%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP187^1 : 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 : n011.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 08:56:15 AM UTC 2026
% Result : Theorem 4.08s 2.19s
% Output : Refutation 4.08s
% 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 : 333 ( 10 ~; 3 |; 4 &; 316 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 27 ( 26 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 130 ( 127 usr; 16 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,
p2: pi ).
thf(func_def_99,type,
q: pi ).
thf(func_def_100,type,
qr: pi ).
thf(func_def_101,type,
q2: pi ).
thf(func_def_102,type,
r: pi ).
thf(func_def_103,type,
rel: set_Pr1834926343_pi_pi ).
thf(func_def_104,type,
alpha: late_freeRes ).
thf(func_def_105,type,
a: name ).
thf(func_def_106,type,
x: name ).
thf(func_def_107,type,
y: name ).
thf(func_def_125,type,
sK0: ( late_freeRes > $o ) > name ).
thf(func_def_126,type,
sK1: ( late_freeRes > $o ) > name ).
thf(func_def_127,type,
sK2: late_residual > pi > pi ).
thf(func_def_128,type,
sK3: ( late_freeRes > late_residual > $o ) > name ).
thf(func_def_129,type,
sK4: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_130,type,
sK5: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_131,type,
sK6: ( late_freeRes > late_residual > $o ) > late_subject ).
thf(func_def_132,type,
sK7: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_133,type,
sK8: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_134,type,
sK9: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_135,type,
sK10: late_freeRes > name ).
thf(func_def_136,type,
sK11: ( late_freeRes > late_residual > $o ) > late_subject ).
thf(func_def_137,type,
sK12: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_138,type,
sK13: ( late_freeRes > late_residual > $o ) > name ).
thf(func_def_139,type,
sK14: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_140,type,
sK15: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_141,type,
sK16: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_142,type,
sK17: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_143,type,
sK18: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_144,type,
sK19: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_145,type,
sK20: pi > name ).
thf(func_def_146,type,
sK21: product_prod_pi_pi > pi ).
thf(func_def_147,type,
sK22: product_prod_pi_pi > pi ).
thf(func_def_148,type,
sK23: product_prod_pi_pi > pi ).
thf(func_def_149,type,
sK24: product_prod_pi_pi > pi ).
thf(func_def_150,type,
sK25: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_151,type,
sK26: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_152,type,
sK27: ( pi > $o ) > pi > pi > name > late_subject > pi ).
thf(func_def_153,type,
sK28: ( pi > $o ) > pi > pi > name > late_subject > pi ).
thf(func_def_154,type,
sK29: ( late_residual > $o ) > late_freeRes ).
thf(func_def_155,type,
sK30: ( late_residual > $o ) > pi ).
thf(func_def_156,type,
sK31: ( late_residual > $o ) > name ).
thf(func_def_157,type,
sK32: ( late_residual > $o ) > pi ).
thf(func_def_158,type,
sK33: ( late_residual > $o ) > late_subject ).
thf(func_def_159,type,
sK34: late_freeRes > name ).
thf(func_def_160,type,
sK35: late_freeRes > name ).
thf(func_def_161,type,
sK36: name > pi > name > late_residual > name ).
thf(func_def_162,type,
sK37: name > pi > name > late_residual > name ).
thf(func_def_163,type,
sK38: name > pi > name > late_residual > pi ).
thf(func_def_164,type,
sK39: pi > pi > name > late_freeRes > late_freeRes ).
thf(func_def_165,type,
sK40: pi > pi > name > late_freeRes > pi ).
thf(func_def_166,type,
sK41: pi > pi > name > late_freeRes > name ).
thf(func_def_167,type,
sK42: pi > pi > name > late_freeRes > pi ).
thf(func_def_168,type,
sK43: pi > name > late_freeRes > ( pi > $o ) > pi ).
thf(func_def_170,type,
ph45:
!>[X0: $tType] : X0 ).
thf(f1106,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1105,f1034]) ).
thf(f1034,plain,
( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f638]) ).
thf(f638,plain,
( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f637]) ).
thf(f637,plain,
late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ),
file('/export/starexec/sandbox/tmp/tmp.OawlmjC21l/DTF2THF_8720.p',fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062) ).
thf(f1105,plain,
( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1102]) ).
thf(f1102,plain,
( ( $true != $true )
| ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f973,f981]) ).
thf(f981,plain,
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
= $true ),
inference(cnf_transformation,[status(thm)],[f418]) ).
thf(f418,plain,
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
= $true ),
inference(fool_elimination,[status(thm)],[f417]) ).
thf(f417,plain,
member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel,
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel,
file('/export/starexec/sandbox/tmp/tmp.OawlmjC21l/DTF2THF_8720.p',fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062) ).
thf(f973,plain,
! [X0: pi] :
( ( $true
!= ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X0 @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) )
| ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f836]) ).
thf(f836,plain,
! [X0: pi] :
( ( $true
!= ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X0 @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) )
| ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ X0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f668]) ).
thf(f668,plain,
~ ? [X0: pi] :
( ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ X0 ) )
= $true )
& ( $true
= ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X0 @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) ) ),
inference(fool_elimination,[status(thm)],[f667]) ).
thf(f667,plain,
~ ? [X0: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X0 @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
& ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ X0 ) ) ),
inference(rectify,[status(thm)],[f325]) ).
thf(f325,negated_conjecture,
~ ? [X80: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X80 @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
& ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ X80 ) ) ),
inference(negated_conjecture,[status(cth)],[f324]) ).
thf(f324,conjecture,
? [X80: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X80 @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel )
& ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ X80 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OawlmjC21l/DTF2THF_8720.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP187^1 : TPTP v9.2.1. Released v7.5.0.
% 0.10/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Feb 24 08:29:02 EST 2026
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.44 ---- Original DTF file ---
% 0.16/0.44 thf(spec,logic,$$dhol).
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % File : ITP187^1 : TPTP v9.2.1. Released v7.5.0.
% 0.16/0.44 % Domain : Interactive Theorem Proving
% 0.16/0.44 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_617__3414780_1
% 0.16/0.44 % Version : Especial.
% 0.16/0.44 % English :
% 0.16/0.44
% 0.16/0.44 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.16/0.44 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.16/0.44 % Source : [Des21]
% 0.16/0.44 % Names : Strong_Late_Sim_SC/prob_617__3414780_1 [Des21]
% 0.16/0.44
% 0.16/0.44 % Status : Theorem
% 0.16/0.44 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.16/0.44 % Syntax : Number of formulae : 432 ( 194 unt; 108 typ; 0 def)
% 0.16/0.44 % Number of atoms : 876 ( 352 equ; 0 cnn)
% 0.16/0.44 % Maximal formula atoms : 16 ( 2 avg)
% 0.16/0.44 % Number of connectives : 4248 ( 169 ~; 11 |; 82 &;3420 @)
% 0.16/0.44 % ( 0 <=>; 566 =>; 0 <=; 0 <~>)
% 0.16/0.44 % Maximal formula depth : 27 ( 9 avg)
% 0.16/0.44 % Number of types : 27 ( 26 usr)
% 0.16/0.44 % Number of type conns : 289 ( 289 >; 0 *; 0 +; 0 <<)
% 0.16/0.44 % Number of symbols : 85 ( 82 usr; 16 con; 0-5 aty)
% 0.16/0.44 % Number of variables : 1651 ( 9 ^;1603 !; 39 ?;1651 :)
% 0.16/0.44 % SPC : TH0_THM_EQU_NAR
% 0.16/0.44
% 0.16/0.44 % Comments : This file was generated by Sledgehammer 2021-02-23 15:31:49.995
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % Could-be-implicit typings (26)
% 0.16/0.44 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,
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% 0.16/0.44
% 0.16/0.44 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,
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% 0.16/0.44 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
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% 0.16/0.44
% 0.16/0.44 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__Osubject_J,type,
% 0.16/0.44 noption_Late_subject: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__OfreeRes_J,type,
% 0.16/0.44 noption_Late_freeRes: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_n_t__Nominal__Onoption_It__Agent__Oname_J,type,
% 0.16/0.44 noption_name: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 0.16/0.44 noption_pi: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_n_t__Late____Semantics__Oresidual,type,
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% 0.16/0.44
% 0.16/0.44 thf(ty_n_t__Late____Semantics__Osubject,type,
% 0.16/0.44 late_subject: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 0.16/0.44 late_freeRes: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_n_t__Agent__Oname,type,
% 0.16/0.44 name: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_n_t__Agent__Opi,type,
% 0.16/0.44 pi: $tType ).
% 0.16/0.44
% 0.16/0.44 % Explicit typings (82)
% 0.16/0.44 thf(sy_c_Agent_Opi_OBang,type,
% 0.16/0.44 bang: pi > pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Agent_Opi_OInput,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Agent_Opi_OMatch,type,
% 0.16/0.44 match: name > name > pi > pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.16/0.44 mismatch: name > name > pi > pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Agent_Opi_OOutput,type,
% 0.16/0.44 output: name > name > pi > pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Agent_Opi_OPar,type,
% 0.16/0.44 par: pi > pi > pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.16/0.44 piNil: pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Agent_Opi_ORes,type,
% 0.16/0.44 res: name > pi > pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Agent_Opi_OSum,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Agent_Opi_OTau,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Agent_Osubs,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Agent_Osubst__name,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_If_001t__Agent__Oname,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
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% 0.16/0.44 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Late__Semantics_Otransitions,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Oname,type,
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% 0.16/0.44
% 0.16/0.44 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Opi,type,
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% 0.16/0.44 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
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% 0.16/0.44 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Opi,type,
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% 0.16/0.44 produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Opi,type,
% 0.16/0.44 produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__OfreeRes,type,
% 0.16/0.44 produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__Osubject,type,
% 0.16/0.44 produc581368530ubject: ( name > noption_pi ) > late_subject > produc691362330ubject ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 0.16/0.44 produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 0.16/0.44 produc607574050ubject: name > late_subject > produc865358760ubject ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 0.16/0.44 product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 0.16/0.44 produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 0.16/0.44 produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 0.16/0.44 produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
% 0.16/0.44 produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 0.16/0.44 produc1647375838t_name: late_subject > name > produc1998742700t_name ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
% 0.16/0.44 produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 0.16/0.44 produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 0.16/0.44 produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 0.16/0.44 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.16/0.44 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.16/0.44 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.16/0.44 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.16/0.44 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_P,type,
% 0.16/0.44 p: pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_PQR____,type,
% 0.16/0.44 pqr: pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_P_H____,type,
% 0.16/0.44 p2: pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_Q,type,
% 0.16/0.44 q: pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_QR____,type,
% 0.16/0.44 qr: pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_Q_H____,type,
% 0.16/0.44 q2: pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_R,type,
% 0.16/0.44 r: pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_Rel,type,
% 0.16/0.44 rel: set_Pr1834926343_pi_pi ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v__092_060alpha_062____,type,
% 0.16/0.44 alpha: late_freeRes ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_a____,type,
% 0.16/0.44 a: name ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_x____,type,
% 0.16/0.44 x: name ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_y____,type,
% 0.16/0.44 y: name ).
% 0.16/0.44
% 0.16/0.44 % Relevant facts (320)
% 0.16/0.44 thf(fact_0_cClose2_Ohyps_I14_J,axiom,
% 0.16/0.44 alpha = late_TauR ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(14)
% 0.16/0.44 thf(fact_1_cClose2_Ohyps_I6_J,axiom,
% 0.16/0.44 x != y ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(6)
% 0.16/0.44 thf(fact_2_cClose2_Ohyps_I10_J,axiom,
% 0.16/0.44 y != a ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(10)
% 0.16/0.44 thf(fact_3_cClose2_Ohyps_I5_J,axiom,
% 0.16/0.44 x != a ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(5)
% 0.16/0.44 thf(fact_4_Ass,axiom,
% 0.16/0.44 ! [S: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S @ T ) @ U ) @ ( par @ S @ ( par @ T @ U ) ) ) @ rel ) ).
% 0.16/0.44
% 0.16/0.44 % Ass
% 0.16/0.44 thf(fact_5_Res,axiom,
% 0.16/0.44 ! [S: pi,T: pi,X: name] :
% 0.16/0.44 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S @ T ) @ rel )
% 0.16/0.44 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X @ S ) @ ( res @ X @ T ) ) @ rel ) ) ).
% 0.16/0.44
% 0.16/0.44 % Res
% 0.16/0.44 thf(fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062,axiom,
% 0.16/0.44 member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ).
% 0.16/0.44
% 0.16/0.44 % \<open>(<\<nu>y>(P' \<parallel> Q'[x::=y]) \<parallel> R, <\<nu>y>(P' \<parallel> (Q' \<parallel> R)[x::=y])) \<in> Rel\<close>
% 0.16/0.44 thf(fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062,axiom,
% 0.16/0.44 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) ).
% 0.16/0.44
% 0.16/0.44 % \<open>(P \<parallel> Q) \<parallel> R \<longmapsto> \<tau> \<prec> <\<nu>y>(P' \<parallel> Q'[x::=y]) \<parallel> R\<close>
% 0.16/0.44 thf(fact_8_Free_Ohyps,axiom,
% 0.16/0.44 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ) ).
% 0.16/0.44
% 0.16/0.44 % Free.hyps
% 0.16/0.44 thf(fact_9__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_A_092_060parallel_062_AR_J_J_A_092_060in_062_ARel_092_060close_062,axiom,
% 0.16/0.44 member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( par @ ( subs @ q2 @ x @ y ) @ r ) ) ) ) @ rel ).
% 0.16/0.44
% 0.16/0.44 % \<open>(<\<nu>y>(P' \<parallel> Q'[x::=y]) \<parallel> R, <\<nu>y>(P' \<parallel> Q'[x::=y] \<parallel> R)) \<in> Rel\<close>
% 0.16/0.44 thf(fact_10__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_092_060close_062,axiom,
% 0.16/0.44 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % \<open>P \<parallel> Q \<longmapsto> \<tau> \<prec> <\<nu>y>(P' \<parallel> Q'[x::=y])\<close>
% 0.16/0.44 thf(fact_11_cClose2_Ohyps_I13_J,axiom,
% 0.16/0.44 fresh_name_pi @ y @ q ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(13)
% 0.16/0.44 thf(fact_12_cClose2_Ohyps_I12_J,axiom,
% 0.16/0.44 fresh_name_pi @ x @ q ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(12)
% 0.16/0.44 thf(fact_13_cClose2_Ohyps_I7_J,axiom,
% 0.16/0.44 fresh_name_pi @ x @ p2 ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(7)
% 0.16/0.44 thf(fact_14_cClose2_Ohyps_I8_J,axiom,
% 0.16/0.44 fresh_name_pi @ y @ p ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(8)
% 0.16/0.44 thf(fact_15_cClose2_Ohyps_I3_J,axiom,
% 0.16/0.44 fresh_name_pi @ x @ p ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(3)
% 0.16/0.44 thf(fact_16_cClose2_Ohyps_I9_J,axiom,
% 0.16/0.44 fresh_name_pi @ y @ ( par @ q @ r ) ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(9)
% 0.16/0.44 thf(fact_17_cClose2_Ohyps_I4_J,axiom,
% 0.16/0.44 fresh_name_pi @ x @ ( par @ q @ r ) ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(4)
% 0.16/0.44 thf(fact_18_simps_I9_J,axiom,
% 0.16/0.44 ! [X: name,C: name,D: name,P: pi] :
% 0.16/0.44 ( ( X != C )
% 0.16/0.44 => ( ( X != D )
% 0.16/0.44 => ( ( subs @ ( res @ X @ P ) @ C @ D )
% 0.16/0.44 = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % simps(9)
% 0.16/0.44 thf(fact_19_simps_I8_J,axiom,
% 0.16/0.44 ! [P: pi,Q: pi,C: name,D: name] :
% 0.16/0.44 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 0.16/0.44 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % simps(8)
% 0.16/0.44 thf(fact_20_FreshExt,axiom,
% 0.16/0.44 ! [X: name,S: pi,T: pi,U: pi] :
% 0.16/0.44 ( ( fresh_name_pi @ X @ S )
% 0.16/0.44 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X @ ( par @ ( par @ S @ T ) @ U ) ) @ ( par @ S @ ( res @ X @ ( par @ T @ U ) ) ) ) @ rel ) ) ).
% 0.16/0.44
% 0.16/0.44 % FreshExt
% 0.16/0.44 thf(fact_21_FreshExt_H,axiom,
% 0.16/0.44 ! [X: name,U: pi,S: pi,T: pi] :
% 0.16/0.44 ( ( fresh_name_pi @ X @ U )
% 0.16/0.44 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X @ ( par @ S @ T ) ) @ U ) @ ( res @ X @ ( par @ S @ ( par @ T @ U ) ) ) ) @ rel ) ) ).
% 0.16/0.44
% 0.16/0.44 % FreshExt'
% 0.16/0.44 thf(fact_22_Par1F,axiom,
% 0.16/0.44 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 0.16/0.44 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Par1F
% 0.16/0.44 thf(fact_23_Par2F,axiom,
% 0.16/0.44 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.16/0.44 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.16/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Par2F
% 0.16/0.44 thf(fact_24_subst__identity,axiom,
% 0.16/0.44 ! [P: pi,A: name] :
% 0.16/0.44 ( ( subs @ P @ A @ A )
% 0.16/0.44 = P ) ).
% 0.16/0.44
% 0.16/0.44 % subst_identity
% 0.16/0.44 thf(fact_25__092_060open_062x_A_092_060sharp_062_AR_092_060close_062,axiom,
% 0.16/0.44 fresh_name_pi @ x @ r ).
% 0.16/0.44
% 0.16/0.44 % \<open>x \<sharp> R\<close>
% 0.16/0.44 thf(fact_26__092_060open_062y_A_092_060sharp_062_AR_092_060close_062,axiom,
% 0.16/0.44 fresh_name_pi @ y @ r ).
% 0.16/0.44
% 0.16/0.44 % \<open>y \<sharp> R\<close>
% 0.16/0.44 thf(fact_27_prod_Oinject,axiom,
% 0.16/0.44 ! [X1: name > noption_pi,X2: late_subject,Y1: name > noption_pi,Y2: late_subject] :
% 0.16/0.44 ( ( ( produc581368530ubject @ X1 @ X2 )
% 0.16/0.44 = ( produc581368530ubject @ Y1 @ Y2 ) )
% 0.16/0.44 = ( ( X1 = Y1 )
% 0.16/0.44 & ( X2 = Y2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.inject
% 0.16/0.44 thf(fact_28_prod_Oinject,axiom,
% 0.16/0.44 ! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y2: late_freeRes] :
% 0.16/0.44 ( ( ( produc1505598906reeRes @ X1 @ X2 )
% 0.16/0.44 = ( produc1505598906reeRes @ Y1 @ Y2 ) )
% 0.16/0.44 = ( ( X1 = Y1 )
% 0.16/0.44 & ( X2 = Y2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.inject
% 0.16/0.44 thf(fact_29_prod_Oinject,axiom,
% 0.16/0.44 ! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y2: name] :
% 0.16/0.44 ( ( ( produc540578151i_name @ X1 @ X2 )
% 0.16/0.44 = ( produc540578151i_name @ Y1 @ Y2 ) )
% 0.16/0.44 = ( ( X1 = Y1 )
% 0.16/0.44 & ( X2 = Y2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.inject
% 0.16/0.44 thf(fact_30_prod_Oinject,axiom,
% 0.16/0.44 ! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y2: pi] :
% 0.16/0.44 ( ( ( produc1820286517_pi_pi @ X1 @ X2 )
% 0.16/0.44 = ( produc1820286517_pi_pi @ Y1 @ Y2 ) )
% 0.16/0.44 = ( ( X1 = Y1 )
% 0.16/0.44 & ( X2 = Y2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.inject
% 0.16/0.44 thf(fact_31_prod_Oinject,axiom,
% 0.16/0.44 ! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y2: name > noption_pi] :
% 0.16/0.44 ( ( ( produc1342893193ion_pi @ X1 @ X2 )
% 0.16/0.44 = ( produc1342893193ion_pi @ Y1 @ Y2 ) )
% 0.16/0.44 = ( ( X1 = Y1 )
% 0.16/0.44 & ( X2 = Y2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.inject
% 0.16/0.44 thf(fact_32_prod_Oinject,axiom,
% 0.16/0.44 ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 0.16/0.44 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 0.16/0.44 = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 0.16/0.44 = ( ( X1 = Y1 )
% 0.16/0.44 & ( X2 = Y2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod.inject
% 0.16/0.44 thf(fact_33_old_Oprod_Oinject,axiom,
% 0.16/0.44 ! [A: name > noption_pi,B: late_subject,A2: name > noption_pi,B2: late_subject] :
% 0.16/0.44 ( ( ( produc581368530ubject @ A @ B )
% 0.16/0.44 = ( produc581368530ubject @ A2 @ B2 ) )
% 0.16/0.44 = ( ( A = A2 )
% 0.16/0.44 & ( B = B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inject
% 0.16/0.44 thf(fact_34_old_Oprod_Oinject,axiom,
% 0.16/0.44 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 0.16/0.44 ( ( ( produc1505598906reeRes @ A @ B )
% 0.16/0.44 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 0.16/0.44 = ( ( A = A2 )
% 0.16/0.44 & ( B = B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inject
% 0.16/0.44 thf(fact_35_old_Oprod_Oinject,axiom,
% 0.16/0.44 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 0.16/0.44 ( ( ( produc540578151i_name @ A @ B )
% 0.16/0.44 = ( produc540578151i_name @ A2 @ B2 ) )
% 0.16/0.44 = ( ( A = A2 )
% 0.16/0.44 & ( B = B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inject
% 0.16/0.44 thf(fact_36_old_Oprod_Oinject,axiom,
% 0.16/0.44 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 0.16/0.44 ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.16/0.44 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 0.16/0.44 = ( ( A = A2 )
% 0.16/0.44 & ( B = B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inject
% 0.16/0.44 thf(fact_37_old_Oprod_Oinject,axiom,
% 0.16/0.44 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 0.16/0.44 ( ( ( produc1342893193ion_pi @ A @ B )
% 0.16/0.44 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 0.16/0.44 = ( ( A = A2 )
% 0.16/0.44 & ( B = B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inject
% 0.16/0.44 thf(fact_38_old_Oprod_Oinject,axiom,
% 0.16/0.44 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.16/0.44 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.16/0.44 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.16/0.44 = ( ( A = A2 )
% 0.16/0.44 & ( B = B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inject
% 0.16/0.44 thf(fact_39_cClose2_Ohyps_I11_J,axiom,
% 0.16/0.44 fresh_name_pi @ y @ qr ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(11)
% 0.16/0.44 thf(fact_40_pi_Ofresh_I8_J,axiom,
% 0.16/0.44 ! [A: name,X2: pi,X1: pi] :
% 0.16/0.44 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 0.16/0.44 = ( ( fresh_name_pi @ A @ X2 )
% 0.16/0.44 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.fresh(8)
% 0.16/0.44 thf(fact_41_substTrans,axiom,
% 0.16/0.44 ! [B: name,P: pi,A: name,C: name] :
% 0.16/0.44 ( ( fresh_name_pi @ B @ P )
% 0.16/0.44 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
% 0.16/0.44 = ( subs @ P @ A @ C ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % substTrans
% 0.16/0.44 thf(fact_42_name__exists__fresh,axiom,
% 0.16/0.44 ! [X: late_subject] :
% 0.16/0.44 ~ ! [C2: name] :
% 0.16/0.44 ~ ( fresh_717452603ubject @ C2 @ X ) ).
% 0.16/0.44
% 0.16/0.44 % name_exists_fresh
% 0.16/0.44 thf(fact_43_name__exists__fresh,axiom,
% 0.16/0.44 ! [X: late_freeRes] :
% 0.16/0.44 ~ ! [C2: name] :
% 0.16/0.44 ~ ( fresh_1641682979reeRes @ C2 @ X ) ).
% 0.16/0.44
% 0.16/0.44 % name_exists_fresh
% 0.16/0.44 thf(fact_44_name__exists__fresh,axiom,
% 0.16/0.44 ! [X: name] :
% 0.16/0.44 ~ ! [C2: name] :
% 0.16/0.44 ~ ( fresh_name_name @ C2 @ X ) ).
% 0.16/0.44
% 0.16/0.44 % name_exists_fresh
% 0.16/0.44 thf(fact_45_name__exists__fresh,axiom,
% 0.16/0.44 ! [X: pi] :
% 0.16/0.44 ~ ! [C2: name] :
% 0.16/0.44 ~ ( fresh_name_pi @ C2 @ X ) ).
% 0.16/0.44
% 0.16/0.44 % name_exists_fresh
% 0.16/0.44 thf(fact_46_freshRes,axiom,
% 0.16/0.44 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 0.16/0.44
% 0.16/0.44 % freshRes
% 0.16/0.44 thf(fact_47_fresh__fact2,axiom,
% 0.16/0.44 ! [A: name,B: name,P: pi] :
% 0.16/0.44 ( ( A != B )
% 0.16/0.44 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_fact2
% 0.16/0.44 thf(fact_48_fresh__fact1,axiom,
% 0.16/0.44 ! [A: name,P: pi,C: name,B: name] :
% 0.16/0.44 ( ( fresh_name_pi @ A @ P )
% 0.16/0.44 => ( ( A != C )
% 0.16/0.44 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_fact1
% 0.16/0.44 thf(fact_49_forget,axiom,
% 0.16/0.44 ! [A: name,P: pi,B: name] :
% 0.16/0.44 ( ( fresh_name_pi @ A @ P )
% 0.16/0.44 => ( ( subs @ P @ A @ B )
% 0.16/0.44 = P ) ) ).
