769])).
% 2.92/1.63 thf(f769,plain,(
% 2.92/1.63 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r))) = $true)),
% 2.92/1.63 inference(fool_elimination,[status(thm)],[f768])).
% 2.92/1.63 thf(f768,plain,(
% 2.92/1.63 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r)))),
% 2.92/1.63 inference(rectify,[status(thm)],[f3])).
% 2.92/1.63 thf(f3,axiom,(
% 2.92/1.63 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r)))),
% 2.92/1.63 file('/export/starexec/sandbox/tmp/tmp.oMnfvnLLzL/DTF2THF_17066.p',fact_2__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_Aa_092_060guillemotleft_062x_092_060guillemotright_062_A_092_060prec_062_A_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_092_060close_062)).
% 2.92/1.63 thf(f958,plain,(
% 2.92/1.63 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r))) != $true)),
% 2.92/1.63 inference(trivial_inequality_removal,[status(thm)],[f955])).
% 2.92/1.63 thf(f955,plain,(
% 2.92/1.63 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ (par @ (par @ p @ q2) @ r))) != $true) | ($true != $true)),
% 2.92/1.63 inference(superposition,[status(thm)],[f875,f945])).
% 2.92/1.63 thf(f945,plain,(
% 2.92/1.63 ((strong2129052853vative @ (par @ (par @ p @ q2) @ r) @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) = $true)),
% 2.92/1.63 inference(cnf_transformation,[status(thm)],[f387])).
% 2.92/1.63 thf(f387,plain,(
% 2.92/1.63 ((strong2129052853vative @ (par @ (par @ p @ q2) @ r) @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) = $true)),
% 2.92/1.63 inference(fool_elimination,[status(thm)],[f386])).
% 2.92/1.63 thf(f386,plain,(
% 2.92/1.63 (strong2129052853vative @ (par @ (par @ p @ q2) @ r) @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel)),
% 2.92/1.63 inference(rectify,[status(thm)],[f1])).
% 2.92/1.63 thf(f1,axiom,(
% 2.92/1.63 (strong2129052853vative @ (par @ (par @ p @ q2) @ r) @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel)),
% 2.92/1.63 file('/export/starexec/sandbox/tmp/tmp.oMnfvnLLzL/DTF2THF_17066.p',fact_0__092_060open_062derivative_A_I_IP_A_092_060parallel_062_AQ_H_J_A_092_060parallel_062_AR_J_A_IP_A_092_060parallel_062_AQ_H_A_092_060parallel_062_AR_J_Aa_Ax_ARel_092_060close_062)).
% 2.92/1.63 thf(f875,plain,(
% 2.92/1.63 ( ! [X0 : pi] : (((strong2129052853vative @ X0 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) != $true) | ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X0)) != $true)) )),
% 2.92/1.63 inference(cnf_transformation,[status(thm)],[f832])).
% 2.92/1.63 thf(f832,plain,(
% 2.92/1.63 ! [X0 : pi] : (((strong2129052853vative @ X0 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) != $true) | ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X0)) != $true))),
% 2.92/1.63 inference(ennf_transformation,[status(thm)],[f757])).
% 2.92/1.63 thf(f757,plain,(
% 2.92/1.63 ~? [X0 : pi] : (((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X0)) = $true) & ((strong2129052853vative @ X0 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) = $true))),
% 2.92/1.63 inference(fool_elimination,[status(thm)],[f756])).
% 2.92/1.63 thf(f756,plain,(
% 2.92/1.63 ~? [X0 : pi] : ((strong2129052853vative @ X0 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X0)))),
% 2.92/1.63 inference(rectify,[status(thm)],[f322])).
% 2.92/1.63 thf(f322,negated_conjecture,(
% 2.92/1.63 ~? [X59 : pi] : ((strong2129052853vative @ X59 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X59)))),
% 2.92/1.63 inference(negated_conjecture,[status(cth)],[f321])).
% 2.92/1.63 thf(f321,conjecture,(
% 2.92/1.63 ? [X59 : pi] : ((strong2129052853vative @ X59 @ (par @ p @ (par @ q2 @ r)) @ a @ x @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_BoundR @ a @ x @ X59)))),
% 2.92/1.63 file('/export/starexec/sandbox/tmp/tmp.oMnfvnLLzL/DTF2THF_17066.p',conj_0)).
% 2.92/1.63 % SZS output end Proof for DTF2THF_17066
% 2.92/1.63 % (17264)------------------------------
% 2.92/1.63 % (17264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.63 % (17264)Termination reason: Refutation
% 2.92/1.63
% 2.92/1.63 % (17264)Memory used [KB]: 7036
% 2.92/1.63 % (17264)Time elapsed: 0.029 s
% 2.92/1.63 % (17264)Instructions burned: 88 (million)
% 2.92/1.63 % (17264)------------------------------
% 2.92/1.63 % (17264)------------------------------
% 2.92/1.63 % (17258)Success in time 0.045 s
%------------------------------------------------------------------------------