% 0.16/0.44
% 0.16/0.44 % forget
% 0.16/0.44 thf(fact_50_freshFreeDerivative_I2_J,axiom,
% 0.16/0.44 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.16/0.44 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.44 => ( ( fresh_name_pi @ Y @ P )
% 0.16/0.44 => ( fresh_name_pi @ Y @ P2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % freshFreeDerivative(2)
% 0.16/0.44 thf(fact_51_substRes3,axiom,
% 0.16/0.44 ! [B: name,P: pi,A: name] :
% 0.16/0.44 ( ( fresh_name_pi @ B @ P )
% 0.16/0.44 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 0.16/0.44 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % substRes3
% 0.16/0.44 thf(fact_52_substRes2,axiom,
% 0.16/0.44 ! [B: name,P: pi,A: name] :
% 0.16/0.44 ( ( fresh_name_pi @ B @ P )
% 0.16/0.44 => ( ( res @ A @ P )
% 0.16/0.44 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % substRes2
% 0.16/0.44 thf(fact_53_old_Oprod_Oinducts,axiom,
% 0.16/0.44 ! [P: produc691362330ubject > $o,Prod: produc691362330ubject] :
% 0.16/0.44 ( ! [A3: name > noption_pi,B3: late_subject] : ( P @ ( produc581368530ubject @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ Prod ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inducts
% 0.16/0.44 thf(fact_54_old_Oprod_Oinducts,axiom,
% 0.16/0.44 ! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
% 0.16/0.44 ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ Prod ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inducts
% 0.16/0.44 thf(fact_55_old_Oprod_Oinducts,axiom,
% 0.16/0.44 ! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
% 0.16/0.44 ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ Prod ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inducts
% 0.16/0.44 thf(fact_56_old_Oprod_Oinducts,axiom,
% 0.16/0.44 ! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
% 0.16/0.44 ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ Prod ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inducts
% 0.16/0.44 thf(fact_57_old_Oprod_Oinducts,axiom,
% 0.16/0.44 ! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
% 0.16/0.44 ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ Prod ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inducts
% 0.16/0.44 thf(fact_58_old_Oprod_Oinducts,axiom,
% 0.16/0.44 ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 0.16/0.44 ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ Prod ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.inducts
% 0.16/0.44 thf(fact_59_old_Oprod_Oexhaust,axiom,
% 0.16/0.44 ! [Y: produc691362330ubject] :
% 0.16/0.44 ~ ! [A3: name > noption_pi,B3: late_subject] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( produc581368530ubject @ A3 @ B3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.exhaust
% 0.16/0.44 thf(fact_60_old_Oprod_Oexhaust,axiom,
% 0.16/0.44 ! [Y: produc1834551554reeRes] :
% 0.16/0.44 ~ ! [A3: name > noption_pi,B3: late_freeRes] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( produc1505598906reeRes @ A3 @ B3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.exhaust
% 0.16/0.44 thf(fact_61_old_Oprod_Oexhaust,axiom,
% 0.16/0.44 ! [Y: produc405342261i_name] :
% 0.16/0.44 ~ ! [A3: name > noption_pi,B3: name] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( produc540578151i_name @ A3 @ B3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.exhaust
% 0.16/0.44 thf(fact_62_old_Oprod_Oexhaust,axiom,
% 0.16/0.44 ! [Y: produc629157763_pi_pi] :
% 0.16/0.44 ~ ! [A3: name > noption_pi,B3: pi] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( produc1820286517_pi_pi @ A3 @ B3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.exhaust
% 0.16/0.44 thf(fact_63_old_Oprod_Oexhaust,axiom,
% 0.16/0.44 ! [Y: produc1462499409ion_pi] :
% 0.16/0.44 ~ ! [A3: name > noption_pi,B3: name > noption_pi] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( produc1342893193ion_pi @ A3 @ B3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.exhaust
% 0.16/0.44 thf(fact_64_old_Oprod_Oexhaust,axiom,
% 0.16/0.44 ! [Y: product_prod_pi_pi] :
% 0.16/0.44 ~ ! [A3: pi,B3: pi] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % old.prod.exhaust
% 0.16/0.44 thf(fact_65_mem__Collect__eq,axiom,
% 0.16/0.44 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 0.16/0.44 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 0.16/0.44 = ( P @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 % mem_Collect_eq
% 0.16/0.44 thf(fact_66_Collect__mem__eq,axiom,
% 0.16/0.44 ! [A4: set_Pr1834926343_pi_pi] :
% 0.16/0.44 ( ( collec1051790738_pi_pi
% 0.16/0.44 @ ^ [X3: product_prod_pi_pi] : ( member558706512_pi_pi @ X3 @ A4 ) )
% 0.16/0.44 = A4 ) ).
% 0.16/0.44
% 0.16/0.44 % Collect_mem_eq
% 0.16/0.44 thf(fact_67_Collect__cong,axiom,
% 0.16/0.44 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 0.16/0.44 ( ! [X4: product_prod_pi_pi] :
% 0.16/0.44 ( ( P @ X4 )
% 0.16/0.44 = ( Q @ X4 ) )
% 0.16/0.44 => ( ( collec1051790738_pi_pi @ P )
% 0.16/0.44 = ( collec1051790738_pi_pi @ Q ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Collect_cong
% 0.16/0.44 thf(fact_68_Pair__inject,axiom,
% 0.16/0.44 ! [A: name > noption_pi,B: late_subject,A2: name > noption_pi,B2: late_subject] :
% 0.16/0.44 ( ( ( produc581368530ubject @ A @ B )
% 0.16/0.44 = ( produc581368530ubject @ A2 @ B2 ) )
% 0.16/0.44 => ~ ( ( A = A2 )
% 0.16/0.44 => ( B != B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Pair_inject
% 0.16/0.44 thf(fact_69_Pair__inject,axiom,
% 0.16/0.44 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 0.16/0.44 ( ( ( produc1505598906reeRes @ A @ B )
% 0.16/0.44 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 0.16/0.44 => ~ ( ( A = A2 )
% 0.16/0.44 => ( B != B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Pair_inject
% 0.16/0.44 thf(fact_70_Pair__inject,axiom,
% 0.16/0.44 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 0.16/0.44 ( ( ( produc540578151i_name @ A @ B )
% 0.16/0.44 = ( produc540578151i_name @ A2 @ B2 ) )
% 0.16/0.44 => ~ ( ( A = A2 )
% 0.16/0.44 => ( B != B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Pair_inject
% 0.16/0.44 thf(fact_71_Pair__inject,axiom,
% 0.16/0.44 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 0.16/0.44 ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.16/0.44 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 0.16/0.44 => ~ ( ( A = A2 )
% 0.16/0.44 => ( B != B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Pair_inject
% 0.16/0.44 thf(fact_72_Pair__inject,axiom,
% 0.16/0.44 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 0.16/0.44 ( ( ( produc1342893193ion_pi @ A @ B )
% 0.16/0.44 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 0.16/0.44 => ~ ( ( A = A2 )
% 0.16/0.44 => ( B != B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Pair_inject
% 0.16/0.44 thf(fact_73_Pair__inject,axiom,
% 0.16/0.44 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.16/0.44 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.16/0.44 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.16/0.44 => ~ ( ( A = A2 )
% 0.16/0.44 => ( B != B2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Pair_inject
% 0.16/0.44 thf(fact_74_prod__cases,axiom,
% 0.16/0.44 ! [P: produc691362330ubject > $o,P3: produc691362330ubject] :
% 0.16/0.44 ( ! [A3: name > noption_pi,B3: late_subject] : ( P @ ( produc581368530ubject @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ P3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases
% 0.16/0.44 thf(fact_75_prod__cases,axiom,
% 0.16/0.44 ! [P: produc1834551554reeRes > $o,P3: produc1834551554reeRes] :
% 0.16/0.44 ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ P3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases
% 0.16/0.44 thf(fact_76_prod__cases,axiom,
% 0.16/0.44 ! [P: produc405342261i_name > $o,P3: produc405342261i_name] :
% 0.16/0.44 ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ P3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases
% 0.16/0.44 thf(fact_77_prod__cases,axiom,
% 0.16/0.44 ! [P: produc629157763_pi_pi > $o,P3: produc629157763_pi_pi] :
% 0.16/0.44 ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ P3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases
% 0.16/0.44 thf(fact_78_prod__cases,axiom,
% 0.16/0.44 ! [P: produc1462499409ion_pi > $o,P3: produc1462499409ion_pi] :
% 0.16/0.44 ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ P3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases
% 0.16/0.44 thf(fact_79_prod__cases,axiom,
% 0.16/0.44 ! [P: product_prod_pi_pi > $o,P3: product_prod_pi_pi] :
% 0.16/0.44 ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.16/0.44 => ( P @ P3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % prod_cases
% 0.16/0.44 thf(fact_80_surj__pair,axiom,
% 0.16/0.44 ! [P3: produc691362330ubject] :
% 0.16/0.44 ? [X4: name > noption_pi,Y3: late_subject] :
% 0.16/0.44 ( P3
% 0.16/0.44 = ( produc581368530ubject @ X4 @ Y3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % surj_pair
% 0.16/0.44 thf(fact_81_surj__pair,axiom,
% 0.16/0.44 ! [P3: produc1834551554reeRes] :
% 0.16/0.44 ? [X4: name > noption_pi,Y3: late_freeRes] :
% 0.16/0.44 ( P3
% 0.16/0.44 = ( produc1505598906reeRes @ X4 @ Y3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % surj_pair
% 0.16/0.44 thf(fact_82_surj__pair,axiom,
% 0.16/0.44 ! [P3: produc405342261i_name] :
% 0.16/0.44 ? [X4: name > noption_pi,Y3: name] :
% 0.16/0.44 ( P3
% 0.16/0.44 = ( produc540578151i_name @ X4 @ Y3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % surj_pair
% 0.16/0.44 thf(fact_83_surj__pair,axiom,
% 0.16/0.44 ! [P3: produc629157763_pi_pi] :
% 0.16/0.44 ? [X4: name > noption_pi,Y3: pi] :
% 0.16/0.44 ( P3
% 0.16/0.44 = ( produc1820286517_pi_pi @ X4 @ Y3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % surj_pair
% 0.16/0.44 thf(fact_84_surj__pair,axiom,
% 0.16/0.44 ! [P3: produc1462499409ion_pi] :
% 0.16/0.44 ? [X4: name > noption_pi,Y3: name > noption_pi] :
% 0.16/0.44 ( P3
% 0.16/0.44 = ( produc1342893193ion_pi @ X4 @ Y3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % surj_pair
% 0.16/0.44 thf(fact_85_surj__pair,axiom,
% 0.16/0.44 ! [P3: product_prod_pi_pi] :
% 0.16/0.44 ? [X4: pi,Y3: pi] :
% 0.16/0.44 ( P3
% 0.16/0.44 = ( product_Pair_pi_pi @ X4 @ Y3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % surj_pair
% 0.16/0.44 thf(fact_86_pi_Oinject_I7_J,axiom,
% 0.16/0.44 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.16/0.44 ( ( ( par @ X2 @ X1 )
% 0.16/0.44 = ( par @ Y2 @ Y1 ) )
% 0.16/0.44 = ( ( X2 = Y2 )
% 0.16/0.44 & ( X1 = Y1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.inject(7)
% 0.16/0.44 thf(fact_87_residual_Oinject_I2_J,axiom,
% 0.16/0.44 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.16/0.44 ( ( ( late_FreeR @ X2 @ X1 )
% 0.16/0.44 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.16/0.44 = ( ( X2 = Y2 )
% 0.16/0.44 & ( X1 = Y1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.inject(2)
% 0.16/0.44 thf(fact_88_pi_Odistinct_I85_J,axiom,
% 0.16/0.44 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.16/0.44 ( ( par @ Pi1 @ Pi2 )
% 0.16/0.44 != ( res @ Name @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(85)
% 0.16/0.44 thf(fact_89_cClose2_Ohyps_I2_J,axiom,
% 0.16/0.44 late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(2)
% 0.16/0.44 thf(fact_90_fresh__prod,axiom,
% 0.16/0.44 ! [A: name,X: late_subject,Y: late_subject] :
% 0.16/0.44 ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y ) )
% 0.16/0.44 = ( ( fresh_717452603ubject @ A @ X )
% 0.16/0.44 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prod
% 0.16/0.44 thf(fact_91_fresh__prod,axiom,
% 0.16/0.44 ! [A: name,X: late_subject,Y: late_freeRes] :
% 0.16/0.44 ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y ) )
% 0.16/0.44 = ( ( fresh_717452603ubject @ A @ X )
% 0.16/0.44 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prod
% 0.16/0.44 thf(fact_92_fresh__prod,axiom,
% 0.16/0.44 ! [A: name,X: late_subject,Y: name] :
% 0.16/0.44 ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y ) )
% 0.16/0.44 = ( ( fresh_717452603ubject @ A @ X )
% 0.16/0.44 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prod
% 0.16/0.44 thf(fact_93_fresh__prod,axiom,
% 0.16/0.44 ! [A: name,X: late_subject,Y: pi] :
% 0.16/0.44 ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y ) )
% 0.16/0.44 = ( ( fresh_717452603ubject @ A @ X )
% 0.16/0.44 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prod
% 0.16/0.44 thf(fact_94_fresh__prod,axiom,
% 0.16/0.44 ! [A: name,X: late_freeRes,Y: late_subject] :
% 0.16/0.44 ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y ) )
% 0.16/0.44 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.16/0.44 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prod
% 0.16/0.44 thf(fact_95_fresh__prod,axiom,
% 0.16/0.44 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 0.16/0.44 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
% 0.16/0.44 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.16/0.44 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prod
% 0.16/0.44 thf(fact_96_fresh__prod,axiom,
% 0.16/0.44 ! [A: name,X: late_freeRes,Y: name] :
% 0.16/0.44 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
% 0.16/0.44 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.16/0.44 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prod
% 0.16/0.44 thf(fact_97_fresh__prod,axiom,
% 0.16/0.44 ! [A: name,X: late_freeRes,Y: pi] :
% 0.16/0.44 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
% 0.16/0.44 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.16/0.44 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prod
% 0.16/0.44 thf(fact_98_fresh__prod,axiom,
% 0.16/0.44 ! [A: name,X: name,Y: late_subject] :
% 0.16/0.44 ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y ) )
% 0.16/0.44 = ( ( fresh_name_name @ A @ X )
% 0.16/0.44 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prod
% 0.16/0.44 thf(fact_99_fresh__prod,axiom,
% 0.16/0.44 ! [A: name,X: name,Y: late_freeRes] :
% 0.16/0.44 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
% 0.16/0.44 = ( ( fresh_name_name @ A @ X )
% 0.16/0.44 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prod
% 0.16/0.44 thf(fact_100_cClose2_Ohyps_I1_J,axiom,
% 0.16/0.44 late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) ).
% 0.16/0.44
% 0.16/0.44 % cClose2.hyps(1)
% 0.16/0.44 thf(fact_101_cPar1_Ohyps,axiom,
% 0.16/0.44 late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) ).
% 0.16/0.44
% 0.16/0.44 % cPar1.hyps
% 0.16/0.44 thf(fact_102_fresh__prodD_I2_J,axiom,
% 0.16/0.44 ! [A: name,X: name > noption_pi,Y: late_subject] :
% 0.16/0.44 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y ) )
% 0.16/0.44 => ( fresh_717452603ubject @ A @ Y ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(2)
% 0.16/0.44 thf(fact_103_fresh__prodD_I2_J,axiom,
% 0.16/0.44 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 0.16/0.44 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 0.16/0.44 => ( fresh_1641682979reeRes @ A @ Y ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(2)
% 0.16/0.44 thf(fact_104_fresh__prodD_I2_J,axiom,
% 0.16/0.44 ! [A: name,X: name > noption_pi,Y: name] :
% 0.16/0.44 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 0.16/0.44 => ( fresh_name_name @ A @ Y ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(2)
% 0.16/0.44 thf(fact_105_fresh__prodD_I2_J,axiom,
% 0.16/0.44 ! [A: name,X: name > noption_pi,Y: pi] :
% 0.16/0.44 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 0.16/0.44 => ( fresh_name_pi @ A @ Y ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(2)
% 0.16/0.44 thf(fact_106_fresh__prodD_I2_J,axiom,
% 0.16/0.44 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 0.16/0.44 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 0.16/0.44 => ( fresh_543891186ion_pi @ A @ Y ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(2)
% 0.16/0.44 thf(fact_107_fresh__prodD_I2_J,axiom,
% 0.16/0.44 ! [A: name,X: pi,Y: pi] :
% 0.16/0.44 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.16/0.44 => ( fresh_name_pi @ A @ Y ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(2)
% 0.16/0.44 thf(fact_108_fresh__prodD_I1_J,axiom,
% 0.16/0.44 ! [A: name,X: name > noption_pi,Y: late_subject] :
% 0.16/0.44 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y ) )
% 0.16/0.44 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(1)
% 0.16/0.44 thf(fact_109_fresh__prodD_I1_J,axiom,
% 0.16/0.44 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 0.16/0.44 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 0.16/0.44 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(1)
% 0.16/0.44 thf(fact_110_fresh__prodD_I1_J,axiom,
% 0.16/0.44 ! [A: name,X: name > noption_pi,Y: name] :
% 0.16/0.44 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 0.16/0.44 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(1)
% 0.16/0.44 thf(fact_111_fresh__prodD_I1_J,axiom,
% 0.16/0.44 ! [A: name,X: name > noption_pi,Y: pi] :
% 0.16/0.44 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 0.16/0.44 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(1)
% 0.16/0.44 thf(fact_112_fresh__prodD_I1_J,axiom,
% 0.16/0.44 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 0.16/0.44 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 0.16/0.44 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(1)
% 0.16/0.44 thf(fact_113_fresh__prodD_I1_J,axiom,
% 0.16/0.44 ! [A: name,X: pi,Y: pi] :
% 0.16/0.44 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.16/0.44 => ( fresh_name_pi @ A @ X ) ) ).
% 0.16/0.44
% 0.16/0.44 % fresh_prodD(1)
% 0.16/0.44 thf(fact_114_resOutputTauTrans,axiom,
% 0.16/0.44 ! [X: name,A: name,B: name,P: pi,P2: pi] :
% 0.16/0.44 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % resOutputTauTrans
% 0.16/0.44 thf(fact_115_subject_Ofresh_I1_J,axiom,
% 0.16/0.44 ! [A: name,X1: name] :
% 0.16/0.44 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 0.16/0.44 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.16/0.44
% 0.16/0.44 % subject.fresh(1)
% 0.16/0.44 thf(fact_116_subject_Ofresh_I2_J,axiom,
% 0.16/0.44 ! [A: name,X1: name] :
% 0.16/0.44 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 0.16/0.44 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.16/0.44
% 0.16/0.44 % subject.fresh(2)
% 0.16/0.44 thf(fact_117_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.16/0.44 ! [X1: name,Y1: name] :
% 0.16/0.44 ( ( ( late_BoundOutputS @ X1 )
% 0.16/0.44 = ( late_BoundOutputS @ Y1 ) )
% 0.16/0.44 = ( X1 = Y1 ) ) ).
% 0.16/0.44
% 0.16/0.44 % Late_Semantics.subject.inject(2)
% 0.16/0.44 thf(fact_118_freeRes_Ofresh_I2_J,axiom,
% 0.16/0.44 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 0.16/0.44
% 0.16/0.44 % freeRes.fresh(2)
% 0.16/0.44 thf(fact_119_residual_Ofresh_I2_J,axiom,
% 0.16/0.44 ! [A: name,X2: late_freeRes,X1: pi] :
% 0.16/0.44 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 0.16/0.44 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 0.16/0.44 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.fresh(2)
% 0.16/0.44 thf(fact_120_pi_Ofresh_I2_J,axiom,
% 0.16/0.44 ! [A: name,X32: name,X2: name,X1: pi] :
% 0.16/0.44 ( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
% 0.16/0.44 = ( ( fresh_name_name @ A @ X32 )
% 0.16/0.44 & ( fresh_name_name @ A @ X2 )
% 0.16/0.44 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.fresh(2)
% 0.16/0.44 thf(fact_121_pi_Oinject_I1_J,axiom,
% 0.16/0.44 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.16/0.44 ( ( ( output @ X32 @ X2 @ X1 )
% 0.16/0.44 = ( output @ Y32 @ Y2 @ Y1 ) )
% 0.16/0.44 = ( ( X32 = Y32 )
% 0.16/0.44 & ( X2 = Y2 )
% 0.16/0.44 & ( X1 = Y1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.inject(1)
% 0.16/0.44 thf(fact_122_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.16/0.44 ! [Name2: name,Name: name] :
% 0.16/0.44 ( ( late_InputS @ Name2 )
% 0.16/0.44 != ( late_BoundOutputS @ Name ) ) ).
% 0.16/0.44
% 0.16/0.44 % Late_Semantics.subject.distinct(1)
% 0.16/0.44 thf(fact_123_subject_Oinducts,axiom,
% 0.16/0.44 ! [P: late_subject > $o,Subject: late_subject] :
% 0.16/0.44 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 0.16/0.44 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 0.16/0.44 => ( P @ Subject ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subject.inducts
% 0.16/0.44 thf(fact_124_outputBoundTrans,axiom,
% 0.16/0.44 ! [A: name,B: name,P: pi,C: late_subject,X: name,P2: pi] :
% 0.16/0.44 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C @ X @ P2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % outputBoundTrans
% 0.16/0.44 thf(fact_125_resOutputInputTrans,axiom,
% 0.16/0.44 ! [X: name,A: name,B: name,P: pi,C: name,Y: name,P2: pi] :
% 0.16/0.44 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % resOutputInputTrans
% 0.16/0.44 thf(fact_126_Late__Semantics_OResB,axiom,
% 0.16/0.44 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.16/0.44 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.16/0.44 => ( ( fresh_717452603ubject @ Y @ A )
% 0.16/0.44 => ( ( Y != X )
% 0.16/0.44 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Late_Semantics.ResB
% 0.16/0.44 thf(fact_127_freshBoundDerivative_I1_J,axiom,
% 0.16/0.44 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.16/0.44 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.16/0.44 => ( ( fresh_name_pi @ Y @ P )
% 0.16/0.44 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % freshBoundDerivative(1)
% 0.16/0.44 thf(fact_128_outputFreshTrans,axiom,
% 0.16/0.44 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.16/0.44 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.44 => ~ ( ( fresh_1641682979reeRes @ A @ Alpha )
% 0.16/0.44 | ( fresh_1641682979reeRes @ B @ Alpha ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % outputFreshTrans
% 0.16/0.44 thf(fact_129_residual_Odistinct_I1_J,axiom,
% 0.16/0.44 ! [Subject: late_subject,Name2: name,Pi3: pi,FreeRes: late_freeRes,Pi: pi] :
% 0.16/0.44 ( ( late_BoundR @ Subject @ Name2 @ Pi3 )
% 0.16/0.44 != ( late_FreeR @ FreeRes @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.distinct(1)
% 0.16/0.44 thf(fact_130_residual_Oinducts,axiom,
% 0.16/0.44 ! [P: late_residual > $o,Residual: late_residual] :
% 0.16/0.44 ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 0.16/0.44 => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.16/0.44 => ( P @ Residual ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.inducts
% 0.16/0.44 thf(fact_131_pi_Odistinct_I29_J,axiom,
% 0.16/0.44 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.44 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.16/0.44 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(29)
% 0.16/0.44 thf(fact_132_pi_Odistinct_I31_J,axiom,
% 0.16/0.44 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.16/0.44 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.16/0.44 != ( res @ Name @ Pi ) ) ).
% 0.16/0.44
% 0.16/0.44 % pi.distinct(31)
% 0.16/0.44 thf(fact_133_parCasesB_H,axiom,
% 0.16/0.44 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 0.16/0.44 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.16/0.44 => ( ! [P4: pi,A3: late_subject,X4: name,P5: pi,Q3: pi] :
% 0.16/0.44 ( ( ( par @ P @ Q )
% 0.16/0.44 = ( par @ P4 @ Q3 ) )
% 0.16/0.44 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.16/0.44 = ( late_BoundR @ A3 @ X4 @ ( par @ P5 @ Q3 ) ) )
% 0.16/0.44 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 0.16/0.44 => ( ( fresh_name_pi @ X4 @ P4 )
% 0.16/0.44 => ( ( fresh_name_pi @ X4 @ Q3 )
% 0.16/0.44 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) )
% 0.16/0.44 => ~ ! [Q3: pi,A3: late_subject,X4: name,Q4: pi,P4: pi] :
% 0.16/0.44 ( ( ( par @ P @ Q )
% 0.16/0.44 = ( par @ P4 @ Q3 ) )
% 0.16/0.44 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.16/0.44 = ( late_BoundR @ A3 @ X4 @ ( par @ P4 @ Q4 ) ) )
% 0.16/0.44 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A3 @ X4 @ Q4 ) )
% 0.16/0.44 => ( ( fresh_name_pi @ X4 @ P4 )
% 0.16/0.44 => ( ( fresh_name_pi @ X4 @ Q3 )
% 0.16/0.44 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % parCasesB'
% 0.16/0.44 thf(fact_134_transitions_OPar1B,axiom,
% 0.16/0.44 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 0.16/0.44 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.16/0.44 => ( ( fresh_name_pi @ X @ P )
% 0.16/0.44 => ( ( fresh_name_pi @ X @ Q )
% 0.16/0.44 => ( ( fresh_717452603ubject @ X @ A )
% 0.16/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % transitions.Par1B
% 0.16/0.44 thf(fact_135_transitions_OPar2B,axiom,
% 0.16/0.44 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.16/0.44 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.16/0.44 => ( ( fresh_name_pi @ X @ P )
% 0.16/0.44 => ( ( fresh_name_pi @ X @ Q )
% 0.16/0.44 => ( ( fresh_717452603ubject @ X @ A )
% 0.16/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % transitions.Par2B
% 0.16/0.44 thf(fact_136_transitions_OResB,axiom,
% 0.16/0.44 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.16/0.44 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.16/0.44 => ( ( fresh_717452603ubject @ Y @ A )
% 0.16/0.44 => ( ( Y != X )
% 0.16/0.44 => ( ( fresh_name_pi @ X @ P )
% 0.16/0.44 => ( ( fresh_717452603ubject @ X @ A )
% 0.16/0.44 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % transitions.ResB
% 0.16/0.44 thf(fact_137_freshResidual,axiom,
% 0.16/0.44 ! [P: pi,Rs: late_residual,X: name] :
% 0.16/0.44 ( ( late_transitions @ P @ Rs )
% 0.16/0.44 => ( ( fresh_name_pi @ X @ P )
% 0.16/0.44 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % freshResidual
% 0.16/0.44 thf(fact_138_freshBoundDerivative_I2_J,axiom,
% 0.16/0.44 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.16/0.44 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.16/0.44 => ( ( fresh_name_pi @ Y @ P )
% 0.16/0.44 => ( ( Y != X )
% 0.16/0.44 => ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % freshBoundDerivative(2)
% 0.16/0.44 thf(fact_139_residual_Ostrong__inducts,axiom,
% 0.16/0.44 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 0.16/0.44 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.44 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.16/0.44 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.16/0.44 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.16/0.44 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.16/0.44 => ( P @ Z @ Residual ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.strong_inducts
% 0.16/0.44 thf(fact_140_residual_Ostrong__inducts,axiom,
% 0.16/0.44 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.16/0.44 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.44 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.16/0.44 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.16/0.44 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.16/0.44 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.16/0.44 => ( P @ Z @ Residual ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.strong_inducts
% 0.16/0.44 thf(fact_141_residual_Ostrong__inducts,axiom,
% 0.16/0.44 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.16/0.44 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 0.16/0.44 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.16/0.44 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.16/0.44 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.16/0.44 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.16/0.44 => ( P @ Z @ Residual ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.strong_inducts
% 0.16/0.44 thf(fact_142_residual_Ostrong__inducts,axiom,
% 0.16/0.44 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.16/0.44 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 0.16/0.44 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.16/0.44 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.16/0.44 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.16/0.44 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.16/0.44 => ( P @ Z @ Residual ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.strong_inducts
% 0.16/0.44 thf(fact_143_residual_Ostrong__induct,axiom,
% 0.16/0.44 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 0.16/0.44 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.44 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.16/0.44 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.16/0.44 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.16/0.44 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.16/0.44 => ( P @ Z @ Residual ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.strong_induct
% 0.16/0.44 thf(fact_144_residual_Ostrong__induct,axiom,
% 0.16/0.44 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.16/0.44 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.44 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.16/0.44 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.16/0.44 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.16/0.44 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.16/0.44 => ( P @ Z @ Residual ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.strong_induct
% 0.16/0.44 thf(fact_145_residual_Ostrong__induct,axiom,
% 0.16/0.44 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.16/0.44 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 0.16/0.44 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.16/0.44 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.16/0.44 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.16/0.44 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.16/0.44 => ( P @ Z @ Residual ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.strong_induct
% 0.16/0.44 thf(fact_146_residual_Ostrong__induct,axiom,
% 0.16/0.44 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.16/0.44 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 0.16/0.44 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.16/0.44 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.16/0.44 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.16/0.44 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.16/0.44 => ( P @ Z @ Residual ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % residual.strong_induct
% 0.16/0.44 thf(fact_147_resTrans_I1_J,axiom,
% 0.16/0.44 ! [X: name,B: name,P: pi,Rs: late_residual] :
% 0.16/0.44 ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 0.16/0.44
% 0.16/0.44 % resTrans(1)
% 0.16/0.44 thf(fact_148_Late__Semantics_OClose1,axiom,
% 0.16/0.44 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.16/0.44 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.16/0.44 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.16/0.44 => ( ( fresh_name_pi @ Y @ P )
% 0.16/0.44 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Late_Semantics.Close1
% 0.16/0.44 thf(fact_149_Late__Semantics_OClose2,axiom,
% 0.16/0.44 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 0.16/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ Y @ Q )
% 0.16/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics.Close2
% 0.16/0.45 thf(fact_150_transitions_OClose1,axiom,
% 0.16/0.45 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.16/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ P )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ Q )
% 0.16/0.45 => ( ( fresh_name_pi @ Y @ P )
% 0.16/0.45 => ( ( fresh_name_pi @ Y @ Q )
% 0.16/0.45 => ( ( X != A )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ Q2 )
% 0.16/0.45 => ( ( Y != A )
% 0.16/0.45 => ( ( fresh_name_pi @ Y @ P2 )
% 0.16/0.45 => ( ( X != Y )
% 0.16/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % transitions.Close1
% 0.16/0.45 thf(fact_151_transitions_OClose2,axiom,
% 0.16/0.45 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 0.16/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ P )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ Q )
% 0.16/0.45 => ( ( fresh_name_pi @ Y @ P )
% 0.16/0.45 => ( ( fresh_name_pi @ Y @ Q )
% 0.16/0.45 => ( ( X != A )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ P2 )
% 0.16/0.45 => ( ( Y != A )
% 0.16/0.45 => ( ( fresh_name_pi @ Y @ Q2 )
% 0.16/0.45 => ( ( X != Y )
% 0.16/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % transitions.Close2
% 0.16/0.45 thf(fact_152_resCasesF,axiom,
% 0.16/0.45 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 0.16/0.45 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.16/0.45 => ( ! [P5: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 0.16/0.45 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.16/0.45 => ( F @ ( res @ X @ P5 ) ) ) )
% 0.16/0.45 => ( F @ XP ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % resCasesF
% 0.16/0.45 thf(fact_153_resCasesF_H,axiom,
% 0.16/0.45 ! [X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.16/0.45 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.45 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.16/0.45 ( ( ( res @ X @ P )
% 0.16/0.45 = ( res @ Y3 @ P4 ) )
% 0.16/0.45 => ( ( ( late_FreeR @ Alpha @ P2 )
% 0.16/0.45 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.16/0.45 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.16/0.45 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % resCasesF'
% 0.16/0.45 thf(fact_154_ResF,axiom,
% 0.16/0.45 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.45 => ( ( fresh_1641682979reeRes @ Y @ Alpha )
% 0.16/0.45 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % ResF
% 0.16/0.45 thf(fact_155_Late__Semantics_OPar1B,axiom,
% 0.16/0.45 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ Q )
% 0.16/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics.Par1B
% 0.16/0.45 thf(fact_156_Late__Semantics_OPar2B,axiom,
% 0.16/0.45 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ P )
% 0.16/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics.Par2B
% 0.16/0.45 thf(fact_157_parCasesB,axiom,
% 0.16/0.45 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 0.16/0.45 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ P )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ Q )
% 0.16/0.45 => ( ! [P5: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P5 ) )
% 0.16/0.45 => ( Prop @ ( par @ P5 @ Q ) ) )
% 0.16/0.45 => ( ! [Q4: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q4 ) )
% 0.16/0.45 => ( Prop @ ( par @ P @ Q4 ) ) )
% 0.16/0.45 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % parCasesB
% 0.16/0.45 thf(fact_158_freshFreeDerivative_I1_J,axiom,
% 0.16/0.45 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ Y @ P )
% 0.16/0.45 => ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % freshFreeDerivative(1)
% 0.16/0.45 thf(fact_159_outputTauTrans,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,P2: pi] :
% 0.16/0.45 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % outputTauTrans
% 0.16/0.45 thf(fact_160_transitions_OComm1,axiom,
% 0.16/0.45 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.16/0.45 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ P )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ Q )
% 0.16/0.45 => ( ( X != A )
% 0.16/0.45 => ( ( X != B )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ Q2 )
% 0.16/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % transitions.Comm1
% 0.16/0.45 thf(fact_161_transitions_OComm2,axiom,
% 0.16/0.45 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.16/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ P )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ Q )
% 0.16/0.45 => ( ( X != A )
% 0.16/0.45 => ( ( X != B )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ P2 )
% 0.16/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % transitions.Comm2
% 0.16/0.45 thf(fact_162_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.16/0.45 ! [X2: name,Y2: name] :
% 0.16/0.45 ( ( ( late_BoundOutputS @ X2 )
% 0.16/0.45 = ( late_BoundOutputS @ Y2 ) )
% 0.16/0.45 = ( X2 = Y2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics1.subject.inject(2)
% 0.16/0.45 thf(fact_163_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.16/0.45 ! [X1: name,Y1: name] :
% 0.16/0.45 ( ( ( late_InputS @ X1 )
% 0.16/0.45 = ( late_InputS @ Y1 ) )
% 0.16/0.45 = ( X1 = Y1 ) ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics1.subject.inject(1)
% 0.16/0.45 thf(fact_164_Late__Semantics_OComm1,axiom,
% 0.16/0.45 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.16/0.45 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.16/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics.Comm1
% 0.16/0.45 thf(fact_165_Late__Semantics_OComm2,axiom,
% 0.16/0.45 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.16/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.16/0.45 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics.Comm2
% 0.16/0.45 thf(fact_166_subject_Oexhaust,axiom,
% 0.16/0.45 ! [Y: late_subject] :
% 0.16/0.45 ( ! [X12: name] :
% 0.16/0.45 ( Y
% 0.16/0.45 != ( late_InputS @ X12 ) )
% 0.16/0.45 => ~ ! [X22: name] :
% 0.16/0.45 ( Y
% 0.16/0.45 != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % subject.exhaust
% 0.16/0.45 thf(fact_167_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.16/0.45 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.16/0.45 ( ( ( late_OutputR @ X11 @ X122 )
% 0.16/0.45 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.16/0.45 = ( ( X11 = Y11 )
% 0.16/0.45 & ( X122 = Y12 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics1.freeRes.inject
% 0.16/0.45 thf(fact_168_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.16/0.45 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.16/0.45 ( ( ( late_OutputR @ X2 @ X1 )
% 0.16/0.45 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.16/0.45 = ( ( X2 = Y2 )
% 0.16/0.45 & ( X1 = Y1 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics.freeRes.inject
% 0.16/0.45 thf(fact_169_name__fresh,axiom,
% 0.16/0.45 ( fresh_name_name
% 0.16/0.45 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % name_fresh
% 0.16/0.45 thf(fact_170_freeRes_Ofresh_I1_J,axiom,
% 0.16/0.45 ! [A: name,X2: name,X1: name] :
% 0.16/0.45 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 0.16/0.45 = ( ( fresh_name_name @ A @ X2 )
% 0.16/0.45 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % freeRes.fresh(1)
% 0.16/0.45 thf(fact_171_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.16/0.45 ! [X11: name,X122: name] :
% 0.16/0.45 ( ( late_OutputR @ X11 @ X122 )
% 0.16/0.45 != late_TauR ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics1.freeRes.distinct(1)
% 0.16/0.45 thf(fact_172_freeRes_Oexhaust,axiom,
% 0.16/0.45 ! [Y: late_freeRes] :
% 0.16/0.45 ( ! [X112: name,X123: name] :
% 0.16/0.45 ( Y
% 0.16/0.45 != ( late_OutputR @ X112 @ X123 ) )
% 0.16/0.45 => ( Y = late_TauR ) ) ).
% 0.16/0.45
% 0.16/0.45 % freeRes.exhaust
% 0.16/0.45 thf(fact_173_freeRes_Oinducts,axiom,
% 0.16/0.45 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.16/0.45 ( ! [Name12: name,Name23: name] : ( P @ ( late_OutputR @ Name12 @ Name23 ) )
% 0.16/0.45 => ( ( P @ late_TauR )
% 0.16/0.45 => ( P @ FreeRes3 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % freeRes.inducts
% 0.16/0.45 thf(fact_174_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name] :
% 0.16/0.45 ( ( late_OutputR @ Name1 @ Name22 )
% 0.16/0.45 != late_TauR ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics.freeRes.distinct(1)
% 0.16/0.45 thf(fact_175_Output,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 0.16/0.45
% 0.16/0.45 % Output
% 0.16/0.45 thf(fact_176_outputIneqTrans,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,C: name,D: name,P2: pi] :
% 0.16/0.45 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P2 ) )
% 0.16/0.45 => ~ ( ( A != C )
% 0.16/0.45 | ( B != D ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % outputIneqTrans
% 0.16/0.45 thf(fact_177_outputCases_H,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.16/0.45 ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 0.16/0.45 => ~ ! [A3: name,B3: name,P4: pi] :
% 0.16/0.45 ( ( ( A = A3 )
% 0.16/0.45 & ( B = B3 )
% 0.16/0.45 & ( P = P4 ) )
% 0.16/0.45 => ( Rs
% 0.16/0.45 != ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P4 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % outputCases'
% 0.16/0.45 thf(fact_178_outputCases,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.16/0.45 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.45 => ( ( ( Alpha
% 0.16/0.45 = ( late_OutputR @ A @ B ) )
% 0.16/0.45 => ( ( P = P2 )
% 0.16/0.45 => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 0.16/0.45 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % outputCases
% 0.16/0.45 thf(fact_179_resOutputOutputTrans,axiom,
% 0.16/0.45 ! [X: name,A: name,P: pi,B: name,Y: name,P2: pi] :
% 0.16/0.45 ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % resOutputOutputTrans
% 0.16/0.45 thf(fact_180_Open,axiom,
% 0.16/0.45 ! [P: pi,A: name,B: name,P2: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.16/0.45 => ( ( A != B )
% 0.16/0.45 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Open
% 0.16/0.45 thf(fact_181_resCasesB_H,axiom,
% 0.16/0.45 ! [X5: name,P: pi,A: late_subject,Y4: name,P2: pi] :
% 0.16/0.45 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y4 @ P2 ) )
% 0.16/0.45 => ( ! [P4: pi,A3: name,B3: name] :
% 0.16/0.45 ( ( ( res @ X5 @ P )
% 0.16/0.45 = ( res @ B3 @ P4 ) )
% 0.16/0.45 => ! [P5: pi] :
% 0.16/0.45 ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 0.16/0.45 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 0.16/0.45 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 0.16/0.45 => ( A3 = B3 ) ) ) )
% 0.16/0.45 => ~ ! [P4: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
% 0.16/0.45 ( ( ( res @ X5 @ P )
% 0.16/0.45 = ( res @ Y3 @ P4 ) )
% 0.16/0.45 => ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 0.16/0.45 = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 0.16/0.45 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 0.16/0.45 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.16/0.45 => ( ( Y3 != X4 )
% 0.16/0.45 => ( ( fresh_name_pi @ X4 @ P4 )
% 0.16/0.45 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % resCasesB'
% 0.16/0.45 thf(fact_182_resCases_H,axiom,
% 0.16/0.45 ! [X: name,P: pi,Rs: late_residual] :
% 0.16/0.45 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 0.16/0.45 => ( ! [P4: pi,A3: name,B3: name] :
% 0.16/0.45 ( ( ( res @ X @ P )
% 0.16/0.45 = ( res @ B3 @ P4 ) )
% 0.16/0.45 => ! [P5: pi] :
% 0.16/0.45 ( ( Rs
% 0.16/0.45 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 0.16/0.45 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 0.16/0.45 => ( A3 = B3 ) ) ) )
% 0.16/0.45 => ( ! [P4: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
% 0.16/0.45 ( ( ( res @ X @ P )
% 0.16/0.45 = ( res @ Y3 @ P4 ) )
% 0.16/0.45 => ( ( Rs
% 0.16/0.45 = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 0.16/0.45 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 0.16/0.45 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.16/0.45 => ( ( Y3 != X4 )
% 0.16/0.45 => ( ( fresh_name_pi @ X4 @ P4 )
% 0.16/0.45 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) )
% 0.16/0.45 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.16/0.45 ( ( ( res @ X @ P )
% 0.16/0.45 = ( res @ Y3 @ P4 ) )
% 0.16/0.45 => ( ( Rs
% 0.16/0.45 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.16/0.45 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.16/0.45 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % resCases'
% 0.16/0.45 thf(fact_183_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.16/0.45 ! [X1: name,X2: name] :
% 0.16/0.45 ( ( late_InputS @ X1 )
% 0.16/0.45 != ( late_BoundOutputS @ X2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics1.subject.distinct(1)
% 0.16/0.45 thf(fact_184_resTauOutputTrans,axiom,
% 0.16/0.45 ! [X: name,P: pi,A: name,B: name,P2: pi] :
% 0.16/0.45 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % resTauOutputTrans
% 0.16/0.45 thf(fact_185_resInputBoundOutputTrans,axiom,
% 0.16/0.45 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 0.16/0.45 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % resInputBoundOutputTrans
% 0.16/0.45 thf(fact_186_pi_Ofresh_I3_J,axiom,
% 0.16/0.45 ! [A: name,X1: pi] :
% 0.16/0.45 ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 0.16/0.45 = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.fresh(3)
% 0.16/0.45 thf(fact_187_simps_I2_J,axiom,
% 0.16/0.45 ! [P: pi,C: name,D: name] :
% 0.16/0.45 ( ( subs @ ( tau @ P ) @ C @ D )
% 0.16/0.45 = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simps(2)
% 0.16/0.45 thf(fact_188_pi_Oinject_I2_J,axiom,
% 0.16/0.45 ! [X1: pi,Y1: pi] :
% 0.16/0.45 ( ( ( tau @ X1 )
% 0.16/0.45 = ( tau @ Y1 ) )
% 0.16/0.45 = ( X1 = Y1 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.inject(2)
% 0.16/0.45 thf(fact_189_pi_Odistinct_I35_J,axiom,
% 0.16/0.45 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( ( tau @ Pi3 )
% 0.16/0.45 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(35)
% 0.16/0.45 thf(fact_190_pi_Odistinct_I55_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.45 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(55)
% 0.16/0.45 thf(fact_191_pi_Odistinct_I57_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.16/0.45 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( res @ Name @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(57)
% 0.16/0.45 thf(fact_192_pi_Odistinct_I43_J,axiom,
% 0.16/0.45 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.45 ( ( tau @ Pi3 )
% 0.16/0.45 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(43)
% 0.16/0.45 thf(fact_193_pi_Odistinct_I45_J,axiom,
% 0.16/0.45 ! [Pi3: pi,Name: name,Pi: pi] :
% 0.16/0.45 ( ( tau @ Pi3 )
% 0.16/0.45 != ( res @ Name @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(45)
% 0.16/0.45 thf(fact_194_pi_Odistinct_I21_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(21)
% 0.16/0.45 thf(fact_195_pi_Odistinct_I19_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.16/0.45 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( tau @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(19)
% 0.16/0.45 thf(fact_196_resTrans_I2_J,axiom,
% 0.16/0.45 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 0.16/0.45 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 0.16/0.45
% 0.16/0.45 % resTrans(2)
% 0.16/0.45 thf(fact_197_inputFreeTrans,axiom,
% 0.16/0.45 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.16/0.45 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % inputFreeTrans
% 0.16/0.45 thf(fact_198_tauBoundTrans,axiom,
% 0.16/0.45 ! [P: pi,A: late_subject,X: name,P2: pi] :
% 0.16/0.45 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % tauBoundTrans
% 0.16/0.45 thf(fact_199_resInputFreeTrans,axiom,
% 0.16/0.45 ! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.16/0.45 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % resInputFreeTrans
% 0.16/0.45 thf(fact_200_Late__Semantics_OInput,axiom,
% 0.16/0.45 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 0.16/0.45
% 0.16/0.45 % Late_Semantics.Input
% 0.16/0.45 thf(fact_201_transitions_OInput,axiom,
% 0.16/0.45 ! [X: name,A: name,P: pi] :
% 0.16/0.45 ( ( X != A )
% 0.16/0.45 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % transitions.Input
% 0.16/0.45 thf(fact_202_inputBoundOutputTrans,axiom,
% 0.16/0.45 ! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
% 0.16/0.45 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % inputBoundOutputTrans
% 0.16/0.45 thf(fact_203_resTauBoundTrans,axiom,
% 0.16/0.45 ! [X: name,P: pi,A: late_subject,Y: name,P2: pi] :
% 0.16/0.45 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % resTauBoundTrans
% 0.16/0.45 thf(fact_204_inputIneqTrans,axiom,
% 0.16/0.45 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 0.16/0.45 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.16/0.45 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 0.16/0.45
% 0.16/0.45 % inputIneqTrans
% 0.16/0.45 thf(fact_205_tauOutputTrans,axiom,
% 0.16/0.45 ! [P: pi,A: name,B: name,P2: pi] :
% 0.16/0.45 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 0.16/0.45
% 0.16/0.45 % tauOutputTrans
% 0.16/0.45 thf(fact_206_tauCases,axiom,
% 0.16/0.45 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.16/0.45 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.16/0.45 => ( ( ( Alpha = late_TauR )
% 0.16/0.45 => ( ( P = P2 )
% 0.16/0.45 => ( Prop @ late_TauR @ P ) ) )
% 0.16/0.45 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % tauCases
% 0.16/0.45 thf(fact_207_tauCases_H,axiom,
% 0.16/0.45 ! [P: pi,Rs: late_residual] :
% 0.16/0.45 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.16/0.45 => ~ ! [P4: pi] :
% 0.16/0.45 ( ( ( tau @ P )
% 0.16/0.45 = ( tau @ P4 ) )
% 0.16/0.45 => ( Rs
% 0.16/0.45 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % tauCases'
% 0.16/0.45 thf(fact_208_Tau,axiom,
% 0.16/0.45 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.16/0.45
% 0.16/0.45 % Tau
% 0.16/0.45 thf(fact_209_residual_Ofresh_I1_J,axiom,
% 0.16/0.45 ! [A: name,X32: late_subject,X1: name,X2: pi] :
% 0.16/0.45 ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.16/0.45 = ( ( fresh_717452603ubject @ A @ X32 )
% 0.16/0.45 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % residual.fresh(1)
% 0.16/0.45 thf(fact_210_simps_I3_J,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.16/0.45 ( ( subs @ ( output @ A @ B @ P ) @ C @ D )
% 0.16/0.45 = ( output @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simps(3)
% 0.16/0.45 thf(fact_211_substInput,axiom,
% 0.16/0.45 ! [X: name,B: name,C: name,A: name,P: pi] :
% 0.16/0.45 ( ( X != B )
% 0.16/0.45 => ( ( X != C )
% 0.16/0.45 => ( ( subs @ ( input @ A @ X @ P ) @ B @ C )
% 0.16/0.45 = ( input @ ( subst_name @ A @ B @ C ) @ X @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % substInput
% 0.16/0.45 thf(fact_212_simps_I4_J,axiom,
% 0.16/0.45 ! [X: name,A: name,C: name,D: name,P: pi] :
% 0.16/0.45 ( ( X != A )
% 0.16/0.45 => ( ( X != C )
% 0.16/0.45 => ( ( X != D )
% 0.16/0.45 => ( ( subs @ ( input @ A @ X @ P ) @ C @ D )
% 0.16/0.45 = ( input @ ( subst_name @ A @ C @ D ) @ X @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simps(4)
% 0.16/0.45 thf(fact_213_pi_Ofresh_I9_J,axiom,
% 0.16/0.45 ! [A: name,X1: name,X2: pi] :
% 0.16/0.45 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 0.16/0.45 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.fresh(9)
% 0.16/0.45 thf(fact_214_pi_Ofresh_I4_J,axiom,
% 0.16/0.45 ! [A: name,X32: name,X1: name,X2: pi] :
% 0.16/0.45 ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
% 0.16/0.45 = ( ( fresh_name_name @ A @ X32 )
% 0.16/0.45 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.fresh(4)
% 0.16/0.45 thf(fact_215_pi_Oinject_I3_J,axiom,
% 0.16/0.45 ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
% 0.16/0.45 ( ( ( input @ X32 @ X1 @ X2 )
% 0.16/0.45 = ( input @ Y32 @ Y1 @ Y2 ) )
% 0.16/0.45 = ( ( X32 = Y32 )
% 0.16/0.45 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.16/0.45 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.inject(3)
% 0.16/0.45 thf(fact_216_abs__fun__eq1,axiom,
% 0.16/0.45 ! [A: name,X: name,Y: name] :
% 0.16/0.45 ( ( ( abs_fun_name_name @ A @ X )
% 0.16/0.45 = ( abs_fun_name_name @ A @ Y ) )
% 0.16/0.45 = ( X = Y ) ) ).
% 0.16/0.45
% 0.16/0.45 % abs_fun_eq1
% 0.16/0.45 thf(fact_217_abs__fun__eq1,axiom,
% 0.16/0.45 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 0.16/0.45 ( ( ( abs_fu681348580reeRes @ A @ X )
% 0.16/0.45 = ( abs_fu681348580reeRes @ A @ Y ) )
% 0.16/0.45 = ( X = Y ) ) ).
% 0.16/0.45
% 0.16/0.45 % abs_fun_eq1
% 0.16/0.45 thf(fact_218_abs__fun__eq1,axiom,
% 0.16/0.45 ! [A: name,X: late_subject,Y: late_subject] :
% 0.16/0.45 ( ( ( abs_fu1904601852ubject @ A @ X )
% 0.16/0.45 = ( abs_fu1904601852ubject @ A @ Y ) )
% 0.16/0.45 = ( X = Y ) ) ).
% 0.16/0.45
% 0.16/0.45 % abs_fun_eq1
% 0.16/0.45 thf(fact_219_abs__fun__eq1,axiom,
% 0.16/0.45 ! [A: name,X: pi,Y: pi] :
% 0.16/0.45 ( ( ( abs_fun_name_pi @ A @ X )
% 0.16/0.45 = ( abs_fun_name_pi @ A @ Y ) )
% 0.16/0.45 = ( X = Y ) ) ).
% 0.16/0.45
% 0.16/0.45 % abs_fun_eq1
% 0.16/0.45 thf(fact_220_subst__name__def,axiom,
% 0.16/0.45 ( subst_name
% 0.16/0.45 = ( ^ [A5: name,B4: name,C3: name] : ( if_name @ ( A5 = B4 ) @ C3 @ A5 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % subst_name_def
% 0.16/0.45 thf(fact_221_name__fresh__abs,axiom,
% 0.16/0.45 ! [B: name,A: name,X: late_subject] :
% 0.16/0.45 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 0.16/0.45 = ( ( B = A )
% 0.16/0.45 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % name_fresh_abs
% 0.16/0.45 thf(fact_222_name__fresh__abs,axiom,
% 0.16/0.45 ! [B: name,A: name,X: late_freeRes] :
% 0.16/0.45 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.16/0.45 = ( ( B = A )
% 0.16/0.45 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % name_fresh_abs
% 0.16/0.45 thf(fact_223_name__fresh__abs,axiom,
% 0.16/0.45 ! [B: name,A: name,X: name] :
% 0.16/0.45 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.16/0.45 = ( ( B = A )
% 0.16/0.45 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % name_fresh_abs
% 0.16/0.45 thf(fact_224_name__fresh__abs,axiom,
% 0.16/0.45 ! [B: name,A: name,X: pi] :
% 0.16/0.45 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.16/0.45 = ( ( B = A )
% 0.16/0.45 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % name_fresh_abs
% 0.16/0.45 thf(fact_225_abs__fresh_I1_J,axiom,
% 0.16/0.45 ! [B: name,A: name,X: late_subject] :
% 0.16/0.45 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 0.16/0.45 = ( ( B = A )
% 0.16/0.45 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % abs_fresh(1)
% 0.16/0.45 thf(fact_226_abs__fresh_I1_J,axiom,
% 0.16/0.45 ! [B: name,A: name,X: late_freeRes] :
% 0.16/0.45 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.16/0.45 = ( ( B = A )
% 0.16/0.45 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % abs_fresh(1)
% 0.16/0.45 thf(fact_227_abs__fresh_I1_J,axiom,
% 0.16/0.45 ! [B: name,A: name,X: name] :
% 0.16/0.45 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.16/0.45 = ( ( B = A )
% 0.16/0.45 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % abs_fresh(1)
% 0.16/0.45 thf(fact_228_abs__fresh_I1_J,axiom,
% 0.16/0.45 ! [B: name,A: name,X: pi] :
% 0.16/0.45 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.16/0.45 = ( ( B = A )
% 0.16/0.45 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % abs_fresh(1)
% 0.16/0.45 thf(fact_229_residual_Oinject_I1_J,axiom,
% 0.16/0.45 ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 0.16/0.45 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 0.16/0.45 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 0.16/0.45 = ( ( X32 = Y32 )
% 0.16/0.45 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.16/0.45 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % residual.inject(1)
% 0.16/0.45 thf(fact_230_pi_Oinject_I8_J,axiom,
% 0.16/0.45 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 0.16/0.45 ( ( ( res @ X1 @ X2 )
% 0.16/0.45 = ( res @ Y1 @ Y2 ) )
% 0.16/0.45 = ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.16/0.45 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.inject(8)
% 0.16/0.45 thf(fact_231_inputCases_H,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.16/0.45 ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 0.16/0.45 => ~ ! [X4: name,A3: name,P4: pi] :
% 0.16/0.45 ( ( ( A = A3 )
% 0.16/0.45 & ( ( abs_fun_name_pi @ B @ P )
% 0.16/0.45 = ( abs_fun_name_pi @ X4 @ P4 ) ) )
% 0.16/0.45 => ( ( Rs
% 0.16/0.45 = ( late_BoundR @ ( late_InputS @ A3 ) @ X4 @ P4 ) )
% 0.16/0.45 => ( X4 = A3 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % inputCases'
% 0.16/0.45 thf(fact_232_resSimCases,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C4: late_subject] :
% 0.16/0.45 ( ( eqvt_pi @ Rel )
% 0.16/0.45 => ( ! [Q4: pi,A3: name] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.16/0.45 => ( ( A3 != X )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.16/0.45 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.16/0.45 => ( ( X != Y3 )
% 0.16/0.45 => ( ( fresh_717452603ubject @ Y3 @ C4 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.16/0.45 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.16/0.45 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.16/0.45 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % resSimCases
% 0.16/0.45 thf(fact_233_resSimCases,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C4: late_freeRes] :
% 0.16/0.45 ( ( eqvt_pi @ Rel )
% 0.16/0.45 => ( ! [Q4: pi,A3: name] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.16/0.45 => ( ( A3 != X )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.16/0.45 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.16/0.45 => ( ( X != Y3 )
% 0.16/0.45 => ( ( fresh_1641682979reeRes @ Y3 @ C4 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.16/0.45 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.16/0.45 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.16/0.45 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % resSimCases
% 0.16/0.45 thf(fact_234_resSimCases,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C4: name] :
% 0.16/0.45 ( ( eqvt_pi @ Rel )
% 0.16/0.45 => ( ! [Q4: pi,A3: name] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.16/0.45 => ( ( A3 != X )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.16/0.45 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.16/0.45 => ( ( X != Y3 )
% 0.16/0.45 => ( ( fresh_name_name @ Y3 @ C4 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.16/0.45 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.16/0.45 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.16/0.45 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % resSimCases
% 0.16/0.45 thf(fact_235_resSimCases,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C4: pi] :
% 0.16/0.45 ( ( eqvt_pi @ Rel )
% 0.16/0.45 => ( ! [Q4: pi,A3: name] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.16/0.45 => ( ( A3 != X )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.16/0.45 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.16/0.45 => ( ( X != Y3 )
% 0.16/0.45 => ( ( fresh_name_pi @ Y3 @ C4 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.16/0.45 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.16/0.45 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.16/0.45 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % resSimCases
% 0.16/0.45 thf(fact_236_parSym,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 0.16/0.45 ( ! [R: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R @ S2 ) @ ( par @ S2 @ R ) ) @ Rel )
% 0.16/0.45 => ( ! [R: pi,S2: pi,X4: name] :
% 0.16/0.45 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R @ S2 ) @ Rel )
% 0.16/0.45 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X4 @ R ) @ ( res @ X4 @ S2 ) ) @ Rel ) )
% 0.16/0.45 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % parSym
% 0.16/0.45 thf(fact_237_simE_I1_J,axiom,
% 0.16/0.45 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 0.16/0.45 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.16/0.45 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X @ P )
% 0.16/0.45 => ? [P5: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P5 ) )
% 0.16/0.45 & ( strong2129052853vative @ P5 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simE(1)
% 0.16/0.45 thf(fact_238_simE_I2_J,axiom,
% 0.16/0.45 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.16/0.45 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.16/0.45 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.16/0.45 => ? [P5: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simE(2)
% 0.16/0.45 thf(fact_239_simCasesCont,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C4: late_subject] :
% 0.16/0.45 ( ( eqvt_pi @ Rel )
% 0.16/0.45 => ( ! [A3: late_subject,X4: name,Q4: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X4 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X4 @ P )
% 0.16/0.45 => ( ( fresh_name_pi @ X4 @ Q )
% 0.16/0.45 => ( ( fresh_717452603ubject @ X4 @ A3 )
% 0.16/0.45 => ( ( fresh_717452603ubject @ X4 @ C4 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P6 ) )
% 0.16/0.45 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X4 @ Rel ) ) ) ) ) ) )
% 0.16/0.45 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.16/0.45 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simCasesCont
% 0.16/0.45 thf(fact_240_simCasesCont,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C4: late_freeRes] :
% 0.16/0.45 ( ( eqvt_pi @ Rel )
% 0.16/0.45 => ( ! [A3: late_subject,X4: name,Q4: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X4 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X4 @ P )
% 0.16/0.45 => ( ( fresh_name_pi @ X4 @ Q )
% 0.16/0.45 => ( ( fresh_717452603ubject @ X4 @ A3 )
% 0.16/0.45 => ( ( fresh_1641682979reeRes @ X4 @ C4 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P6 ) )
% 0.16/0.45 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X4 @ Rel ) ) ) ) ) ) )
% 0.16/0.45 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.16/0.45 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simCasesCont
% 0.16/0.45 thf(fact_241_simCasesCont,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C4: name] :
% 0.16/0.45 ( ( eqvt_pi @ Rel )
% 0.16/0.45 => ( ! [A3: late_subject,X4: name,Q4: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X4 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X4 @ P )
% 0.16/0.45 => ( ( fresh_name_pi @ X4 @ Q )
% 0.16/0.45 => ( ( fresh_717452603ubject @ X4 @ A3 )
% 0.16/0.45 => ( ( fresh_name_name @ X4 @ C4 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P6 ) )
% 0.16/0.45 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X4 @ Rel ) ) ) ) ) ) )
% 0.16/0.45 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.16/0.45 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simCasesCont
% 0.16/0.45 thf(fact_242_simCasesCont,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C4: pi] :
% 0.16/0.45 ( ( eqvt_pi @ Rel )
% 0.16/0.45 => ( ! [A3: late_subject,X4: name,Q4: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X4 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ X4 @ P )
% 0.16/0.45 => ( ( fresh_name_pi @ X4 @ Q )
% 0.16/0.45 => ( ( fresh_717452603ubject @ X4 @ A3 )
% 0.16/0.45 => ( ( fresh_name_pi @ X4 @ C4 )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P6 ) )
% 0.16/0.45 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X4 @ Rel ) ) ) ) ) ) )
% 0.16/0.45 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.16/0.45 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simCasesCont
% 0.16/0.45 thf(fact_243_simCases,axiom,
% 0.16/0.45 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 0.16/0.45 ( ! [A3: late_subject,Y3: name,Q4: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.16/0.45 => ( ( fresh_name_pi @ Y3 @ P )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.16/0.45 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ Y3 @ Rel ) ) ) )
% 0.16/0.45 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.16/0.45 => ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.16/0.45 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simCases
% 0.16/0.45 thf(fact_244_simulation__def,axiom,
% 0.16/0.45 ( strong743114133lation
% 0.16/0.45 = ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 0.16/0.45 ( ! [A5: late_subject,X3: name,Q6: pi] :
% 0.16/0.45 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X3 @ Q6 ) )
% 0.16/0.45 & ( fresh_name_pi @ X3 @ P7 ) )
% 0.16/0.45 => ? [P8: pi] :
% 0.16/0.45 ( ( late_transitions @ P7 @ ( late_BoundR @ A5 @ X3 @ P8 ) )
% 0.16/0.45 & ( strong2129052853vative @ P8 @ Q6 @ A5 @ X3 @ Rel2 ) ) )
% 0.16/0.45 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.16/0.45 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.16/0.45 => ? [P8: pi] :
% 0.16/0.45 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simulation_def
% 0.16/0.45 thf(fact_245_parZeroRight,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.16/0.45 ( ! [Q3: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ Q3 @ ( par @ Q3 @ piNil ) ) @ Rel )
% 0.16/0.45 => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % parZeroRight
% 0.16/0.45 thf(fact_246_parZeroLeft,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.16/0.45 ( ! [Q3: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ Q3 @ piNil ) @ Q3 ) @ Rel )
% 0.16/0.45 => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 0.16/0.45
% 0.16/0.45 % parZeroLeft
% 0.16/0.45 thf(fact_247_simps_I5_J,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.16/0.45 ( ( subs @ ( match @ A @ B @ P ) @ C @ D )
% 0.16/0.45 = ( match @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simps(5)
% 0.16/0.45 thf(fact_248_pi_Ofresh_I1_J,axiom,
% 0.16/0.45 ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 0.16/0.45
% 0.16/0.45 % pi.fresh(1)
% 0.16/0.45 thf(fact_249_simps_I1_J,axiom,
% 0.16/0.45 ! [C: name,D: name] :
% 0.16/0.45 ( ( subs @ piNil @ C @ D )
% 0.16/0.45 = piNil ) ).
% 0.16/0.45
% 0.16/0.45 % simps(1)
% 0.16/0.45 thf(fact_250_pi_Ofresh_I5_J,axiom,
% 0.16/0.45 ! [A: name,X32: name,X2: name,X1: pi] :
% 0.16/0.45 ( ( fresh_name_pi @ A @ ( match @ X32 @ X2 @ X1 ) )
% 0.16/0.45 = ( ( fresh_name_name @ A @ X32 )
% 0.16/0.45 & ( fresh_name_name @ A @ X2 )
% 0.16/0.45 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.fresh(5)
% 0.16/0.45 thf(fact_251_matchNilLeft,axiom,
% 0.16/0.45 ! [A: name,B: name,Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.16/0.45 ( ( A != B )
% 0.16/0.45 => ( strong743114133lation @ piNil @ Rel @ ( match @ A @ B @ P ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % matchNilLeft
% 0.16/0.45 thf(fact_252_nilSimRight,axiom,
% 0.16/0.45 ! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.16/0.45
% 0.16/0.45 % nilSimRight
% 0.16/0.45 thf(fact_253_pi_Odistinct_I49_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(49)
% 0.16/0.45 thf(fact_254_pi_Odistinct_I5_J,axiom,
% 0.16/0.45 ! [Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( piNil
% 0.16/0.45 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(5)
% 0.16/0.45 thf(fact_255_matchCases,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.16/0.45 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.16/0.45 => ( ( ( late_transitions @ P @ Rs )
% 0.16/0.45 => ( ( A = B )
% 0.16/0.45 => ( F @ A @ A ) ) )
% 0.16/0.45 => ( F @ A @ B ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % matchCases
% 0.16/0.45 thf(fact_256_matchTrans,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.16/0.45 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.16/0.45 => ( A = B ) ) ).
% 0.16/0.45
% 0.16/0.45 % matchTrans
% 0.16/0.45 thf(fact_257_matchCases_H,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.16/0.45 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.16/0.45 => ~ ! [P4: pi] :
% 0.16/0.45 ( ( ( B = A )
% 0.16/0.45 & ( P = P4 ) )
% 0.16/0.45 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % matchCases'
% 0.16/0.45 thf(fact_258_Match,axiom,
% 0.16/0.45 ! [P: pi,Rs: late_residual,B: name] :
% 0.16/0.45 ( ( late_transitions @ P @ Rs )
% 0.16/0.45 => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 0.16/0.45
% 0.16/0.45 % Match
% 0.16/0.45 thf(fact_259_nilCases_H,axiom,
% 0.16/0.45 ! [Rs: late_residual] :
% 0.16/0.45 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.16/0.45
% 0.16/0.45 % nilCases'
% 0.16/0.45 thf(fact_260_zeroTrans,axiom,
% 0.16/0.45 ! [Rs: late_residual] :
% 0.16/0.45 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.16/0.45
% 0.16/0.45 % zeroTrans
% 0.16/0.45 thf(fact_261_pi_Odistinct_I65_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.45 ( ( match @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(65)
% 0.16/0.45 thf(fact_262_pi_Odistinct_I67_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.16/0.45 ( ( match @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( res @ Name @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(67)
% 0.16/0.45 thf(fact_263_pi_Odistinct_I13_J,axiom,
% 0.16/0.45 ! [Pi12: pi,Pi22: pi] :
% 0.16/0.45 ( piNil
% 0.16/0.45 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(13)
% 0.16/0.45 thf(fact_264_pi_Odistinct_I15_J,axiom,
% 0.16/0.45 ! [Name: name,Pi: pi] :
% 0.16/0.45 ( piNil
% 0.16/0.45 != ( res @ Name @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(15)
% 0.16/0.45 thf(fact_265_pi_Odistinct_I7_J,axiom,
% 0.16/0.45 ! [Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( piNil
% 0.16/0.45 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(7)
% 0.16/0.45 thf(fact_266_pi_Oinject_I4_J,axiom,
% 0.16/0.45 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.16/0.45 ( ( ( match @ X32 @ X2 @ X1 )
% 0.16/0.45 = ( match @ Y32 @ Y2 @ Y1 ) )
% 0.16/0.45 = ( ( X32 = Y32 )
% 0.16/0.45 & ( X2 = Y2 )
% 0.16/0.45 & ( X1 = Y1 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.inject(4)
% 0.16/0.45 thf(fact_267_pi_Odistinct_I3_J,axiom,
% 0.16/0.45 ! [Pi: pi] :
% 0.16/0.45 ( piNil
% 0.16/0.45 != ( tau @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(3)
% 0.16/0.45 thf(fact_268_pi_Odistinct_I37_J,axiom,
% 0.16/0.45 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( ( tau @ Pi3 )
% 0.16/0.45 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(37)
% 0.16/0.45 thf(fact_269_pi_Odistinct_I1_J,axiom,
% 0.16/0.45 ! [Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( piNil
% 0.16/0.45 != ( output @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(1)
% 0.16/0.45 thf(fact_270_pi_Odistinct_I23_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(23)
% 0.16/0.45 thf(fact_271_resZeroTrans,axiom,
% 0.16/0.45 ! [X: name,Rs: late_residual] :
% 0.16/0.45 ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 0.16/0.45
% 0.16/0.45 % resZeroTrans
% 0.16/0.45 thf(fact_272_nilSim_I2_J,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
% 0.16/0.45 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% 0.16/0.45
% 0.16/0.45 % nilSim(2)
% 0.16/0.45 thf(fact_273_nilSim_I3_J,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 0.16/0.45 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% 0.16/0.45
% 0.16/0.45 % nilSim(3)
% 0.16/0.45 thf(fact_274_nilSim_I1_J,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.16/0.45 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.16/0.45
% 0.16/0.45 % nilSim(1)
% 0.16/0.45 thf(fact_275_simps_I6_J,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.16/0.45 ( ( subs @ ( mismatch @ A @ B @ P ) @ C @ D )
% 0.16/0.45 = ( mismatch @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simps(6)
% 0.16/0.45 thf(fact_276_pi_Ofresh_I6_J,axiom,
% 0.16/0.45 ! [A: name,X32: name,X2: name,X1: pi] :
% 0.16/0.45 ( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
% 0.16/0.45 = ( ( fresh_name_name @ A @ X32 )
% 0.16/0.45 & ( fresh_name_name @ A @ X2 )
% 0.16/0.45 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.fresh(6)
% 0.16/0.45 thf(fact_277_pi_Odistinct_I9_J,axiom,
% 0.16/0.45 ! [Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( piNil
% 0.16/0.45 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(9)
% 0.16/0.45 thf(fact_278_pi_Odistinct_I61_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( ( match @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(61)
% 0.16/0.45 thf(fact_279_pi_Odistinct_I25_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(25)
% 0.16/0.45 thf(fact_280_pi_Odistinct_I39_J,axiom,
% 0.16/0.45 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( ( tau @ Pi3 )
% 0.16/0.45 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(39)
% 0.16/0.45 thf(fact_281_pi_Oinject_I5_J,axiom,
% 0.16/0.45 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.16/0.45 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 0.16/0.45 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 0.16/0.45 = ( ( X32 = Y32 )
% 0.16/0.45 & ( X2 = Y2 )
% 0.16/0.45 & ( X1 = Y1 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.inject(5)
% 0.16/0.45 thf(fact_282_pi_Odistinct_I75_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.16/0.45 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( res @ Name @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(75)
% 0.16/0.45 thf(fact_283_pi_Odistinct_I73_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.45 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(73)
% 0.16/0.45 thf(fact_284_Mismatch,axiom,
% 0.16/0.45 ! [P: pi,Rs: late_residual,A: name,B: name] :
% 0.16/0.45 ( ( late_transitions @ P @ Rs )
% 0.16/0.45 => ( ( A != B )
% 0.16/0.45 => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Mismatch
% 0.16/0.45 thf(fact_285_mismatchCases_H,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.16/0.45 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.16/0.45 => ~ ! [P4: pi,A3: name,B3: name] :
% 0.16/0.45 ( ( ( A = A3 )
% 0.16/0.45 & ( B = B3 )
% 0.16/0.45 & ( P = P4 ) )
% 0.16/0.45 => ( ( late_transitions @ P4 @ Rs )
% 0.16/0.45 => ( A3 = B3 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % mismatchCases'
% 0.16/0.45 thf(fact_286_mismatchTrans,axiom,
% 0.16/0.45 ! [A: name,P: pi,Rs: late_residual] :
% 0.16/0.45 ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% 0.16/0.45
% 0.16/0.45 % mismatchTrans
% 0.16/0.45 thf(fact_287_mismatchCases,axiom,
% 0.16/0.45 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.16/0.45 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.16/0.45 => ( ( ( late_transitions @ P @ Rs )
% 0.16/0.45 => ( ( A != B )
% 0.16/0.45 => ( F @ A @ B ) ) )
% 0.16/0.45 => ( F @ A @ B ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % mismatchCases
% 0.16/0.45 thf(fact_288_pi_Odistinct_I51_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 0.16/0.45 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(51)
% 0.16/0.45 thf(fact_289_mismatchNilLeft,axiom,
% 0.16/0.45 ! [Rel: set_Pr1834926343_pi_pi,A: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A @ A @ P ) ) ).
% 0.16/0.45
% 0.16/0.45 % mismatchNilLeft
% 0.16/0.45 thf(fact_290_pi_Ostrong__induct,axiom,
% 0.16/0.45 ! [P: late_subject > pi > $o,Z: late_subject,Pi3: pi] :
% 0.16/0.45 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 0.16/0.45 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.16/0.45 => ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Name3: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.16/0.45 => ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.16/0.45 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.strong_induct
% 0.16/0.45 thf(fact_291_pi_Ostrong__induct,axiom,
% 0.16/0.45 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi3: pi] :
% 0.16/0.45 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 0.16/0.45 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.16/0.45 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Name3: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.16/0.45 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.16/0.45 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.strong_induct
% 0.16/0.45 thf(fact_292_pi_Ostrong__induct,axiom,
% 0.16/0.45 ! [P: name > pi > $o,Z: name,Pi3: pi] :
% 0.16/0.45 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 0.16/0.45 ( ( fresh_name_name @ Name23 @ Z2 )
% 0.16/0.45 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.16/0.45 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Name3: name,Pi4: pi,Z2: name] :
% 0.16/0.45 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.16/0.45 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.16/0.45 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.strong_induct
% 0.16/0.45 thf(fact_293_pi_Ostrong__induct,axiom,
% 0.16/0.45 ! [P: pi > pi > $o,Z: pi,Pi3: pi] :
% 0.16/0.45 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ( fresh_name_pi @ Name23 @ Z2 )
% 0.16/0.45 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.16/0.45 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Name3: name,Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.16/0.45 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.16/0.45 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.strong_induct
% 0.16/0.45 thf(fact_294_pi_Ostrong__inducts,axiom,
% 0.16/0.45 ! [P: late_subject > pi > $o,Z: late_subject,Pi3: pi] :
% 0.16/0.45 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 0.16/0.45 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.16/0.45 => ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Name3: name,Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.16/0.45 => ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: late_subject] :
% 0.16/0.45 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.16/0.45 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.strong_inducts
% 0.16/0.45 thf(fact_295_pi_Ostrong__inducts,axiom,
% 0.16/0.45 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi3: pi] :
% 0.16/0.45 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 0.16/0.45 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.16/0.45 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Name3: name,Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.16/0.45 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 0.16/0.45 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.16/0.45 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.strong_inducts
% 0.16/0.45 thf(fact_296_pi_Ostrong__inducts,axiom,
% 0.16/0.45 ! [P: name > pi > $o,Z: name,Pi3: pi] :
% 0.16/0.45 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 0.16/0.45 ( ( fresh_name_name @ Name23 @ Z2 )
% 0.16/0.45 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.16/0.45 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Name3: name,Pi4: pi,Z2: name] :
% 0.16/0.45 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.16/0.45 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: name] :
% 0.16/0.45 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.16/0.45 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.strong_inducts
% 0.16/0.45 thf(fact_297_pi_Ostrong__inducts,axiom,
% 0.16/0.45 ! [P: pi > pi > $o,Z: pi,Pi3: pi] :
% 0.16/0.45 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ( fresh_name_pi @ Name23 @ Z2 )
% 0.16/0.45 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.16/0.45 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.16/0.45 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.16/0.45 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.16/0.45 => ( ! [Name3: name,Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.16/0.45 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 0.16/0.45 => ( ! [Pi4: pi,Z2: pi] :
% 0.16/0.45 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 0.16/0.45 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 0.16/0.45 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.strong_inducts
% 0.16/0.45 thf(fact_298_pi_Ofresh_I10_J,axiom,
% 0.16/0.45 ! [A: name,X1: pi] :
% 0.16/0.45 ( ( fresh_name_pi @ A @ ( bang @ X1 ) )
% 0.16/0.45 = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.fresh(10)
% 0.16/0.45 thf(fact_299_pi_Ofresh_I7_J,axiom,
% 0.16/0.45 ! [A: name,X2: pi,X1: pi] :
% 0.16/0.45 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 0.16/0.45 = ( ( fresh_name_pi @ A @ X2 )
% 0.16/0.45 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.fresh(7)
% 0.16/0.45 thf(fact_300_simps_I10_J,axiom,
% 0.16/0.45 ! [P: pi,C: name,D: name] :
% 0.16/0.45 ( ( subs @ ( bang @ P ) @ C @ D )
% 0.16/0.45 = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simps(10)
% 0.16/0.45 thf(fact_301_simps_I7_J,axiom,
% 0.16/0.45 ! [P: pi,Q: pi,C: name,D: name] :
% 0.16/0.45 ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 0.16/0.45 = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % simps(7)
% 0.16/0.45 thf(fact_302_pi_Odistinct_I77_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.16/0.45 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( bang @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(77)
% 0.16/0.45 thf(fact_303_pi_Odistinct_I71_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.45 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(71)
% 0.16/0.45 thf(fact_304_pi_Odistinct_I59_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.16/0.45 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( bang @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(59)
% 0.16/0.45 thf(fact_305_pi_Odistinct_I53_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.45 ( ( input @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(53)
% 0.16/0.45 thf(fact_306_pi_Odistinct_I47_J,axiom,
% 0.16/0.45 ! [Pi3: pi,Pi: pi] :
% 0.16/0.45 ( ( tau @ Pi3 )
% 0.16/0.45 != ( bang @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(47)
% 0.16/0.45 thf(fact_307_pi_Odistinct_I41_J,axiom,
% 0.16/0.45 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.45 ( ( tau @ Pi3 )
% 0.16/0.45 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(41)
% 0.16/0.45 thf(fact_308_pi_Odistinct_I79_J,axiom,
% 0.16/0.45 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.45 ( ( sum @ Pi1 @ Pi2 )
% 0.16/0.45 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(79)
% 0.16/0.45 thf(fact_309_pi_Odistinct_I81_J,axiom,
% 0.16/0.45 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.16/0.45 ( ( sum @ Pi1 @ Pi2 )
% 0.16/0.45 != ( res @ Name @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(81)
% 0.16/0.45 thf(fact_310_pi_Odistinct_I27_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.16/0.45 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(27)
% 0.16/0.45 thf(fact_311_pi_Odistinct_I83_J,axiom,
% 0.16/0.45 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.16/0.45 ( ( sum @ Pi1 @ Pi2 )
% 0.16/0.45 != ( bang @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(83)
% 0.16/0.45 thf(fact_312_pi_Oinject_I6_J,axiom,
% 0.16/0.45 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.16/0.45 ( ( ( sum @ X2 @ X1 )
% 0.16/0.45 = ( sum @ Y2 @ Y1 ) )
% 0.16/0.45 = ( ( X2 = Y2 )
% 0.16/0.45 & ( X1 = Y1 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.inject(6)
% 0.16/0.45 thf(fact_313_pi_Oinject_I9_J,axiom,
% 0.16/0.45 ! [X1: pi,Y1: pi] :
% 0.16/0.45 ( ( ( bang @ X1 )
% 0.16/0.45 = ( bang @ Y1 ) )
% 0.16/0.45 = ( X1 = Y1 ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.inject(9)
% 0.16/0.45 thf(fact_314_sumCases,axiom,
% 0.16/0.45 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.16/0.45 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.16/0.45 => ( ~ ( late_transitions @ P @ Rs )
% 0.16/0.45 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % sumCases
% 0.16/0.45 thf(fact_315_sumCases_H,axiom,
% 0.16/0.45 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.16/0.45 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.16/0.45 => ( ~ ( late_transitions @ P @ Rs )
% 0.16/0.45 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % sumCases'
% 0.16/0.45 thf(fact_316_Sum1,axiom,
% 0.16/0.45 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.16/0.45 ( ( late_transitions @ P @ Rs )
% 0.16/0.45 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.16/0.45
% 0.16/0.45 % Sum1
% 0.16/0.45 thf(fact_317_Sum2,axiom,
% 0.16/0.45 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.16/0.45 ( ( late_transitions @ Q @ Rs )
% 0.16/0.45 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.16/0.45
% 0.16/0.45 % Sum2
% 0.16/0.45 thf(fact_318_pi_Odistinct_I33_J,axiom,
% 0.16/0.45 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.16/0.45 ( ( output @ Name1 @ Name22 @ Pi3 )
% 0.16/0.45 != ( bang @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(33)
% 0.16/0.45 thf(fact_319_pi_Odistinct_I89_J,axiom,
% 0.16/0.45 ! [Name2: name,Pi3: pi,Pi: pi] :
% 0.16/0.45 ( ( res @ Name2 @ Pi3 )
% 0.16/0.45 != ( bang @ Pi ) ) ).
% 0.16/0.45
% 0.16/0.45 % pi.distinct(89)
% 0.16/0.45
% 0.16/0.45 % Helper facts (3)
% 0.16/0.45 thf(help_If_3_1_If_001t__Agent__Oname_T,axiom,
% 0.16/0.45 ! [P: $o] :
% 0.16/0.45 ( ( P = $true )
% 0.16/0.45 | ( P = $false ) ) ).
% 0.16/0.45
% 0.16/0.45 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 0.16/0.45 ! [X: name,Y: name] :
% 0.16/0.45 ( ( if_name @ $false @ X @ Y )
% 0.16/0.45 = Y ) ).
% 0.16/0.45
% 0.16/0.45 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 0.16/0.45 ! [X: name,Y: name] :
% 0.16/0.45 ( ( if_name @ $true @ X @ Y )
% 0.16/0.45 = X ) ).
% 0.16/0.45
% 0.16/0.45 % Conjectures (1)
% 0.16/0.45 thf(conj_0,conjecture,
% 0.16/0.45 ? [P6: pi] :
% 0.16/0.45 ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ P6 ) )
% 0.16/0.45 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) ) ).
% 0.16/0.45
% 0.16/0.45 %------------------------------------------------------------------------------
% 0.16/0.45 ------------------------
% 3.71/1.99 ---- Embedded in THF ---
% 3.71/2.00 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.71/2.00 %%% Generated on Tue Feb 24 08:29:04 EST 2026
% 3.71/2.00 %%% using '$$dhol' embedding, version 1.3.0.
% 3.71/2.00 %%% Logic specification used:
% 3.71/2.00 %%% thf(spec, logic, $$dhol).
% 3.71/2.00
% 3.71/2.00 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OawlmjC21l/DTF2DTF8720.p
% See solution above
% 3.71/2.00 ------------------------
% 4.00/2.07 ---- Cleaned THF ---
% 4.00/2.07 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,
% 4.00/2.07 produc1462499409ion_pi: $tType ).
% 4.00/2.07
% 4.00/2.07 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,
% 4.00/2.07 produc691362330ubject: $tType ).
% 4.00/2.07
% 4.00/2.07 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,
% 4.00/2.07 produc1834551554reeRes: $tType ).
% 4.00/2.07
% 4.00/2.07 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,
% 4.00/2.07 produc405342261i_name: $tType ).
% 4.00/2.07
% 4.00/2.07 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,
% 4.00/2.07 produc629157763_pi_pi: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 4.00/2.07 produc1359399907ubject: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 4.00/2.07 produc355105483reeRes: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 4.00/2.07 produc214645451ubject: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 4.00/2.07 produc1357834675reeRes: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 4.00/2.07 produc1998742700t_name: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 4.00/2.07 produc2052722628s_name: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
% 4.00/2.07 produc865358760ubject: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 4.00/2.07 produc2008547984reeRes: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 4.00/2.07 produc140253050ect_pi: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 4.00/2.07 produc992857746Res_pi: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 4.00/2.07 set_Pr1834926343_pi_pi: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 4.00/2.07 product_prod_pi_pi: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__Osubject_J,type,
% 4.00/2.07 noption_Late_subject: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__OfreeRes_J,type,
% 4.00/2.07 noption_Late_freeRes: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Nominal__Onoption_It__Agent__Oname_J,type,
% 4.00/2.07 noption_name: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 4.00/2.07 noption_pi: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Late____Semantics__Oresidual,type,
% 4.00/2.07 late_residual: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Late____Semantics__Osubject,type,
% 4.00/2.07 late_subject: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 4.00/2.07 late_freeRes: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Agent__Oname,type,
% 4.00/2.07 name: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(ty_n_t__Agent__Opi,type,
% 4.00/2.07 pi: $tType ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Opi_OBang,type,
% 4.00/2.07 bang: pi > pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Opi_OInput,type,
% 4.00/2.07 input: name > name > pi > pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Opi_OMatch,type,
% 4.00/2.07 match: name > name > pi > pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Opi_OMismatch,type,
% 4.00/2.07 mismatch: name > name > pi > pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Opi_OOutput,type,
% 4.00/2.07 output: name > name > pi > pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Opi_OPar,type,
% 4.00/2.07 par: pi > pi > pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Opi_OPiNil,type,
% 4.00/2.07 piNil: pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Opi_ORes,type,
% 4.00/2.07 res: name > pi > pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Opi_OSum,type,
% 4.00/2.07 sum: pi > pi > pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Opi_OTau,type,
% 4.00/2.07 tau: pi > pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Osubs,type,
% 4.00/2.07 subs: pi > name > name > pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Agent_Osubst__name,type,
% 4.00/2.07 subst_name: name > name > name > name ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_If_001t__Agent__Oname,type,
% 4.00/2.07 if_name: $o > name > name > name ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 4.00/2.07 late_OutputR: name > name > late_freeRes ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 4.00/2.07 late_TauR: late_freeRes ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 4.00/2.07 late_BoundR: late_subject > name > pi > late_residual ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 4.00/2.07 late_FreeR: late_freeRes > pi > late_residual ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 4.00/2.07 late_BoundOutputS: name > late_subject ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 4.00/2.07 late_InputS: name > late_subject ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Late__Semantics_Otransitions,type,
% 4.00/2.07 late_transitions: pi > late_residual > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Oname,type,
% 4.00/2.07 abs_fun_name_name: name > name > name > noption_name ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Opi,type,
% 4.00/2.07 abs_fun_name_pi: name > pi > name > noption_pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 4.00/2.07 abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 4.00/2.07 abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J,type,
% 4.00/2.07 fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 4.00/2.07 fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J,type,
% 4.00/2.07 fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J,type,
% 4.00/2.07 fresh_728038529ubject: name > ( name > noption_Late_subject ) > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Oname,type,
% 4.00/2.07 fresh_name_name: name > name > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Opi,type,
% 4.00/2.07 fresh_name_pi: name > pi > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 4.00/2.07 fresh_1641682979reeRes: name > late_freeRes > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Oresidual,type,
% 4.00/2.07 fresh_81631222sidual: name > late_residual > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 4.00/2.07 fresh_717452603ubject: name > late_subject > $o ).
% 4.00/2.07
% 4.00/2.07 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,
% 4.00/2.07 fresh_225680151ion_pi: name > produc1462499409ion_pi > $o ).
% 4.00/2.07
% 4.00/2.07 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,
% 4.00/2.07 fresh_453496559i_name: name > produc405342261i_name > $o ).
% 4.00/2.07
% 4.00/2.07 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,
% 4.00/2.07 fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o ).
% 4.00/2.07
% 4.00/2.07 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,
% 4.00/2.07 fresh_1711070152reeRes: name > produc1834551554reeRes > $o ).
% 4.00/2.07
% 4.00/2.07 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,
% 4.00/2.07 fresh_567880928ubject: name > produc691362330ubject > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 4.00/2.07 fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
% 4.00/2.07 fresh_820177506ubject: name > produc865358760ubject > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 4.00/2.07 fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 4.00/2.07 fresh_2007541374s_name: name > produc2052722628s_name > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 4.00/2.07 fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 4.00/2.07 fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 4.00/2.07 fresh_1498103185ubject: name > produc214645451ubject > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 4.00/2.07 fresh_1953561446t_name: name > produc1998742700t_name > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 4.00/2.07 fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 4.00/2.07 fresh_1638563217reeRes: name > produc355105483reeRes > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 4.00/2.07 fresh_495373993ubject: name > produc1359399907ubject > $o ).
% 4.00/2.07
% 4.00/2.07 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,
% 4.00/2.07 produc1342893193ion_pi: ( name > noption_pi ) > ( name > noption_pi ) > produc1462499409ion_pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Oname,type,
% 4.00/2.07 produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Opi,type,
% 4.00/2.07 produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__OfreeRes,type,
% 4.00/2.07 produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__Osubject,type,
% 4.00/2.07 produc581368530ubject: ( name > noption_pi ) > late_subject > produc691362330ubject ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 4.00/2.07 produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 4.00/2.07 produc607574050ubject: name > late_subject > produc865358760ubject ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 4.00/2.07 product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 4.00/2.07 produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 4.00/2.07 produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 4.00/2.07 produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
% 4.00/2.07 produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 4.00/2.07 produc1647375838t_name: late_subject > name > produc1998742700t_name ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
% 4.00/2.07 produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 4.00/2.07 produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 4.00/2.07 produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 4.00/2.07 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 4.00/2.07 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 4.00/2.07 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 4.00/2.07 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 4.00/2.07 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v_P,type,
% 4.00/2.07 p: pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v_PQR____,type,
% 4.00/2.07 pqr: pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v_P_H____,type,
% 4.00/2.07 p2: pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v_Q,type,
% 4.00/2.07 q: pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v_QR____,type,
% 4.00/2.07 qr: pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v_Q_H____,type,
% 4.00/2.07 q2: pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v_R,type,
% 4.00/2.07 r: pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v_Rel,type,
% 4.00/2.07 rel: set_Pr1834926343_pi_pi ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v__092_060alpha_062____,type,
% 4.00/2.07 alpha: late_freeRes ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v_a____,type,
% 4.00/2.07 a: name ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v_x____,type,
% 4.00/2.07 x: name ).
% 4.00/2.07
% 4.00/2.07 thf(sy_v_y____,type,
% 4.00/2.07 y: name ).
% 4.00/2.07
% 4.00/2.07 thf(fact_0_cClose2_Ohyps_I14_J,axiom,
% 4.00/2.07 alpha = late_TauR ).
% 4.00/2.07
% 4.00/2.07 thf(fact_1_cClose2_Ohyps_I6_J,axiom,
% 4.00/2.07 x != y ).
% 4.00/2.07
% 4.00/2.07 thf(fact_2_cClose2_Ohyps_I10_J,axiom,
% 4.00/2.07 y != a ).
% 4.00/2.07
% 4.00/2.07 thf(fact_3_cClose2_Ohyps_I5_J,axiom,
% 4.00/2.07 x != a ).
% 4.00/2.07
% 4.00/2.07 thf(fact_4_Ass,axiom,
% 4.00/2.07 ! [S: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S @ T ) @ U ) @ ( par @ S @ ( par @ T @ U ) ) ) @ rel ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_5_Res,axiom,
% 4.00/2.07 ! [S: pi,T: pi,X: name] :
% 4.00/2.07 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S @ T ) @ rel )
% 4.00/2.07 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X @ S ) @ ( res @ X @ T ) ) @ rel ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062,axiom,
% 4.00/2.07 member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ).
% 4.00/2.07
% 4.00/2.07 thf(fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062,axiom,
% 4.00/2.07 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_8_Free_Ohyps,axiom,
% 4.00/2.07 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_9__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_A_092_060parallel_062_AR_J_J_A_092_060in_062_ARel_092_060close_062,axiom,
% 4.00/2.07 member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) @ r ) @ ( res @ y @ ( par @ p2 @ ( par @ ( subs @ q2 @ x @ y ) @ r ) ) ) ) @ rel ).
% 4.00/2.07
% 4.00/2.07 thf(fact_10__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_092_060close_062,axiom,
% 4.00/2.07 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ p2 @ ( subs @ q2 @ x @ y ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_11_cClose2_Ohyps_I13_J,axiom,
% 4.00/2.07 fresh_name_pi @ y @ q ).
% 4.00/2.07
% 4.00/2.07 thf(fact_12_cClose2_Ohyps_I12_J,axiom,
% 4.00/2.07 fresh_name_pi @ x @ q ).
% 4.00/2.07
% 4.00/2.07 thf(fact_13_cClose2_Ohyps_I7_J,axiom,
% 4.00/2.07 fresh_name_pi @ x @ p2 ).
% 4.00/2.07
% 4.00/2.07 thf(fact_14_cClose2_Ohyps_I8_J,axiom,
% 4.00/2.07 fresh_name_pi @ y @ p ).
% 4.00/2.07
% 4.00/2.07 thf(fact_15_cClose2_Ohyps_I3_J,axiom,
% 4.00/2.07 fresh_name_pi @ x @ p ).
% 4.00/2.07
% 4.00/2.07 thf(fact_16_cClose2_Ohyps_I9_J,axiom,
% 4.00/2.07 fresh_name_pi @ y @ ( par @ q @ r ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_17_cClose2_Ohyps_I4_J,axiom,
% 4.00/2.07 fresh_name_pi @ x @ ( par @ q @ r ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_18_simps_I9_J,axiom,
% 4.00/2.07 ! [X: name,C: name,D: name,P: pi] :
% 4.00/2.07 ( ( X != C )
% 4.00/2.07 => ( ( X != D )
% 4.00/2.07 => ( ( subs @ ( res @ X @ P ) @ C @ D )
% 4.00/2.07 = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_19_simps_I8_J,axiom,
% 4.00/2.07 ! [P: pi,Q: pi,C: name,D: name] :
% 4.00/2.07 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 4.00/2.07 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_20_FreshExt,axiom,
% 4.00/2.07 ! [X: name,S: pi,T: pi,U: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ X @ S )
% 4.00/2.07 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X @ ( par @ ( par @ S @ T ) @ U ) ) @ ( par @ S @ ( res @ X @ ( par @ T @ U ) ) ) ) @ rel ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_21_FreshExt_H,axiom,
% 4.00/2.07 ! [X: name,U: pi,S: pi,T: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ X @ U )
% 4.00/2.07 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X @ ( par @ S @ T ) ) @ U ) @ ( res @ X @ ( par @ S @ ( par @ T @ U ) ) ) ) @ rel ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_22_Par1F,axiom,
% 4.00/2.07 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_23_Par2F,axiom,
% 4.00/2.07 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_24_subst__identity,axiom,
% 4.00/2.07 ! [P: pi,A: name] :
% 4.00/2.07 ( ( subs @ P @ A @ A )
% 4.00/2.07 = P ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_25__092_060open_062x_A_092_060sharp_062_AR_092_060close_062,axiom,
% 4.00/2.07 fresh_name_pi @ x @ r ).
% 4.00/2.07
% 4.00/2.07 thf(fact_26__092_060open_062y_A_092_060sharp_062_AR_092_060close_062,axiom,
% 4.00/2.07 fresh_name_pi @ y @ r ).
% 4.00/2.07
% 4.00/2.07 thf(fact_27_prod_Oinject,axiom,
% 4.00/2.07 ! [X1: name > noption_pi,X2: late_subject,Y1: name > noption_pi,Y2: late_subject] :
% 4.00/2.07 ( ( ( produc581368530ubject @ X1 @ X2 )
% 4.00/2.07 = ( produc581368530ubject @ Y1 @ Y2 ) )
% 4.00/2.07 = ( ( X1 = Y1 )
% 4.00/2.07 & ( X2 = Y2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_28_prod_Oinject,axiom,
% 4.00/2.07 ! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y2: late_freeRes] :
% 4.00/2.07 ( ( ( produc1505598906reeRes @ X1 @ X2 )
% 4.00/2.07 = ( produc1505598906reeRes @ Y1 @ Y2 ) )
% 4.00/2.07 = ( ( X1 = Y1 )
% 4.00/2.07 & ( X2 = Y2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_29_prod_Oinject,axiom,
% 4.00/2.07 ! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y2: name] :
% 4.00/2.07 ( ( ( produc540578151i_name @ X1 @ X2 )
% 4.00/2.07 = ( produc540578151i_name @ Y1 @ Y2 ) )
% 4.00/2.07 = ( ( X1 = Y1 )
% 4.00/2.07 & ( X2 = Y2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_30_prod_Oinject,axiom,
% 4.00/2.07 ! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y2: pi] :
% 4.00/2.07 ( ( ( produc1820286517_pi_pi @ X1 @ X2 )
% 4.00/2.07 = ( produc1820286517_pi_pi @ Y1 @ Y2 ) )
% 4.00/2.07 = ( ( X1 = Y1 )
% 4.00/2.07 & ( X2 = Y2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_31_prod_Oinject,axiom,
% 4.00/2.07 ! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y2: name > noption_pi] :
% 4.00/2.07 ( ( ( produc1342893193ion_pi @ X1 @ X2 )
% 4.00/2.07 = ( produc1342893193ion_pi @ Y1 @ Y2 ) )
% 4.00/2.07 = ( ( X1 = Y1 )
% 4.00/2.07 & ( X2 = Y2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_32_prod_Oinject,axiom,
% 4.00/2.07 ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 4.00/2.07 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 4.00/2.07 = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 4.00/2.07 = ( ( X1 = Y1 )
% 4.00/2.07 & ( X2 = Y2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_33_old_Oprod_Oinject,axiom,
% 4.00/2.07 ! [A: name > noption_pi,B: late_subject,A2: name > noption_pi,B2: late_subject] :
% 4.00/2.07 ( ( ( produc581368530ubject @ A @ B )
% 4.00/2.07 = ( produc581368530ubject @ A2 @ B2 ) )
% 4.00/2.07 = ( ( A = A2 )
% 4.00/2.07 & ( B = B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_34_old_Oprod_Oinject,axiom,
% 4.00/2.07 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 4.00/2.07 ( ( ( produc1505598906reeRes @ A @ B )
% 4.00/2.07 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 4.00/2.07 = ( ( A = A2 )
% 4.00/2.07 & ( B = B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_35_old_Oprod_Oinject,axiom,
% 4.00/2.07 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 4.00/2.07 ( ( ( produc540578151i_name @ A @ B )
% 4.00/2.07 = ( produc540578151i_name @ A2 @ B2 ) )
% 4.00/2.07 = ( ( A = A2 )
% 4.00/2.07 & ( B = B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_36_old_Oprod_Oinject,axiom,
% 4.00/2.07 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 4.00/2.07 ( ( ( produc1820286517_pi_pi @ A @ B )
% 4.00/2.07 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 4.00/2.07 = ( ( A = A2 )
% 4.00/2.07 & ( B = B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_37_old_Oprod_Oinject,axiom,
% 4.00/2.07 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 4.00/2.07 ( ( ( produc1342893193ion_pi @ A @ B )
% 4.00/2.07 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 4.00/2.07 = ( ( A = A2 )
% 4.00/2.07 & ( B = B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_38_old_Oprod_Oinject,axiom,
% 4.00/2.07 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 4.00/2.07 ( ( ( product_Pair_pi_pi @ A @ B )
% 4.00/2.07 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 4.00/2.07 = ( ( A = A2 )
% 4.00/2.07 & ( B = B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_39_cClose2_Ohyps_I11_J,axiom,
% 4.00/2.07 fresh_name_pi @ y @ qr ).
% 4.00/2.07
% 4.00/2.07 thf(fact_40_pi_Ofresh_I8_J,axiom,
% 4.00/2.07 ! [A: name,X2: pi,X1: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 4.00/2.07 = ( ( fresh_name_pi @ A @ X2 )
% 4.00/2.07 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_41_substTrans,axiom,
% 4.00/2.07 ! [B: name,P: pi,A: name,C: name] :
% 4.00/2.07 ( ( fresh_name_pi @ B @ P )
% 4.00/2.07 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
% 4.00/2.07 = ( subs @ P @ A @ C ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_42_name__exists__fresh,axiom,
% 4.00/2.07 ! [X: late_subject] :
% 4.00/2.07 ~ ! [C2: name] :
% 4.00/2.07 ~ ( fresh_717452603ubject @ C2 @ X ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_43_name__exists__fresh,axiom,
% 4.00/2.07 ! [X: late_freeRes] :
% 4.00/2.07 ~ ! [C2: name] :
% 4.00/2.07 ~ ( fresh_1641682979reeRes @ C2 @ X ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_44_name__exists__fresh,axiom,
% 4.00/2.07 ! [X: name] :
% 4.00/2.07 ~ ! [C2: name] :
% 4.00/2.07 ~ ( fresh_name_name @ C2 @ X ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_45_name__exists__fresh,axiom,
% 4.00/2.07 ! [X: pi] :
% 4.00/2.07 ~ ! [C2: name] :
% 4.00/2.07 ~ ( fresh_name_pi @ C2 @ X ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_46_freshRes,axiom,
% 4.00/2.07 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_47_fresh__fact2,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi] :
% 4.00/2.07 ( ( A != B )
% 4.00/2.07 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_48_fresh__fact1,axiom,
% 4.00/2.07 ! [A: name,P: pi,C: name,B: name] :
% 4.00/2.07 ( ( fresh_name_pi @ A @ P )
% 4.00/2.07 => ( ( A != C )
% 4.00/2.07 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_49_forget,axiom,
% 4.00/2.07 ! [A: name,P: pi,B: name] :
% 4.00/2.07 ( ( fresh_name_pi @ A @ P )
% 4.00/2.07 => ( ( subs @ P @ A @ B )
% 4.00/2.07 = P ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_50_freshFreeDerivative_I2_J,axiom,
% 4.00/2.07 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ P )
% 4.00/2.07 => ( fresh_name_pi @ Y @ P2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_51_substRes3,axiom,
% 4.00/2.07 ! [B: name,P: pi,A: name] :
% 4.00/2.07 ( ( fresh_name_pi @ B @ P )
% 4.00/2.07 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 4.00/2.07 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_52_substRes2,axiom,
% 4.00/2.07 ! [B: name,P: pi,A: name] :
% 4.00/2.07 ( ( fresh_name_pi @ B @ P )
% 4.00/2.07 => ( ( res @ A @ P )
% 4.00/2.07 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_53_old_Oprod_Oinducts,axiom,
% 4.00/2.07 ! [P: produc691362330ubject > $o,Prod: produc691362330ubject] :
% 4.00/2.07 ( ! [A3: name > noption_pi,B3: late_subject] : ( P @ ( produc581368530ubject @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ Prod ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_54_old_Oprod_Oinducts,axiom,
% 4.00/2.07 ! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
% 4.00/2.07 ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ Prod ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_55_old_Oprod_Oinducts,axiom,
% 4.00/2.07 ! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
% 4.00/2.07 ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ Prod ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_56_old_Oprod_Oinducts,axiom,
% 4.00/2.07 ! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
% 4.00/2.07 ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ Prod ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_57_old_Oprod_Oinducts,axiom,
% 4.00/2.07 ! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
% 4.00/2.07 ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ Prod ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_58_old_Oprod_Oinducts,axiom,
% 4.00/2.07 ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 4.00/2.07 ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ Prod ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_59_old_Oprod_Oexhaust,axiom,
% 4.00/2.07 ! [Y: produc691362330ubject] :
% 4.00/2.07 ~ ! [A3: name > noption_pi,B3: late_subject] :
% 4.00/2.07 ( Y
% 4.00/2.07 != ( produc581368530ubject @ A3 @ B3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_60_old_Oprod_Oexhaust,axiom,
% 4.00/2.07 ! [Y: produc1834551554reeRes] :
% 4.00/2.07 ~ ! [A3: name > noption_pi,B3: late_freeRes] :
% 4.00/2.07 ( Y
% 4.00/2.07 != ( produc1505598906reeRes @ A3 @ B3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_61_old_Oprod_Oexhaust,axiom,
% 4.00/2.07 ! [Y: produc405342261i_name] :
% 4.00/2.07 ~ ! [A3: name > noption_pi,B3: name] :
% 4.00/2.07 ( Y
% 4.00/2.07 != ( produc540578151i_name @ A3 @ B3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_62_old_Oprod_Oexhaust,axiom,
% 4.00/2.07 ! [Y: produc629157763_pi_pi] :
% 4.00/2.07 ~ ! [A3: name > noption_pi,B3: pi] :
% 4.00/2.07 ( Y
% 4.00/2.07 != ( produc1820286517_pi_pi @ A3 @ B3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_63_old_Oprod_Oexhaust,axiom,
% 4.00/2.07 ! [Y: produc1462499409ion_pi] :
% 4.00/2.07 ~ ! [A3: name > noption_pi,B3: name > noption_pi] :
% 4.00/2.07 ( Y
% 4.00/2.07 != ( produc1342893193ion_pi @ A3 @ B3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_64_old_Oprod_Oexhaust,axiom,
% 4.00/2.07 ! [Y: product_prod_pi_pi] :
% 4.00/2.07 ~ ! [A3: pi,B3: pi] :
% 4.00/2.07 ( Y
% 4.00/2.07 != ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_65_mem__Collect__eq,axiom,
% 4.00/2.07 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 4.00/2.07 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 4.00/2.07 = ( P @ A ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_66_Collect__mem__eq,axiom,
% 4.00/2.07 ! [A4: set_Pr1834926343_pi_pi] :
% 4.00/2.07 ( ( collec1051790738_pi_pi
% 4.00/2.07 @ ^ [X3: product_prod_pi_pi] : ( member558706512_pi_pi @ X3 @ A4 ) )
% 4.00/2.07 = A4 ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_67_Collect__cong,axiom,
% 4.00/2.07 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 4.00/2.07 ( ! [X4: product_prod_pi_pi] :
% 4.00/2.07 ( ( P @ X4 )
% 4.00/2.07 = ( Q @ X4 ) )
% 4.00/2.07 => ( ( collec1051790738_pi_pi @ P )
% 4.00/2.07 = ( collec1051790738_pi_pi @ Q ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_68_Pair__inject,axiom,
% 4.00/2.07 ! [A: name > noption_pi,B: late_subject,A2: name > noption_pi,B2: late_subject] :
% 4.00/2.07 ( ( ( produc581368530ubject @ A @ B )
% 4.00/2.07 = ( produc581368530ubject @ A2 @ B2 ) )
% 4.00/2.07 => ~ ( ( A = A2 )
% 4.00/2.07 => ( B != B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_69_Pair__inject,axiom,
% 4.00/2.07 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 4.00/2.07 ( ( ( produc1505598906reeRes @ A @ B )
% 4.00/2.07 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 4.00/2.07 => ~ ( ( A = A2 )
% 4.00/2.07 => ( B != B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_70_Pair__inject,axiom,
% 4.00/2.07 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 4.00/2.07 ( ( ( produc540578151i_name @ A @ B )
% 4.00/2.07 = ( produc540578151i_name @ A2 @ B2 ) )
% 4.00/2.07 => ~ ( ( A = A2 )
% 4.00/2.07 => ( B != B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_71_Pair__inject,axiom,
% 4.00/2.07 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 4.00/2.07 ( ( ( produc1820286517_pi_pi @ A @ B )
% 4.00/2.07 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 4.00/2.07 => ~ ( ( A = A2 )
% 4.00/2.07 => ( B != B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_72_Pair__inject,axiom,
% 4.00/2.07 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 4.00/2.07 ( ( ( produc1342893193ion_pi @ A @ B )
% 4.00/2.07 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 4.00/2.07 => ~ ( ( A = A2 )
% 4.00/2.07 => ( B != B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_73_Pair__inject,axiom,
% 4.00/2.07 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 4.00/2.07 ( ( ( product_Pair_pi_pi @ A @ B )
% 4.00/2.07 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 4.00/2.07 => ~ ( ( A = A2 )
% 4.00/2.07 => ( B != B2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_74_prod__cases,axiom,
% 4.00/2.07 ! [P: produc691362330ubject > $o,P3: produc691362330ubject] :
% 4.00/2.07 ( ! [A3: name > noption_pi,B3: late_subject] : ( P @ ( produc581368530ubject @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ P3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_75_prod__cases,axiom,
% 4.00/2.07 ! [P: produc1834551554reeRes > $o,P3: produc1834551554reeRes] :
% 4.00/2.07 ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ P3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_76_prod__cases,axiom,
% 4.00/2.07 ! [P: produc405342261i_name > $o,P3: produc405342261i_name] :
% 4.00/2.07 ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ P3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_77_prod__cases,axiom,
% 4.00/2.07 ! [P: produc629157763_pi_pi > $o,P3: produc629157763_pi_pi] :
% 4.00/2.07 ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ P3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_78_prod__cases,axiom,
% 4.00/2.07 ! [P: produc1462499409ion_pi > $o,P3: produc1462499409ion_pi] :
% 4.00/2.07 ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ P3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_79_prod__cases,axiom,
% 4.00/2.07 ! [P: product_prod_pi_pi > $o,P3: product_prod_pi_pi] :
% 4.00/2.07 ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 4.00/2.07 => ( P @ P3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_80_surj__pair,axiom,
% 4.00/2.07 ! [P3: produc691362330ubject] :
% 4.00/2.07 ? [X4: name > noption_pi,Y3: late_subject] :
% 4.00/2.07 ( P3
% 4.00/2.07 = ( produc581368530ubject @ X4 @ Y3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_81_surj__pair,axiom,
% 4.00/2.07 ! [P3: produc1834551554reeRes] :
% 4.00/2.07 ? [X4: name > noption_pi,Y3: late_freeRes] :
% 4.00/2.07 ( P3
% 4.00/2.07 = ( produc1505598906reeRes @ X4 @ Y3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_82_surj__pair,axiom,
% 4.00/2.07 ! [P3: produc405342261i_name] :
% 4.00/2.07 ? [X4: name > noption_pi,Y3: name] :
% 4.00/2.07 ( P3
% 4.00/2.07 = ( produc540578151i_name @ X4 @ Y3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_83_surj__pair,axiom,
% 4.00/2.07 ! [P3: produc629157763_pi_pi] :
% 4.00/2.07 ? [X4: name > noption_pi,Y3: pi] :
% 4.00/2.07 ( P3
% 4.00/2.07 = ( produc1820286517_pi_pi @ X4 @ Y3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_84_surj__pair,axiom,
% 4.00/2.07 ! [P3: produc1462499409ion_pi] :
% 4.00/2.07 ? [X4: name > noption_pi,Y3: name > noption_pi] :
% 4.00/2.07 ( P3
% 4.00/2.07 = ( produc1342893193ion_pi @ X4 @ Y3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_85_surj__pair,axiom,
% 4.00/2.07 ! [P3: product_prod_pi_pi] :
% 4.00/2.07 ? [X4: pi,Y3: pi] :
% 4.00/2.07 ( P3
% 4.00/2.07 = ( product_Pair_pi_pi @ X4 @ Y3 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_86_pi_Oinject_I7_J,axiom,
% 4.00/2.07 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 4.00/2.07 ( ( ( par @ X2 @ X1 )
% 4.00/2.07 = ( par @ Y2 @ Y1 ) )
% 4.00/2.07 = ( ( X2 = Y2 )
% 4.00/2.07 & ( X1 = Y1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_87_residual_Oinject_I2_J,axiom,
% 4.00/2.07 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 4.00/2.07 ( ( ( late_FreeR @ X2 @ X1 )
% 4.00/2.07 = ( late_FreeR @ Y2 @ Y1 ) )
% 4.00/2.07 = ( ( X2 = Y2 )
% 4.00/2.07 & ( X1 = Y1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_88_pi_Odistinct_I85_J,axiom,
% 4.00/2.07 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 4.00/2.07 ( ( par @ Pi1 @ Pi2 )
% 4.00/2.07 != ( res @ Name @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_89_cClose2_Ohyps_I2_J,axiom,
% 4.00/2.07 late_transitions @ ( par @ q @ r ) @ ( late_BoundR @ ( late_InputS @ a ) @ x @ qr ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_90_fresh__prod,axiom,
% 4.00/2.07 ! [A: name,X: late_subject,Y: late_subject] :
% 4.00/2.07 ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y ) )
% 4.00/2.07 = ( ( fresh_717452603ubject @ A @ X )
% 4.00/2.07 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_91_fresh__prod,axiom,
% 4.00/2.07 ! [A: name,X: late_subject,Y: late_freeRes] :
% 4.00/2.07 ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y ) )
% 4.00/2.07 = ( ( fresh_717452603ubject @ A @ X )
% 4.00/2.07 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_92_fresh__prod,axiom,
% 4.00/2.07 ! [A: name,X: late_subject,Y: name] :
% 4.00/2.07 ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y ) )
% 4.00/2.07 = ( ( fresh_717452603ubject @ A @ X )
% 4.00/2.07 & ( fresh_name_name @ A @ Y ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_93_fresh__prod,axiom,
% 4.00/2.07 ! [A: name,X: late_subject,Y: pi] :
% 4.00/2.07 ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y ) )
% 4.00/2.07 = ( ( fresh_717452603ubject @ A @ X )
% 4.00/2.07 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_94_fresh__prod,axiom,
% 4.00/2.07 ! [A: name,X: late_freeRes,Y: late_subject] :
% 4.00/2.07 ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y ) )
% 4.00/2.07 = ( ( fresh_1641682979reeRes @ A @ X )
% 4.00/2.07 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_95_fresh__prod,axiom,
% 4.00/2.07 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 4.00/2.07 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
% 4.00/2.07 = ( ( fresh_1641682979reeRes @ A @ X )
% 4.00/2.07 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_96_fresh__prod,axiom,
% 4.00/2.07 ! [A: name,X: late_freeRes,Y: name] :
% 4.00/2.07 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
% 4.00/2.07 = ( ( fresh_1641682979reeRes @ A @ X )
% 4.00/2.07 & ( fresh_name_name @ A @ Y ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_97_fresh__prod,axiom,
% 4.00/2.07 ! [A: name,X: late_freeRes,Y: pi] :
% 4.00/2.07 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
% 4.00/2.07 = ( ( fresh_1641682979reeRes @ A @ X )
% 4.00/2.07 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_98_fresh__prod,axiom,
% 4.00/2.07 ! [A: name,X: name,Y: late_subject] :
% 4.00/2.07 ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y ) )
% 4.00/2.07 = ( ( fresh_name_name @ A @ X )
% 4.00/2.07 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_99_fresh__prod,axiom,
% 4.00/2.07 ! [A: name,X: name,Y: late_freeRes] :
% 4.00/2.07 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
% 4.00/2.07 = ( ( fresh_name_name @ A @ X )
% 4.00/2.07 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_100_cClose2_Ohyps_I1_J,axiom,
% 4.00/2.07 late_transitions @ p @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ p2 ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_101_cPar1_Ohyps,axiom,
% 4.00/2.07 late_transitions @ q @ ( late_BoundR @ ( late_InputS @ a ) @ x @ q2 ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_102_fresh__prodD_I2_J,axiom,
% 4.00/2.07 ! [A: name,X: name > noption_pi,Y: late_subject] :
% 4.00/2.07 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y ) )
% 4.00/2.07 => ( fresh_717452603ubject @ A @ Y ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_103_fresh__prodD_I2_J,axiom,
% 4.00/2.07 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 4.00/2.07 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 4.00/2.07 => ( fresh_1641682979reeRes @ A @ Y ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_104_fresh__prodD_I2_J,axiom,
% 4.00/2.07 ! [A: name,X: name > noption_pi,Y: name] :
% 4.00/2.07 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 4.00/2.07 => ( fresh_name_name @ A @ Y ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_105_fresh__prodD_I2_J,axiom,
% 4.00/2.07 ! [A: name,X: name > noption_pi,Y: pi] :
% 4.00/2.07 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 4.00/2.07 => ( fresh_name_pi @ A @ Y ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_106_fresh__prodD_I2_J,axiom,
% 4.00/2.07 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 4.00/2.07 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 4.00/2.07 => ( fresh_543891186ion_pi @ A @ Y ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_107_fresh__prodD_I2_J,axiom,
% 4.00/2.07 ! [A: name,X: pi,Y: pi] :
% 4.00/2.07 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 4.00/2.07 => ( fresh_name_pi @ A @ Y ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_108_fresh__prodD_I1_J,axiom,
% 4.00/2.07 ! [A: name,X: name > noption_pi,Y: late_subject] :
% 4.00/2.07 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y ) )
% 4.00/2.07 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_109_fresh__prodD_I1_J,axiom,
% 4.00/2.07 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 4.00/2.07 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 4.00/2.07 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_110_fresh__prodD_I1_J,axiom,
% 4.00/2.07 ! [A: name,X: name > noption_pi,Y: name] :
% 4.00/2.07 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 4.00/2.07 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_111_fresh__prodD_I1_J,axiom,
% 4.00/2.07 ! [A: name,X: name > noption_pi,Y: pi] :
% 4.00/2.07 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 4.00/2.07 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_112_fresh__prodD_I1_J,axiom,
% 4.00/2.07 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 4.00/2.07 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 4.00/2.07 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_113_fresh__prodD_I1_J,axiom,
% 4.00/2.07 ! [A: name,X: pi,Y: pi] :
% 4.00/2.07 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 4.00/2.07 => ( fresh_name_pi @ A @ X ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_114_resOutputTauTrans,axiom,
% 4.00/2.07 ! [X: name,A: name,B: name,P: pi,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_115_subject_Ofresh_I1_J,axiom,
% 4.00/2.07 ! [A: name,X1: name] :
% 4.00/2.07 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 4.00/2.07 = ( fresh_name_name @ A @ X1 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_116_subject_Ofresh_I2_J,axiom,
% 4.00/2.07 ! [A: name,X1: name] :
% 4.00/2.07 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 4.00/2.07 = ( fresh_name_name @ A @ X1 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_117_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 4.00/2.07 ! [X1: name,Y1: name] :
% 4.00/2.07 ( ( ( late_BoundOutputS @ X1 )
% 4.00/2.07 = ( late_BoundOutputS @ Y1 ) )
% 4.00/2.07 = ( X1 = Y1 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_118_freeRes_Ofresh_I2_J,axiom,
% 4.00/2.07 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_119_residual_Ofresh_I2_J,axiom,
% 4.00/2.07 ! [A: name,X2: late_freeRes,X1: pi] :
% 4.00/2.07 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 4.00/2.07 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 4.00/2.07 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_120_pi_Ofresh_I2_J,axiom,
% 4.00/2.07 ! [A: name,X32: name,X2: name,X1: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
% 4.00/2.07 = ( ( fresh_name_name @ A @ X32 )
% 4.00/2.07 & ( fresh_name_name @ A @ X2 )
% 4.00/2.07 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_121_pi_Oinject_I1_J,axiom,
% 4.00/2.07 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 4.00/2.07 ( ( ( output @ X32 @ X2 @ X1 )
% 4.00/2.07 = ( output @ Y32 @ Y2 @ Y1 ) )
% 4.00/2.07 = ( ( X32 = Y32 )
% 4.00/2.07 & ( X2 = Y2 )
% 4.00/2.07 & ( X1 = Y1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_122_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 4.00/2.07 ! [Name2: name,Name: name] :
% 4.00/2.07 ( ( late_InputS @ Name2 )
% 4.00/2.07 != ( late_BoundOutputS @ Name ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_123_subject_Oinducts,axiom,
% 4.00/2.07 ! [P: late_subject > $o,Subject: late_subject] :
% 4.00/2.07 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 4.00/2.07 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 4.00/2.07 => ( P @ Subject ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_124_outputBoundTrans,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,C: late_subject,X: name,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C @ X @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_125_resOutputInputTrans,axiom,
% 4.00/2.07 ! [X: name,A: name,B: name,P: pi,C: name,Y: name,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_126_Late__Semantics_OResB,axiom,
% 4.00/2.07 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Y @ A )
% 4.00/2.07 => ( ( Y != X )
% 4.00/2.07 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_127_freshBoundDerivative_I1_J,axiom,
% 4.00/2.07 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ P )
% 4.00/2.07 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_128_outputFreshTrans,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 4.00/2.07 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 4.00/2.07 => ~ ( ( fresh_1641682979reeRes @ A @ Alpha )
% 4.00/2.07 | ( fresh_1641682979reeRes @ B @ Alpha ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_129_residual_Odistinct_I1_J,axiom,
% 4.00/2.07 ! [Subject: late_subject,Name2: name,Pi3: pi,FreeRes: late_freeRes,Pi: pi] :
% 4.00/2.07 ( ( late_BoundR @ Subject @ Name2 @ Pi3 )
% 4.00/2.07 != ( late_FreeR @ FreeRes @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_130_residual_Oinducts,axiom,
% 4.00/2.07 ! [P: late_residual > $o,Residual: late_residual] :
% 4.00/2.07 ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 4.00/2.07 => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 4.00/2.07 => ( P @ Residual ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_131_pi_Odistinct_I29_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 4.00/2.07 ( ( output @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( par @ Pi12 @ Pi22 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_132_pi_Odistinct_I31_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 4.00/2.07 ( ( output @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( res @ Name @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_133_parCasesB_H,axiom,
% 4.00/2.07 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 4.00/2.07 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 4.00/2.07 => ( ! [P4: pi,A3: late_subject,X4: name,P5: pi,Q3: pi] :
% 4.00/2.07 ( ( ( par @ P @ Q )
% 4.00/2.07 = ( par @ P4 @ Q3 ) )
% 4.00/2.07 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 4.00/2.07 = ( late_BoundR @ A3 @ X4 @ ( par @ P5 @ Q3 ) ) )
% 4.00/2.07 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ P4 )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ Q3 )
% 4.00/2.07 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) )
% 4.00/2.07 => ~ ! [Q3: pi,A3: late_subject,X4: name,Q4: pi,P4: pi] :
% 4.00/2.07 ( ( ( par @ P @ Q )
% 4.00/2.07 = ( par @ P4 @ Q3 ) )
% 4.00/2.07 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 4.00/2.07 = ( late_BoundR @ A3 @ X4 @ ( par @ P4 @ Q4 ) ) )
% 4.00/2.07 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A3 @ X4 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ P4 )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ Q3 )
% 4.00/2.07 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_134_transitions_OPar1B,axiom,
% 4.00/2.07 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ Q )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X @ A )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_135_transitions_OPar2B,axiom,
% 4.00/2.07 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ Q )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X @ A )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_136_transitions_OResB,axiom,
% 4.00/2.07 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Y @ A )
% 4.00/2.07 => ( ( Y != X )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X @ A )
% 4.00/2.07 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_137_freshResidual,axiom,
% 4.00/2.07 ! [P: pi,Rs: late_residual,X: name] :
% 4.00/2.07 ( ( late_transitions @ P @ Rs )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P )
% 4.00/2.07 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_138_freshBoundDerivative_I2_J,axiom,
% 4.00/2.07 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ P )
% 4.00/2.07 => ( ( Y != X )
% 4.00/2.07 => ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_139_residual_Ostrong__inducts,axiom,
% 4.00/2.07 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 4.00/2.07 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 4.00/2.07 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 4.00/2.07 => ( P @ Z @ Residual ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_140_residual_Ostrong__inducts,axiom,
% 4.00/2.07 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 4.00/2.07 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 4.00/2.07 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 4.00/2.07 => ( P @ Z @ Residual ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_141_residual_Ostrong__inducts,axiom,
% 4.00/2.07 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 4.00/2.07 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ( fresh_name_name @ Name3 @ Z2 )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 4.00/2.07 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 4.00/2.07 => ( P @ Z @ Residual ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_142_residual_Ostrong__inducts,axiom,
% 4.00/2.07 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 4.00/2.07 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ Name3 @ Z2 )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 4.00/2.07 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 4.00/2.07 => ( P @ Z @ Residual ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_143_residual_Ostrong__induct,axiom,
% 4.00/2.07 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 4.00/2.07 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 4.00/2.07 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 4.00/2.07 => ( P @ Z @ Residual ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_144_residual_Ostrong__induct,axiom,
% 4.00/2.07 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 4.00/2.07 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 4.00/2.07 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 4.00/2.07 => ( P @ Z @ Residual ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_145_residual_Ostrong__induct,axiom,
% 4.00/2.07 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 4.00/2.07 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ( fresh_name_name @ Name3 @ Z2 )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 4.00/2.07 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 4.00/2.07 => ( P @ Z @ Residual ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_146_residual_Ostrong__induct,axiom,
% 4.00/2.07 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 4.00/2.07 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ Name3 @ Z2 )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 4.00/2.07 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 4.00/2.07 => ( P @ Z @ Residual ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_147_resTrans_I1_J,axiom,
% 4.00/2.07 ! [X: name,B: name,P: pi,Rs: late_residual] :
% 4.00/2.07 ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_148_Late__Semantics_OClose1,axiom,
% 4.00/2.07 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 4.00/2.07 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ P )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_149_Late__Semantics_OClose2,axiom,
% 4.00/2.07 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 4.00/2.07 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ Q )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_150_transitions_OClose1,axiom,
% 4.00/2.07 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 4.00/2.07 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ Q )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ Q )
% 4.00/2.07 => ( ( X != A )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ Q2 )
% 4.00/2.07 => ( ( Y != A )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ P2 )
% 4.00/2.07 => ( ( X != Y )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_151_transitions_OClose2,axiom,
% 4.00/2.07 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 4.00/2.07 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ Q )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ Q )
% 4.00/2.07 => ( ( X != A )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P2 )
% 4.00/2.07 => ( ( Y != A )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ Q2 )
% 4.00/2.07 => ( ( X != Y )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_152_resCasesF,axiom,
% 4.00/2.07 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 4.00/2.07 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 4.00/2.07 => ( ! [P5: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 4.00/2.07 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 4.00/2.07 => ( F @ ( res @ X @ P5 ) ) ) )
% 4.00/2.07 => ( F @ XP ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_153_resCasesF_H,axiom,
% 4.00/2.07 ! [X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 4.00/2.07 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 4.00/2.07 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 4.00/2.07 ( ( ( res @ X @ P )
% 4.00/2.07 = ( res @ Y3 @ P4 ) )
% 4.00/2.07 => ( ( ( late_FreeR @ Alpha @ P2 )
% 4.00/2.07 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 4.00/2.07 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 4.00/2.07 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_154_ResF,axiom,
% 4.00/2.07 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 4.00/2.07 => ( ( fresh_1641682979reeRes @ Y @ Alpha )
% 4.00/2.07 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_155_Late__Semantics_OPar1B,axiom,
% 4.00/2.07 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ Q )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_156_Late__Semantics_OPar2B,axiom,
% 4.00/2.07 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_157_parCasesB,axiom,
% 4.00/2.07 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 4.00/2.07 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ Q )
% 4.00/2.07 => ( ! [P5: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P5 ) )
% 4.00/2.07 => ( Prop @ ( par @ P5 @ Q ) ) )
% 4.00/2.07 => ( ! [Q4: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q4 ) )
% 4.00/2.07 => ( Prop @ ( par @ P @ Q4 ) ) )
% 4.00/2.07 => ( Prop @ PQ ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_158_freshFreeDerivative_I1_J,axiom,
% 4.00/2.07 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ Y @ P )
% 4.00/2.07 => ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_159_outputTauTrans,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_160_transitions_OComm1,axiom,
% 4.00/2.07 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 4.00/2.07 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ Q )
% 4.00/2.07 => ( ( X != A )
% 4.00/2.07 => ( ( X != B )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ Q2 )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_161_transitions_OComm2,axiom,
% 4.00/2.07 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 4.00/2.07 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ Q )
% 4.00/2.07 => ( ( X != A )
% 4.00/2.07 => ( ( X != B )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P2 )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_162_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 4.00/2.07 ! [X2: name,Y2: name] :
% 4.00/2.07 ( ( ( late_BoundOutputS @ X2 )
% 4.00/2.07 = ( late_BoundOutputS @ Y2 ) )
% 4.00/2.07 = ( X2 = Y2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_163_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 4.00/2.07 ! [X1: name,Y1: name] :
% 4.00/2.07 ( ( ( late_InputS @ X1 )
% 4.00/2.07 = ( late_InputS @ Y1 ) )
% 4.00/2.07 = ( X1 = Y1 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_164_Late__Semantics_OComm1,axiom,
% 4.00/2.07 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 4.00/2.07 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_165_Late__Semantics_OComm2,axiom,
% 4.00/2.07 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 4.00/2.07 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 4.00/2.07 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_166_subject_Oexhaust,axiom,
% 4.00/2.07 ! [Y: late_subject] :
% 4.00/2.07 ( ! [X12: name] :
% 4.00/2.07 ( Y
% 4.00/2.07 != ( late_InputS @ X12 ) )
% 4.00/2.07 => ~ ! [X22: name] :
% 4.00/2.07 ( Y
% 4.00/2.07 != ( late_BoundOutputS @ X22 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_167_Late__Semantics1_OfreeRes_Oinject,axiom,
% 4.00/2.07 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 4.00/2.07 ( ( ( late_OutputR @ X11 @ X122 )
% 4.00/2.07 = ( late_OutputR @ Y11 @ Y12 ) )
% 4.00/2.07 = ( ( X11 = Y11 )
% 4.00/2.07 & ( X122 = Y12 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_168_Late__Semantics_OfreeRes_Oinject,axiom,
% 4.00/2.07 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 4.00/2.07 ( ( ( late_OutputR @ X2 @ X1 )
% 4.00/2.07 = ( late_OutputR @ Y2 @ Y1 ) )
% 4.00/2.07 = ( ( X2 = Y2 )
% 4.00/2.07 & ( X1 = Y1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_169_name__fresh,axiom,
% 4.00/2.07 ( fresh_name_name
% 4.00/2.07 = ( ^ [A5: name,B4: name] : ( A5 != B4 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_170_freeRes_Ofresh_I1_J,axiom,
% 4.00/2.07 ! [A: name,X2: name,X1: name] :
% 4.00/2.07 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 4.00/2.07 = ( ( fresh_name_name @ A @ X2 )
% 4.00/2.07 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_171_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 4.00/2.07 ! [X11: name,X122: name] :
% 4.00/2.07 ( ( late_OutputR @ X11 @ X122 )
% 4.00/2.07 != late_TauR ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_172_freeRes_Oexhaust,axiom,
% 4.00/2.07 ! [Y: late_freeRes] :
% 4.00/2.07 ( ! [X112: name,X123: name] :
% 4.00/2.07 ( Y
% 4.00/2.07 != ( late_OutputR @ X112 @ X123 ) )
% 4.00/2.07 => ( Y = late_TauR ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_173_freeRes_Oinducts,axiom,
% 4.00/2.07 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 4.00/2.07 ( ! [Name12: name,Name23: name] : ( P @ ( late_OutputR @ Name12 @ Name23 ) )
% 4.00/2.07 => ( ( P @ late_TauR )
% 4.00/2.07 => ( P @ FreeRes3 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_174_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name] :
% 4.00/2.07 ( ( late_OutputR @ Name1 @ Name22 )
% 4.00/2.07 != late_TauR ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_175_Output,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_176_outputIneqTrans,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,C: name,D: name,P2: pi] :
% 4.00/2.07 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P2 ) )
% 4.00/2.07 => ~ ( ( A != C )
% 4.00/2.07 | ( B != D ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_177_outputCases_H,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 4.00/2.07 ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 4.00/2.07 => ~ ! [A3: name,B3: name,P4: pi] :
% 4.00/2.07 ( ( ( A = A3 )
% 4.00/2.07 & ( B = B3 )
% 4.00/2.07 & ( P = P4 ) )
% 4.00/2.07 => ( Rs
% 4.00/2.07 != ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P4 ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_178_outputCases,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 4.00/2.07 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 4.00/2.07 => ( ( ( Alpha
% 4.00/2.07 = ( late_OutputR @ A @ B ) )
% 4.00/2.07 => ( ( P = P2 )
% 4.00/2.07 => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 4.00/2.07 => ( Prop @ Alpha @ P2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_179_resOutputOutputTrans,axiom,
% 4.00/2.07 ! [X: name,A: name,P: pi,B: name,Y: name,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_180_Open,axiom,
% 4.00/2.07 ! [P: pi,A: name,B: name,P2: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 4.00/2.07 => ( ( A != B )
% 4.00/2.07 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_181_resCasesB_H,axiom,
% 4.00/2.07 ! [X5: name,P: pi,A: late_subject,Y4: name,P2: pi] :
% 4.00/2.07 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y4 @ P2 ) )
% 4.00/2.07 => ( ! [P4: pi,A3: name,B3: name] :
% 4.00/2.07 ( ( ( res @ X5 @ P )
% 4.00/2.07 = ( res @ B3 @ P4 ) )
% 4.00/2.07 => ! [P5: pi] :
% 4.00/2.07 ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 4.00/2.07 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 4.00/2.07 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 4.00/2.07 => ( A3 = B3 ) ) ) )
% 4.00/2.07 => ~ ! [P4: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
% 4.00/2.07 ( ( ( res @ X5 @ P )
% 4.00/2.07 = ( res @ Y3 @ P4 ) )
% 4.00/2.07 => ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 4.00/2.07 = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 4.00/2.07 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 4.00/2.07 => ( ( Y3 != X4 )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ P4 )
% 4.00/2.07 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_182_resCases_H,axiom,
% 4.00/2.07 ! [X: name,P: pi,Rs: late_residual] :
% 4.00/2.07 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 4.00/2.07 => ( ! [P4: pi,A3: name,B3: name] :
% 4.00/2.07 ( ( ( res @ X @ P )
% 4.00/2.07 = ( res @ B3 @ P4 ) )
% 4.00/2.07 => ! [P5: pi] :
% 4.00/2.07 ( ( Rs
% 4.00/2.07 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 4.00/2.07 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 4.00/2.07 => ( A3 = B3 ) ) ) )
% 4.00/2.07 => ( ! [P4: pi,A3: late_subject,X4: name,P5: pi,Y3: name] :
% 4.00/2.07 ( ( ( res @ X @ P )
% 4.00/2.07 = ( res @ Y3 @ P4 ) )
% 4.00/2.07 => ( ( Rs
% 4.00/2.07 = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P5 ) ) )
% 4.00/2.07 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P5 ) )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 4.00/2.07 => ( ( Y3 != X4 )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ P4 )
% 4.00/2.07 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) )
% 4.00/2.07 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 4.00/2.07 ( ( ( res @ X @ P )
% 4.00/2.07 = ( res @ Y3 @ P4 ) )
% 4.00/2.07 => ( ( Rs
% 4.00/2.07 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 4.00/2.07 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 4.00/2.07 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_183_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 4.00/2.07 ! [X1: name,X2: name] :
% 4.00/2.07 ( ( late_InputS @ X1 )
% 4.00/2.07 != ( late_BoundOutputS @ X2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_184_resTauOutputTrans,axiom,
% 4.00/2.07 ! [X: name,P: pi,A: name,B: name,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_185_resInputBoundOutputTrans,axiom,
% 4.00/2.07 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_186_pi_Ofresh_I3_J,axiom,
% 4.00/2.07 ! [A: name,X1: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 4.00/2.07 = ( fresh_name_pi @ A @ X1 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_187_simps_I2_J,axiom,
% 4.00/2.07 ! [P: pi,C: name,D: name] :
% 4.00/2.07 ( ( subs @ ( tau @ P ) @ C @ D )
% 4.00/2.07 = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_188_pi_Oinject_I2_J,axiom,
% 4.00/2.07 ! [X1: pi,Y1: pi] :
% 4.00/2.07 ( ( ( tau @ X1 )
% 4.00/2.07 = ( tau @ Y1 ) )
% 4.00/2.07 = ( X1 = Y1 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_189_pi_Odistinct_I35_J,axiom,
% 4.00/2.07 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( ( tau @ Pi3 )
% 4.00/2.07 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_190_pi_Odistinct_I55_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 4.00/2.07 ( ( input @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( par @ Pi12 @ Pi22 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_191_pi_Odistinct_I57_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 4.00/2.07 ( ( input @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( res @ Name @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_192_pi_Odistinct_I43_J,axiom,
% 4.00/2.07 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 4.00/2.07 ( ( tau @ Pi3 )
% 4.00/2.07 != ( par @ Pi12 @ Pi22 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_193_pi_Odistinct_I45_J,axiom,
% 4.00/2.07 ! [Pi3: pi,Name: name,Pi: pi] :
% 4.00/2.07 ( ( tau @ Pi3 )
% 4.00/2.07 != ( res @ Name @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_194_pi_Odistinct_I21_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( ( output @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_195_pi_Odistinct_I19_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 4.00/2.07 ( ( output @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( tau @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_196_resTrans_I2_J,axiom,
% 4.00/2.07 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 4.00/2.07 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_197_inputFreeTrans,axiom,
% 4.00/2.07 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_198_tauBoundTrans,axiom,
% 4.00/2.07 ! [P: pi,A: late_subject,X: name,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_199_resInputFreeTrans,axiom,
% 4.00/2.07 ! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_200_Late__Semantics_OInput,axiom,
% 4.00/2.07 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_201_transitions_OInput,axiom,
% 4.00/2.07 ! [X: name,A: name,P: pi] :
% 4.00/2.07 ( ( X != A )
% 4.00/2.07 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_202_inputBoundOutputTrans,axiom,
% 4.00/2.07 ! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_203_resTauBoundTrans,axiom,
% 4.00/2.07 ! [X: name,P: pi,A: late_subject,Y: name,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_204_inputIneqTrans,axiom,
% 4.00/2.07 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 4.00/2.07 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 4.00/2.07 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_205_tauOutputTrans,axiom,
% 4.00/2.07 ! [P: pi,A: name,B: name,P2: pi] :
% 4.00/2.07 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_206_tauCases,axiom,
% 4.00/2.07 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 4.00/2.07 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 4.00/2.07 => ( ( ( Alpha = late_TauR )
% 4.00/2.07 => ( ( P = P2 )
% 4.00/2.07 => ( Prop @ late_TauR @ P ) ) )
% 4.00/2.07 => ( Prop @ Alpha @ P2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_207_tauCases_H,axiom,
% 4.00/2.07 ! [P: pi,Rs: late_residual] :
% 4.00/2.07 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 4.00/2.07 => ~ ! [P4: pi] :
% 4.00/2.07 ( ( ( tau @ P )
% 4.00/2.07 = ( tau @ P4 ) )
% 4.00/2.07 => ( Rs
% 4.00/2.07 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_208_Tau,axiom,
% 4.00/2.07 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_209_residual_Ofresh_I1_J,axiom,
% 4.00/2.07 ! [A: name,X32: late_subject,X1: name,X2: pi] :
% 4.00/2.07 ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 4.00/2.07 = ( ( fresh_717452603ubject @ A @ X32 )
% 4.00/2.07 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_210_simps_I3_J,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,C: name,D: name] :
% 4.00/2.07 ( ( subs @ ( output @ A @ B @ P ) @ C @ D )
% 4.00/2.07 = ( output @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_211_substInput,axiom,
% 4.00/2.07 ! [X: name,B: name,C: name,A: name,P: pi] :
% 4.00/2.07 ( ( X != B )
% 4.00/2.07 => ( ( X != C )
% 4.00/2.07 => ( ( subs @ ( input @ A @ X @ P ) @ B @ C )
% 4.00/2.07 = ( input @ ( subst_name @ A @ B @ C ) @ X @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_212_simps_I4_J,axiom,
% 4.00/2.07 ! [X: name,A: name,C: name,D: name,P: pi] :
% 4.00/2.07 ( ( X != A )
% 4.00/2.07 => ( ( X != C )
% 4.00/2.07 => ( ( X != D )
% 4.00/2.07 => ( ( subs @ ( input @ A @ X @ P ) @ C @ D )
% 4.00/2.07 = ( input @ ( subst_name @ A @ C @ D ) @ X @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_213_pi_Ofresh_I9_J,axiom,
% 4.00/2.07 ! [A: name,X1: name,X2: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 4.00/2.07 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_214_pi_Ofresh_I4_J,axiom,
% 4.00/2.07 ! [A: name,X32: name,X1: name,X2: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
% 4.00/2.07 = ( ( fresh_name_name @ A @ X32 )
% 4.00/2.07 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_215_pi_Oinject_I3_J,axiom,
% 4.00/2.07 ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
% 4.00/2.07 ( ( ( input @ X32 @ X1 @ X2 )
% 4.00/2.07 = ( input @ Y32 @ Y1 @ Y2 ) )
% 4.00/2.07 = ( ( X32 = Y32 )
% 4.00/2.07 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 4.00/2.07 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_216_abs__fun__eq1,axiom,
% 4.00/2.07 ! [A: name,X: name,Y: name] :
% 4.00/2.07 ( ( ( abs_fun_name_name @ A @ X )
% 4.00/2.07 = ( abs_fun_name_name @ A @ Y ) )
% 4.00/2.07 = ( X = Y ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_217_abs__fun__eq1,axiom,
% 4.00/2.07 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 4.00/2.07 ( ( ( abs_fu681348580reeRes @ A @ X )
% 4.00/2.07 = ( abs_fu681348580reeRes @ A @ Y ) )
% 4.00/2.07 = ( X = Y ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_218_abs__fun__eq1,axiom,
% 4.00/2.07 ! [A: name,X: late_subject,Y: late_subject] :
% 4.00/2.07 ( ( ( abs_fu1904601852ubject @ A @ X )
% 4.00/2.07 = ( abs_fu1904601852ubject @ A @ Y ) )
% 4.00/2.07 = ( X = Y ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_219_abs__fun__eq1,axiom,
% 4.00/2.07 ! [A: name,X: pi,Y: pi] :
% 4.00/2.07 ( ( ( abs_fun_name_pi @ A @ X )
% 4.00/2.07 = ( abs_fun_name_pi @ A @ Y ) )
% 4.00/2.07 = ( X = Y ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_220_subst__name__def,axiom,
% 4.00/2.07 ( subst_name
% 4.00/2.07 = ( ^ [A5: name,B4: name,C3: name] : ( if_name @ ( A5 = B4 ) @ C3 @ A5 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_221_name__fresh__abs,axiom,
% 4.00/2.07 ! [B: name,A: name,X: late_subject] :
% 4.00/2.07 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 4.00/2.07 = ( ( B = A )
% 4.00/2.07 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_222_name__fresh__abs,axiom,
% 4.00/2.07 ! [B: name,A: name,X: late_freeRes] :
% 4.00/2.07 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 4.00/2.07 = ( ( B = A )
% 4.00/2.07 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_223_name__fresh__abs,axiom,
% 4.00/2.07 ! [B: name,A: name,X: name] :
% 4.00/2.07 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 4.00/2.07 = ( ( B = A )
% 4.00/2.07 | ( fresh_name_name @ B @ X ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_224_name__fresh__abs,axiom,
% 4.00/2.07 ! [B: name,A: name,X: pi] :
% 4.00/2.07 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 4.00/2.07 = ( ( B = A )
% 4.00/2.07 | ( fresh_name_pi @ B @ X ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_225_abs__fresh_I1_J,axiom,
% 4.00/2.07 ! [B: name,A: name,X: late_subject] :
% 4.00/2.07 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 4.00/2.07 = ( ( B = A )
% 4.00/2.07 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_226_abs__fresh_I1_J,axiom,
% 4.00/2.07 ! [B: name,A: name,X: late_freeRes] :
% 4.00/2.07 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 4.00/2.07 = ( ( B = A )
% 4.00/2.07 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_227_abs__fresh_I1_J,axiom,
% 4.00/2.07 ! [B: name,A: name,X: name] :
% 4.00/2.07 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 4.00/2.07 = ( ( B = A )
% 4.00/2.07 | ( fresh_name_name @ B @ X ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_228_abs__fresh_I1_J,axiom,
% 4.00/2.07 ! [B: name,A: name,X: pi] :
% 4.00/2.07 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 4.00/2.07 = ( ( B = A )
% 4.00/2.07 | ( fresh_name_pi @ B @ X ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_229_residual_Oinject_I1_J,axiom,
% 4.00/2.07 ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 4.00/2.07 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 4.00/2.07 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 4.00/2.07 = ( ( X32 = Y32 )
% 4.00/2.07 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 4.00/2.07 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_230_pi_Oinject_I8_J,axiom,
% 4.00/2.07 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 4.00/2.07 ( ( ( res @ X1 @ X2 )
% 4.00/2.07 = ( res @ Y1 @ Y2 ) )
% 4.00/2.07 = ( ( abs_fun_name_pi @ X1 @ X2 )
% 4.00/2.07 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_231_inputCases_H,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 4.00/2.07 ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 4.00/2.07 => ~ ! [X4: name,A3: name,P4: pi] :
% 4.00/2.07 ( ( ( A = A3 )
% 4.00/2.07 & ( ( abs_fun_name_pi @ B @ P )
% 4.00/2.07 = ( abs_fun_name_pi @ X4 @ P4 ) ) )
% 4.00/2.07 => ( ( Rs
% 4.00/2.07 = ( late_BoundR @ ( late_InputS @ A3 ) @ X4 @ P4 ) )
% 4.00/2.07 => ( X4 = A3 ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_232_resSimCases,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C4: late_subject] :
% 4.00/2.07 ( ( eqvt_pi @ Rel )
% 4.00/2.07 => ( ! [Q4: pi,A3: name] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 4.00/2.07 => ( ( A3 != X )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 4.00/2.07 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X @ A3 )
% 4.00/2.07 => ( ( X != Y3 )
% 4.00/2.07 => ( ( fresh_717452603ubject @ Y3 @ C4 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 4.00/2.07 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 4.00/2.07 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 4.00/2.07 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_233_resSimCases,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C4: late_freeRes] :
% 4.00/2.07 ( ( eqvt_pi @ Rel )
% 4.00/2.07 => ( ! [Q4: pi,A3: name] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 4.00/2.07 => ( ( A3 != X )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 4.00/2.07 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X @ A3 )
% 4.00/2.07 => ( ( X != Y3 )
% 4.00/2.07 => ( ( fresh_1641682979reeRes @ Y3 @ C4 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 4.00/2.07 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 4.00/2.07 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 4.00/2.07 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_234_resSimCases,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C4: name] :
% 4.00/2.07 ( ( eqvt_pi @ Rel )
% 4.00/2.07 => ( ! [Q4: pi,A3: name] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 4.00/2.07 => ( ( A3 != X )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 4.00/2.07 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X @ A3 )
% 4.00/2.07 => ( ( X != Y3 )
% 4.00/2.07 => ( ( fresh_name_name @ Y3 @ C4 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 4.00/2.07 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 4.00/2.07 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 4.00/2.07 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_235_resSimCases,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C4: pi] :
% 4.00/2.07 ( ( eqvt_pi @ Rel )
% 4.00/2.07 => ( ! [Q4: pi,A3: name] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 4.00/2.07 => ( ( A3 != X )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 4.00/2.07 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X @ A3 )
% 4.00/2.07 => ( ( X != Y3 )
% 4.00/2.07 => ( ( fresh_name_pi @ Y3 @ C4 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 4.00/2.07 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 4.00/2.07 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 4.00/2.07 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_236_parSym,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 4.00/2.07 ( ! [R: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R @ S2 ) @ ( par @ S2 @ R ) ) @ Rel )
% 4.00/2.07 => ( ! [R: pi,S2: pi,X4: name] :
% 4.00/2.07 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R @ S2 ) @ Rel )
% 4.00/2.07 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X4 @ R ) @ ( res @ X4 @ S2 ) ) @ Rel ) )
% 4.00/2.07 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_237_simE_I1_J,axiom,
% 4.00/2.07 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 4.00/2.07 ( ( strong743114133lation @ P @ Rel @ Q )
% 4.00/2.07 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X @ P )
% 4.00/2.07 => ? [P5: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P5 ) )
% 4.00/2.07 & ( strong2129052853vative @ P5 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_238_simE_I2_J,axiom,
% 4.00/2.07 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 4.00/2.07 ( ( strong743114133lation @ P @ Rel @ Q )
% 4.00/2.07 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 4.00/2.07 => ? [P5: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_239_simCasesCont,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C4: late_subject] :
% 4.00/2.07 ( ( eqvt_pi @ Rel )
% 4.00/2.07 => ( ! [A3: late_subject,X4: name,Q4: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X4 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ Q )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X4 @ A3 )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X4 @ C4 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P6 ) )
% 4.00/2.07 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X4 @ Rel ) ) ) ) ) ) )
% 4.00/2.07 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 4.00/2.07 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_240_simCasesCont,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C4: late_freeRes] :
% 4.00/2.07 ( ( eqvt_pi @ Rel )
% 4.00/2.07 => ( ! [A3: late_subject,X4: name,Q4: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X4 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ Q )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X4 @ A3 )
% 4.00/2.07 => ( ( fresh_1641682979reeRes @ X4 @ C4 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P6 ) )
% 4.00/2.07 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X4 @ Rel ) ) ) ) ) ) )
% 4.00/2.07 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 4.00/2.07 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_241_simCasesCont,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C4: name] :
% 4.00/2.07 ( ( eqvt_pi @ Rel )
% 4.00/2.07 => ( ! [A3: late_subject,X4: name,Q4: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X4 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ Q )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X4 @ A3 )
% 4.00/2.07 => ( ( fresh_name_name @ X4 @ C4 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P6 ) )
% 4.00/2.07 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X4 @ Rel ) ) ) ) ) ) )
% 4.00/2.07 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 4.00/2.07 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_242_simCasesCont,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C4: pi] :
% 4.00/2.07 ( ( eqvt_pi @ Rel )
% 4.00/2.07 => ( ! [A3: late_subject,X4: name,Q4: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X4 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ P )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ Q )
% 4.00/2.07 => ( ( fresh_717452603ubject @ X4 @ A3 )
% 4.00/2.07 => ( ( fresh_name_pi @ X4 @ C4 )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X4 @ P6 ) )
% 4.00/2.07 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X4 @ Rel ) ) ) ) ) ) )
% 4.00/2.07 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 4.00/2.07 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_243_simCases,axiom,
% 4.00/2.07 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 4.00/2.07 ( ! [A3: late_subject,Y3: name,Q4: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 4.00/2.07 => ( ( fresh_name_pi @ Y3 @ P )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 4.00/2.07 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ Y3 @ Rel ) ) ) )
% 4.00/2.07 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 4.00/2.07 => ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 4.00/2.07 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_244_simulation__def,axiom,
% 4.00/2.07 ( strong743114133lation
% 4.00/2.07 = ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 4.00/2.07 ( ! [A5: late_subject,X3: name,Q6: pi] :
% 4.00/2.07 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X3 @ Q6 ) )
% 4.00/2.07 & ( fresh_name_pi @ X3 @ P7 ) )
% 4.00/2.07 => ? [P8: pi] :
% 4.00/2.07 ( ( late_transitions @ P7 @ ( late_BoundR @ A5 @ X3 @ P8 ) )
% 4.00/2.07 & ( strong2129052853vative @ P8 @ Q6 @ A5 @ X3 @ Rel2 ) ) )
% 4.00/2.07 & ! [Alpha3: late_freeRes,Q6: pi] :
% 4.00/2.07 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 4.00/2.07 => ? [P8: pi] :
% 4.00/2.07 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_245_parZeroRight,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 4.00/2.07 ( ! [Q3: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ Q3 @ ( par @ Q3 @ piNil ) ) @ Rel )
% 4.00/2.07 => ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_246_parZeroLeft,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 4.00/2.07 ( ! [Q3: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ Q3 @ piNil ) @ Q3 ) @ Rel )
% 4.00/2.07 => ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_247_simps_I5_J,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,C: name,D: name] :
% 4.00/2.07 ( ( subs @ ( match @ A @ B @ P ) @ C @ D )
% 4.00/2.07 = ( match @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_248_pi_Ofresh_I1_J,axiom,
% 4.00/2.07 ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_249_simps_I1_J,axiom,
% 4.00/2.07 ! [C: name,D: name] :
% 4.00/2.07 ( ( subs @ piNil @ C @ D )
% 4.00/2.07 = piNil ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_250_pi_Ofresh_I5_J,axiom,
% 4.00/2.07 ! [A: name,X32: name,X2: name,X1: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ A @ ( match @ X32 @ X2 @ X1 ) )
% 4.00/2.07 = ( ( fresh_name_name @ A @ X32 )
% 4.00/2.07 & ( fresh_name_name @ A @ X2 )
% 4.00/2.07 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_251_matchNilLeft,axiom,
% 4.00/2.07 ! [A: name,B: name,Rel: set_Pr1834926343_pi_pi,P: pi] :
% 4.00/2.07 ( ( A != B )
% 4.00/2.07 => ( strong743114133lation @ piNil @ Rel @ ( match @ A @ B @ P ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_252_nilSimRight,axiom,
% 4.00/2.07 ! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_253_pi_Odistinct_I49_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( ( input @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_254_pi_Odistinct_I5_J,axiom,
% 4.00/2.07 ! [Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( piNil
% 4.00/2.07 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_255_matchCases,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 4.00/2.07 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 4.00/2.07 => ( ( ( late_transitions @ P @ Rs )
% 4.00/2.07 => ( ( A = B )
% 4.00/2.07 => ( F @ A @ A ) ) )
% 4.00/2.07 => ( F @ A @ B ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_256_matchTrans,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 4.00/2.07 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 4.00/2.07 => ( A = B ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_257_matchCases_H,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 4.00/2.07 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 4.00/2.07 => ~ ! [P4: pi] :
% 4.00/2.07 ( ( ( B = A )
% 4.00/2.07 & ( P = P4 ) )
% 4.00/2.07 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_258_Match,axiom,
% 4.00/2.07 ! [P: pi,Rs: late_residual,B: name] :
% 4.00/2.07 ( ( late_transitions @ P @ Rs )
% 4.00/2.07 => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_259_nilCases_H,axiom,
% 4.00/2.07 ! [Rs: late_residual] :
% 4.00/2.07 ~ ( late_transitions @ piNil @ Rs ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_260_zeroTrans,axiom,
% 4.00/2.07 ! [Rs: late_residual] :
% 4.00/2.07 ~ ( late_transitions @ piNil @ Rs ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_261_pi_Odistinct_I65_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 4.00/2.07 ( ( match @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( par @ Pi12 @ Pi22 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_262_pi_Odistinct_I67_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 4.00/2.07 ( ( match @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( res @ Name @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_263_pi_Odistinct_I13_J,axiom,
% 4.00/2.07 ! [Pi12: pi,Pi22: pi] :
% 4.00/2.07 ( piNil
% 4.00/2.07 != ( par @ Pi12 @ Pi22 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_264_pi_Odistinct_I15_J,axiom,
% 4.00/2.07 ! [Name: name,Pi: pi] :
% 4.00/2.07 ( piNil
% 4.00/2.07 != ( res @ Name @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_265_pi_Odistinct_I7_J,axiom,
% 4.00/2.07 ! [Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( piNil
% 4.00/2.07 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_266_pi_Oinject_I4_J,axiom,
% 4.00/2.07 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 4.00/2.07 ( ( ( match @ X32 @ X2 @ X1 )
% 4.00/2.07 = ( match @ Y32 @ Y2 @ Y1 ) )
% 4.00/2.07 = ( ( X32 = Y32 )
% 4.00/2.07 & ( X2 = Y2 )
% 4.00/2.07 & ( X1 = Y1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_267_pi_Odistinct_I3_J,axiom,
% 4.00/2.07 ! [Pi: pi] :
% 4.00/2.07 ( piNil
% 4.00/2.07 != ( tau @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_268_pi_Odistinct_I37_J,axiom,
% 4.00/2.07 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( ( tau @ Pi3 )
% 4.00/2.07 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_269_pi_Odistinct_I1_J,axiom,
% 4.00/2.07 ! [Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( piNil
% 4.00/2.07 != ( output @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_270_pi_Odistinct_I23_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( ( output @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_271_resZeroTrans,axiom,
% 4.00/2.07 ! [X: name,Rs: late_residual] :
% 4.00/2.07 ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_272_nilSim_I2_J,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
% 4.00/2.07 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_273_nilSim_I3_J,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 4.00/2.07 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_274_nilSim_I1_J,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 4.00/2.07 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_275_simps_I6_J,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,C: name,D: name] :
% 4.00/2.07 ( ( subs @ ( mismatch @ A @ B @ P ) @ C @ D )
% 4.00/2.07 = ( mismatch @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_276_pi_Ofresh_I6_J,axiom,
% 4.00/2.07 ! [A: name,X32: name,X2: name,X1: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
% 4.00/2.07 = ( ( fresh_name_name @ A @ X32 )
% 4.00/2.07 & ( fresh_name_name @ A @ X2 )
% 4.00/2.07 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_277_pi_Odistinct_I9_J,axiom,
% 4.00/2.07 ! [Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( piNil
% 4.00/2.07 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_278_pi_Odistinct_I61_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( ( match @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_279_pi_Odistinct_I25_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( ( output @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_280_pi_Odistinct_I39_J,axiom,
% 4.00/2.07 ! [Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( ( tau @ Pi3 )
% 4.00/2.07 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_281_pi_Oinject_I5_J,axiom,
% 4.00/2.07 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 4.00/2.07 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 4.00/2.07 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 4.00/2.07 = ( ( X32 = Y32 )
% 4.00/2.07 & ( X2 = Y2 )
% 4.00/2.07 & ( X1 = Y1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_282_pi_Odistinct_I75_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 4.00/2.07 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( res @ Name @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_283_pi_Odistinct_I73_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 4.00/2.07 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( par @ Pi12 @ Pi22 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_284_Mismatch,axiom,
% 4.00/2.07 ! [P: pi,Rs: late_residual,A: name,B: name] :
% 4.00/2.07 ( ( late_transitions @ P @ Rs )
% 4.00/2.07 => ( ( A != B )
% 4.00/2.07 => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_285_mismatchCases_H,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 4.00/2.07 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 4.00/2.07 => ~ ! [P4: pi,A3: name,B3: name] :
% 4.00/2.07 ( ( ( A = A3 )
% 4.00/2.07 & ( B = B3 )
% 4.00/2.07 & ( P = P4 ) )
% 4.00/2.07 => ( ( late_transitions @ P4 @ Rs )
% 4.00/2.07 => ( A3 = B3 ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_286_mismatchTrans,axiom,
% 4.00/2.07 ! [A: name,P: pi,Rs: late_residual] :
% 4.00/2.07 ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_287_mismatchCases,axiom,
% 4.00/2.07 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 4.00/2.07 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 4.00/2.07 => ( ( ( late_transitions @ P @ Rs )
% 4.00/2.07 => ( ( A != B )
% 4.00/2.07 => ( F @ A @ B ) ) )
% 4.00/2.07 => ( F @ A @ B ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_288_pi_Odistinct_I51_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Name13: name,Name24: name,Pi: pi] :
% 4.00/2.07 ( ( input @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_289_mismatchNilLeft,axiom,
% 4.00/2.07 ! [Rel: set_Pr1834926343_pi_pi,A: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A @ A @ P ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_290_pi_Ostrong__induct,axiom,
% 4.00/2.07 ! [P: late_subject > pi > $o,Z: late_subject,Pi3: pi] :
% 4.00/2.07 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 4.00/2.07 => ( ( fresh_name_name @ Name23 @ Name12 )
% 4.00/2.07 => ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Name3: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 4.00/2.07 => ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 4.00/2.07 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_291_pi_Ostrong__induct,axiom,
% 4.00/2.07 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi3: pi] :
% 4.00/2.07 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 4.00/2.07 => ( ( fresh_name_name @ Name23 @ Name12 )
% 4.00/2.07 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Name3: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 4.00/2.07 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 4.00/2.07 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_292_pi_Ostrong__induct,axiom,
% 4.00/2.07 ! [P: name > pi > $o,Z: name,Pi3: pi] :
% 4.00/2.07 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ( fresh_name_name @ Name23 @ Z2 )
% 4.00/2.07 => ( ( fresh_name_name @ Name23 @ Name12 )
% 4.00/2.07 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Name3: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ( fresh_name_name @ Name3 @ Z2 )
% 4.00/2.07 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 4.00/2.07 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_293_pi_Ostrong__induct,axiom,
% 4.00/2.07 ! [P: pi > pi > $o,Z: pi,Pi3: pi] :
% 4.00/2.07 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ Name23 @ Z2 )
% 4.00/2.07 => ( ( fresh_name_name @ Name23 @ Name12 )
% 4.00/2.07 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Name3: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ Name3 @ Z2 )
% 4.00/2.07 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 4.00/2.07 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_294_pi_Ostrong__inducts,axiom,
% 4.00/2.07 ! [P: late_subject > pi > $o,Z: late_subject,Pi3: pi] :
% 4.00/2.07 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 4.00/2.07 => ( ( fresh_name_name @ Name23 @ Name12 )
% 4.00/2.07 => ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Name3: name,Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 4.00/2.07 => ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: late_subject] :
% 4.00/2.07 ( ! [Za: late_subject] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 4.00/2.07 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_295_pi_Ostrong__inducts,axiom,
% 4.00/2.07 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi3: pi] :
% 4.00/2.07 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 4.00/2.07 => ( ( fresh_name_name @ Name23 @ Name12 )
% 4.00/2.07 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Name3: name,Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 4.00/2.07 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: late_freeRes] :
% 4.00/2.07 ( ! [Za: late_freeRes] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 4.00/2.07 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_296_pi_Ostrong__inducts,axiom,
% 4.00/2.07 ! [P: name > pi > $o,Z: name,Pi3: pi] :
% 4.00/2.07 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ( fresh_name_name @ Name23 @ Z2 )
% 4.00/2.07 => ( ( fresh_name_name @ Name23 @ Name12 )
% 4.00/2.07 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Name3: name,Pi4: pi,Z2: name] :
% 4.00/2.07 ( ( fresh_name_name @ Name3 @ Z2 )
% 4.00/2.07 => ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: name] :
% 4.00/2.07 ( ! [Za: name] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 4.00/2.07 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_297_pi_Ostrong__inducts,axiom,
% 4.00/2.07 ! [P: pi > pi > $o,Z: pi,Pi3: pi] :
% 4.00/2.07 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( tau @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ Name23 @ Z2 )
% 4.00/2.07 => ( ( fresh_name_name @ Name23 @ Name12 )
% 4.00/2.07 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi4 ) ) ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Name12: name,Name23: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi4 ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 4.00/2.07 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 4.00/2.07 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 4.00/2.07 => ( ! [Name3: name,Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ Name3 @ Z2 )
% 4.00/2.07 => ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( res @ Name3 @ Pi4 ) ) ) )
% 4.00/2.07 => ( ! [Pi4: pi,Z2: pi] :
% 4.00/2.07 ( ! [Za: pi] : ( P @ Za @ Pi4 )
% 4.00/2.07 => ( P @ Z2 @ ( bang @ Pi4 ) ) )
% 4.00/2.07 => ( P @ Z @ Pi3 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_298_pi_Ofresh_I10_J,axiom,
% 4.00/2.07 ! [A: name,X1: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ A @ ( bang @ X1 ) )
% 4.00/2.07 = ( fresh_name_pi @ A @ X1 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_299_pi_Ofresh_I7_J,axiom,
% 4.00/2.07 ! [A: name,X2: pi,X1: pi] :
% 4.00/2.07 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 4.00/2.07 = ( ( fresh_name_pi @ A @ X2 )
% 4.00/2.07 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_300_simps_I10_J,axiom,
% 4.00/2.07 ! [P: pi,C: name,D: name] :
% 4.00/2.07 ( ( subs @ ( bang @ P ) @ C @ D )
% 4.00/2.07 = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_301_simps_I7_J,axiom,
% 4.00/2.07 ! [P: pi,Q: pi,C: name,D: name] :
% 4.00/2.07 ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 4.00/2.07 = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_302_pi_Odistinct_I77_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 4.00/2.07 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( bang @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_303_pi_Odistinct_I71_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 4.00/2.07 ( ( mismatch @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( sum @ Pi12 @ Pi22 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_304_pi_Odistinct_I59_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 4.00/2.07 ( ( input @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( bang @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_305_pi_Odistinct_I53_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 4.00/2.07 ( ( input @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( sum @ Pi12 @ Pi22 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_306_pi_Odistinct_I47_J,axiom,
% 4.00/2.07 ! [Pi3: pi,Pi: pi] :
% 4.00/2.07 ( ( tau @ Pi3 )
% 4.00/2.07 != ( bang @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_307_pi_Odistinct_I41_J,axiom,
% 4.00/2.07 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 4.00/2.07 ( ( tau @ Pi3 )
% 4.00/2.07 != ( sum @ Pi12 @ Pi22 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_308_pi_Odistinct_I79_J,axiom,
% 4.00/2.07 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 4.00/2.07 ( ( sum @ Pi1 @ Pi2 )
% 4.00/2.07 != ( par @ Pi12 @ Pi22 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_309_pi_Odistinct_I81_J,axiom,
% 4.00/2.07 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 4.00/2.07 ( ( sum @ Pi1 @ Pi2 )
% 4.00/2.07 != ( res @ Name @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_310_pi_Odistinct_I27_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 4.00/2.07 ( ( output @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( sum @ Pi12 @ Pi22 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_311_pi_Odistinct_I83_J,axiom,
% 4.00/2.07 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 4.00/2.07 ( ( sum @ Pi1 @ Pi2 )
% 4.00/2.07 != ( bang @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_312_pi_Oinject_I6_J,axiom,
% 4.00/2.07 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 4.00/2.07 ( ( ( sum @ X2 @ X1 )
% 4.00/2.07 = ( sum @ Y2 @ Y1 ) )
% 4.00/2.07 = ( ( X2 = Y2 )
% 4.00/2.07 & ( X1 = Y1 ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_313_pi_Oinject_I9_J,axiom,
% 4.00/2.07 ! [X1: pi,Y1: pi] :
% 4.00/2.07 ( ( ( bang @ X1 )
% 4.00/2.07 = ( bang @ Y1 ) )
% 4.00/2.07 = ( X1 = Y1 ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_314_sumCases,axiom,
% 4.00/2.07 ! [P: pi,Q: pi,Rs: late_residual] :
% 4.00/2.07 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 4.00/2.07 => ( ~ ( late_transitions @ P @ Rs )
% 4.00/2.07 => ( late_transitions @ Q @ Rs ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_315_sumCases_H,axiom,
% 4.00/2.07 ! [P: pi,Q: pi,Rs: late_residual] :
% 4.00/2.07 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 4.00/2.07 => ( ~ ( late_transitions @ P @ Rs )
% 4.00/2.07 => ( late_transitions @ Q @ Rs ) ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_316_Sum1,axiom,
% 4.00/2.07 ! [P: pi,Rs: late_residual,Q: pi] :
% 4.00/2.07 ( ( late_transitions @ P @ Rs )
% 4.00/2.07 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_317_Sum2,axiom,
% 4.00/2.07 ! [Q: pi,Rs: late_residual,P: pi] :
% 4.00/2.07 ( ( late_transitions @ Q @ Rs )
% 4.00/2.07 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_318_pi_Odistinct_I33_J,axiom,
% 4.00/2.07 ! [Name1: name,Name22: name,Pi3: pi,Pi: pi] :
% 4.00/2.07 ( ( output @ Name1 @ Name22 @ Pi3 )
% 4.00/2.07 != ( bang @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(fact_319_pi_Odistinct_I89_J,axiom,
% 4.00/2.07 ! [Name2: name,Pi3: pi,Pi: pi] :
% 4.00/2.07 ( ( res @ Name2 @ Pi3 )
% 4.00/2.07 != ( bang @ Pi ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(help_If_3_1_If_001t__Agent__Oname_T,axiom,
% 4.00/2.07 ! [P: $o] :
% 4.00/2.07 ( ( P = $true )
% 4.00/2.07 | ( P = $false ) ) ).
% 4.00/2.07
% 4.00/2.07 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 4.00/2.07 ! [X: name,Y: name] :
% 4.00/2.07 ( ( if_name @ $false @ X @ Y )
% 4.00/2.07 = Y ) ).
% 4.00/2.07
% 4.00/2.07 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 4.00/2.07 ! [X: name,Y: name] :
% 4.00/2.07 ( ( if_name @ $true @ X @ Y )
% 4.00/2.07 = X ) ).
% 4.00/2.07
% 4.00/2.07 thf(conj_0,conjecture,
% 4.00/2.07 ? [P6: pi] :
% 4.00/2.07 ( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ P6 ) )
% 4.00/2.07 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ y @ ( par @ p2 @ ( subs @ ( par @ q2 @ r ) @ x @ y ) ) ) ) @ rel ) ) ).
% 4.00/2.07 ------------------------
% 4.08/2.13 % (8820)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8720 for (2999ds/183Mi)
% 4.08/2.13 % (8821)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_8720 for (2999ds/4Mi)
% 4.08/2.13 % (8822)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_8720 for (2999ds/27Mi)
% 4.08/2.13 % (8826)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8720 for (2999ds/18Mi)
% 4.08/2.13 % (8824)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_8720 for (2999ds/2Mi)
% 4.08/2.13 % (8825)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_8720 for (2999ds/275Mi)
% 4.08/2.13 % (8823)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8720 for (2999ds/2Mi)
% 4.08/2.13 % (8823)Instruction limit reached!
% 4.08/2.13 % (8823)------------------------------
% 4.08/2.13 % (8823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.13 % (8823)Termination reason: Unknown
% 4.08/2.13 % (8823)Termination phase: shuffling
% 4.08/2.13 % (8824)Instruction limit reached!
% 4.08/2.13 % (8824)------------------------------
% 4.08/2.13 % (8824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.13 % (8824)Termination reason: Unknown
% 4.08/2.13 % (8824)Termination phase: shuffling
% 4.08/2.13
% 4.08/2.13 % (8824)Memory used [KB]: 1535
% 4.08/2.13 % (8824)Time elapsed: 0.004 s
% 4.08/2.13 % (8824)Instructions burned: 2 (million)
% 4.08/2.13 % (8824)------------------------------
% 4.08/2.13 % (8824)------------------------------
% 4.08/2.13
% 4.08/2.13 % (8823)Memory used [KB]: 1535
% 4.08/2.13 % (8823)Time elapsed: 0.004 s
% 4.08/2.13 % (8823)Instructions burned: 2 (million)
% 4.08/2.13 % (8823)------------------------------
% 4.08/2.13 % (8823)------------------------------
% 4.08/2.13 % (8821)Instruction limit reached!
% 4.08/2.13 % (8821)------------------------------
% 4.08/2.13 % (8821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.13 % (8821)Termination reason: Unknown
% 4.08/2.13 % (8821)Termination phase: shuffling
% 4.08/2.13
% 4.08/2.13 % (8821)Memory used [KB]: 1535
% 4.08/2.13 % (8821)Time elapsed: 0.004 s
% 4.08/2.13 % (8821)Instructions burned: 4 (million)
% 4.08/2.13 % (8821)------------------------------
% 4.08/2.13 % (8821)------------------------------
% 4.08/2.14 % (8826)Instruction limit reached!
% 4.08/2.14 % (8826)------------------------------
% 4.08/2.14 % (8826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.14 % (8826)Termination reason: Unknown
% 4.08/2.14 % (8826)Termination phase: shuffling
% 4.08/2.14
% 4.08/2.14 % (8826)Memory used [KB]: 1791
% 4.08/2.14 % (8826)Time elapsed: 0.012 s
% 4.08/2.14 % (8826)Instructions burned: 18 (million)
% 4.08/2.14 % (8826)------------------------------
% 4.08/2.14 % (8826)------------------------------
% 4.08/2.14 % (8822)Instruction limit reached!
% 4.08/2.14 % (8822)------------------------------
% 4.08/2.14 % (8822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.14 % (8822)Termination reason: Unknown
% 4.08/2.14 % (8822)Termination phase: shuffling
% 4.08/2.14
% 4.08/2.14 % (8822)Memory used [KB]: 2046
% 4.08/2.14 % (8822)Time elapsed: 0.017 s
% 4.08/2.14 % (8822)Instructions burned: 28 (million)
% 4.08/2.14 % (8822)------------------------------
% 4.08/2.14 % (8822)------------------------------
% 4.08/2.15 % (8829)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_8720 for (2999ds/15Mi)
% 4.08/2.15 % (8827)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8720 for (2999ds/3Mi)
% 4.08/2.15 % (8828)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_8720 for (2999ds/37Mi)
% 4.08/2.15 % (8827)Instruction limit reached!
% 4.08/2.15 % (8827)------------------------------
% 4.08/2.15 % (8827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.15 % (8827)Termination reason: Unknown
% 4.08/2.15 % (8827)Termination phase: shuffling
% 4.08/2.15
% 4.08/2.15 % (8827)Memory used [KB]: 1535
% 4.08/2.15 % (8827)Time elapsed: 0.004 s
% 4.08/2.15 % (8827)Instructions burned: 3 (million)
% 4.08/2.15 % (8827)------------------------------
% 4.08/2.15 % (8827)------------------------------
% 4.08/2.16 % (8829)Instruction limit reached!
% 4.08/2.16 % (8829)------------------------------
% 4.08/2.16 % (8829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.16 % (8830)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_8720 for (2999ds/3Mi)
% 4.08/2.16 % (8829)Termination reason: Unknown
% 4.08/2.16 % (8829)Termination phase: shuffling
% 4.08/2.16
% 4.08/2.16 % (8829)Memory used [KB]: 1791
% 4.08/2.16 % (8829)Time elapsed: 0.011 s
% 4.08/2.16 % (8829)Instructions burned: 15 (million)
% 4.08/2.16 % (8829)------------------------------
% 4.08/2.16 % (8829)------------------------------
% 4.08/2.16 % (8830)Instruction limit reached!
% 4.08/2.16 % (8830)------------------------------
% 4.08/2.16 % (8830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.16 % (8830)Termination reason: Unknown
% 4.08/2.16 % (8830)Termination phase: shuffling
% 4.08/2.16
% 4.08/2.16 % (8830)Memory used [KB]: 1535
% 4.08/2.16 % (8830)Time elapsed: 0.004 s
% 4.08/2.16 % (8830)Instructions burned: 3 (million)
% 4.08/2.16 % (8830)------------------------------
% 4.08/2.16 % (8830)------------------------------
% 4.08/2.16 % (8831)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_8720 for (2999ds/1041Mi)
% 4.08/2.17 % (8828)Instruction limit reached!
% 4.08/2.17 % (8828)------------------------------
% 4.08/2.17 % (8828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.17 % (8828)Termination reason: Unknown
% 4.08/2.17 % (8828)Termination phase: shuffling
% 4.08/2.17
% 4.08/2.17 % (8828)Memory used [KB]: 2302
% 4.08/2.17 % (8828)Time elapsed: 0.021 s
% 4.08/2.17 % (8828)Instructions burned: 37 (million)
% 4.08/2.17 % (8828)------------------------------
% 4.08/2.17 % (8828)------------------------------
% 4.08/2.17 % (8832)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8720 for (2999ds/7Mi)
% 4.08/2.18 % (8832)Instruction limit reached!
% 4.08/2.18 % (8832)------------------------------
% 4.08/2.18 % (8832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.18 % (8832)Termination reason: Unknown
% 4.08/2.18 % (8832)Termination phase: shuffling
% 4.08/2.18
% 4.08/2.18 % (8832)Memory used [KB]: 1663
% 4.08/2.18 % (8832)Time elapsed: 0.006 s
% 4.08/2.18 % (8832)Instructions burned: 8 (million)
% 4.08/2.18 % (8832)------------------------------
% 4.08/2.18 % (8832)------------------------------
% 4.08/2.18 % (8834)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_8720 for (2999ds/3Mi)
% 4.08/2.18 % (8833)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8720 for (2999ds/16Mi)
% 4.08/2.18 % (8834)Instruction limit reached!
% 4.08/2.18 % (8834)------------------------------
% 4.08/2.18 % (8834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.18 % (8834)Termination reason: Unknown
% 4.08/2.18 % (8834)Termination phase: shuffling
% 4.08/2.18
% 4.08/2.18 % (8834)Memory used [KB]: 1535
% 4.08/2.18 % (8834)Time elapsed: 0.004 s
% 4.08/2.18 % (8834)Instructions burned: 4 (million)
% 4.08/2.18 % (8834)------------------------------
% 4.08/2.18 % (8834)------------------------------
% 4.08/2.18 % (8825)First to succeed.
% 4.08/2.19 % (8833)Instruction limit reached!
% 4.08/2.19 % (8833)------------------------------
% 4.08/2.19 % (8833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.19 % (8833)Termination reason: Unknown
% 4.08/2.19 % (8833)Termination phase: shuffling
% 4.08/2.19
% 4.08/2.19 % (8833)Memory used [KB]: 1791
% 4.08/2.19 % (8833)Time elapsed: 0.011 s
% 4.08/2.19 % (8833)Instructions burned: 16 (million)
% 4.08/2.19 % (8833)------------------------------
% 4.08/2.19 % (8833)------------------------------
% 4.08/2.19 % (8825)Refutation found. Thanks to Tanya!
% 4.08/2.19 % SZS status Theorem for DTF2THF_8720
% 4.08/2.19 % SZS output start Proof for DTF2THF_8720
% 4.08/2.19 thf(type_def_5, type, pi: $tType).
% 4.08/2.19 thf(type_def_7, type, name: $tType).
% 4.08/2.19 thf(type_def_8, type, late_freeRes: $tType).
% 4.08/2.19 thf(type_def_9, type, late_subject: $tType).
% 4.08/2.19 thf(type_def_10, type, late_residual: $tType).
% 4.08/2.19 thf(type_def_11, type, noption_name: $tType).
% 4.08/2.19 thf(type_def_12, type, noption_pi: $tType).
% 4.08/2.19 thf(type_def_13, type, noption_Late_freeRes: $tType).
% 4.08/2.19 thf(type_def_14, type, noption_Late_subject: $tType).
% 4.08/2.19 thf(type_def_15, type, produc1462499409ion_pi: $tType).
% 4.08/2.19 thf(type_def_16, type, produc405342261i_name: $tType).
% 4.08/2.19 thf(type_def_17, type, produc629157763_pi_pi: $tType).
% 4.08/2.19 thf(type_def_18, type, produc1834551554reeRes: $tType).
% 4.08/2.19 thf(type_def_19, type, produc691362330ubject: $tType).
% 4.08/2.19 thf(type_def_20, type, produc2008547984reeRes: $tType).
% 4.08/2.19 thf(type_def_21, type, produc865358760ubject: $tType).
% 4.08/2.19 thf(type_def_22, type, product_prod_pi_pi: $tType).
% 4.08/2.19 thf(type_def_23, type, produc2052722628s_name: $tType).
% 4.08/2.19 thf(type_def_24, type, produc992857746Res_pi: $tType).
% 4.08/2.19 thf(type_def_25, type, produc1357834675reeRes: $tType).
% 4.08/2.19 thf(type_def_26, type, produc214645451ubject: $tType).
% 4.08/2.19 thf(type_def_27, type, produc1998742700t_name: $tType).
% 4.08/2.19 thf(type_def_28, type, produc140253050ect_pi: $tType).
% 4.08/2.19 thf(type_def_29, type, produc355105483reeRes: $tType).
% 4.08/2.19 thf(type_def_30, type, produc1359399907ubject: $tType).
% 4.08/2.19 thf(type_def_31, type, set_Pr1834926343_pi_pi: $tType).
% 4.08/2.19 thf(func_def_0, type, produc1462499409ion_pi: $tType).
% 4.08/2.19 thf(func_def_1, type, produc691362330ubject: $tType).
% 4.08/2.19 thf(func_def_2, type, produc1834551554reeRes: $tType).
% 4.08/2.19 thf(func_def_3, type, produc405342261i_name: $tType).
% 4.08/2.19 thf(func_def_4, type, produc629157763_pi_pi: $tType).
% 4.08/2.19 thf(func_def_5, type, produc1359399907ubject: $tType).
% 4.08/2.19 thf(func_def_6, type, produc355105483reeRes: $tType).
% 4.08/2.19 thf(func_def_7, type, produc214645451ubject: $tType).
% 4.08/2.19 thf(func_def_8, type, produc1357834675reeRes: $tType).
% 4.08/2.19 thf(func_def_9, type, produc1998742700t_name: $tType).
% 4.08/2.19 thf(func_def_10, type, produc2052722628s_name: $tType).
% 4.08/2.19 thf(func_def_11, type, produc865358760ubject: $tType).
% 4.08/2.19 thf(func_def_12, type, produc2008547984reeRes: $tType).
% 4.08/2.19 thf(func_def_13, type, produc140253050ect_pi: $tType).
% 4.08/2.19 thf(func_def_14, type, produc992857746Res_pi: $tType).
% 4.08/2.19 thf(func_def_15, type, set_Pr1834926343_pi_pi: $tType).
% 4.08/2.19 thf(func_def_16, type, product_prod_pi_pi: $tType).
% 4.08/2.19 thf(func_def_17, type, noption_Late_subject: $tType).
% 4.08/2.19 thf(func_def_18, type, noption_Late_freeRes: $tType).
% 4.08/2.19 thf(func_def_19, type, noption_name: $tType).
% 4.08/2.19 thf(func_def_20, type, noption_pi: $tType).
% 4.08/2.19 thf(func_def_21, type, late_residual: $tType).
% 4.08/2.19 thf(func_def_22, type, late_subject: $tType).
% 4.08/2.19 thf(func_def_23, type, late_freeRes: $tType).
% 4.08/2.19 thf(func_def_24, type, name: $tType).
% 4.08/2.19 thf(func_def_25, type, pi: $tType).
% 4.08/2.19 thf(func_def_26, type, bang: pi > pi).
% 4.08/2.19 thf(func_def_27, type, input: name > name > pi > pi).
% 4.08/2.19 thf(func_def_28, type, match: name > name > pi > pi).
% 4.08/2.19 thf(func_def_29, type, mismatch: name > name > pi > pi).
% 4.08/2.19 thf(func_def_30, type, output: name > name > pi > pi).
% 4.08/2.19 thf(func_def_31, type, par: pi > pi > pi).
% 4.08/2.19 thf(func_def_32, type, piNil: pi).
% 4.08/2.19 thf(func_def_33, type, res: name > pi > pi).
% 4.08/2.19 thf(func_def_34, type, sum: pi > pi > pi).
% 4.08/2.19 thf(func_def_35, type, tau: pi > pi).
% 4.08/2.19 thf(func_def_36, type, subs: pi > name > name > pi).
% 4.08/2.19 thf(func_def_37, type, subst_name: name > name > name > name).
% 4.08/2.19 thf(func_def_38, type, if_name: $o > name > name > name).
% 4.08/2.19 thf(func_def_39, type, late_OutputR: name > name > late_freeRes).
% 4.08/2.19 thf(func_def_40, type, late_TauR: late_freeRes).
% 4.08/2.19 thf(func_def_41, type, late_BoundR: late_subject > name > pi > late_residual).
% 4.08/2.19 thf(func_def_42, type, late_FreeR: late_freeRes > pi > late_residual).
% 4.08/2.19 thf(func_def_43, type, late_BoundOutputS: name > late_subject).
% 4.08/2.19 thf(func_def_44, type, late_InputS: name > late_subject).
% 4.08/2.19 thf(func_def_45, type, late_transitions: pi > late_residual > $o).
% 4.08/2.19 thf(func_def_46, type, abs_fun_name_name: name > name > name > noption_name).
% 4.08/2.19 thf(func_def_47, type, abs_fun_name_pi: name > pi > name > noption_pi).
% 4.08/2.19 thf(func_def_48, type, abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes).
% 4.08/2.19 thf(func_def_49, type, abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject).
% 4.08/2.19 thf(func_def_50, type, fresh_1093033124n_name: name > (name > noption_name) > $o).
% 4.08/2.19 thf(func_def_51, type, fresh_543891186ion_pi: name > (name > noption_pi) > $o).
% 4.08/2.19 thf(func_def_52, type, fresh_785364841reeRes: name > (name > noption_Late_freeRes) > $o).
% 4.08/2.19 thf(func_def_53, type, fresh_728038529ubject: name > (name > noption_Late_subject) > $o).
% 4.08/2.19 thf(func_def_54, type, fresh_name_name: name > name > $o).
% 4.08/2.19 thf(func_def_55, type, fresh_name_pi: name > pi > $o).
% 4.08/2.19 thf(func_def_56, type, fresh_1641682979reeRes: name > late_freeRes > $o).
% 4.08/2.19 thf(func_def_57, type, fresh_81631222sidual: name > late_residual > $o).
% 4.08/2.19 thf(func_def_58, type, fresh_717452603ubject: name > late_subject > $o).
% 4.08/2.19 thf(func_def_59, type, fresh_225680151ion_pi: name > produc1462499409ion_pi > $o).
% 4.08/2.19 thf(func_def_60, type, fresh_453496559i_name: name > produc405342261i_name > $o).
% 4.08/2.19 thf(func_def_61, type, fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o).
% 4.08/2.19 thf(func_def_62, type, fresh_1711070152reeRes: name > produc1834551554reeRes > $o).
% 4.08/2.19 thf(func_def_63, type, fresh_567880928ubject: name > produc691362330ubject > $o).
% 4.08/2.19 thf(func_def_64, type, fresh_1963366730reeRes: name > produc2008547984reeRes > $o).
% 4.08/2.19 thf(func_def_65, type, fresh_820177506ubject: name > produc865358760ubject > $o).
% 4.08/2.19 thf(func_def_66, type, fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o).
% 4.08/2.19 thf(func_def_67, type, fresh_2007541374s_name: name > produc2052722628s_name > $o).
% 4.08/2.19 thf(func_def_68, type, fresh_1847501388Res_pi: name > produc992857746Res_pi > $o).
% 4.08/2.19 thf(func_def_69, type, fresh_493808761reeRes: name > produc1357834675reeRes > $o).
% 4.08/2.19 thf(func_def_70, type, fresh_1498103185ubject: name > produc214645451ubject > $o).
% 4.08/2.19 thf(func_def_71, type, fresh_1953561446t_name: name > produc1998742700t_name > $o).
% 4.08/2.19 thf(func_def_72, type, fresh_994896692ect_pi: name > produc140253050ect_pi > $o).
% 4.08/2.19 thf(func_def_73, type, fresh_1638563217reeRes: name > produc355105483reeRes > $o).
% 4.08/2.19 thf(func_def_74, type, fresh_495373993ubject: name > produc1359399907ubject > $o).
% 4.08/2.19 thf(func_def_75, type, produc1342893193ion_pi: (name > noption_pi) > (name > noption_pi) > produc1462499409ion_pi).
% 4.08/2.19 thf(func_def_76, type, produc540578151i_name: (name > noption_pi) > name > produc405342261i_name).
% 4.08/2.19 thf(func_def_77, type, produc1820286517_pi_pi: (name > noption_pi) > pi > produc629157763_pi_pi).
% 4.08/2.19 thf(func_def_78, type, produc1505598906reeRes: (name > noption_pi) > late_freeRes > produc1834551554reeRes).
% 4.08/2.19 thf(func_def_79, type, produc581368530ubject: (name > noption_pi) > late_subject > produc691362330ubject).
% 4.08/2.19 thf(func_def_80, type, produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes).
% 4.08/2.19 thf(func_def_81, type, produc607574050ubject: name > late_subject > produc865358760ubject).
% 4.08/2.19 thf(func_def_82, type, product_Pair_pi_pi: pi > pi > product_prod_pi_pi).
% 4.08/2.19 thf(func_def_83, type, produc1701355766s_name: late_freeRes > name > produc2052722628s_name).
% 4.08/2.19 thf(func_def_84, type, produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi).
% 4.08/2.19 thf(func_def_85, type, produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes).
% 4.08/2.19 thf(func_def_86, type, produc320590723ubject: late_freeRes > late_subject > produc214645451ubject).
% 4.08/2.19 thf(func_def_87, type, produc1647375838t_name: late_subject > name > produc1998742700t_name).
% 4.08/2.19 thf(func_def_88, type, produc324947500ect_pi: late_subject > pi > produc140253050ect_pi).
% 4.08/2.19 thf(func_def_89, type, produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes).
% 4.08/2.19 thf(func_def_90, type, produc1465345179ubject: late_subject > late_subject > produc1359399907ubject).
% 4.08/2.19 thf(func_def_91, type, eqvt_pi: set_Pr1834926343_pi_pi > $o).
% 4.08/2.19 thf(func_def_92, type, collec1051790738_pi_pi: (product_prod_pi_pi > $o) > set_Pr1834926343_pi_pi).
% 4.08/2.19 thf(func_def_93, type, strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o).
% 4.08/2.19 thf(func_def_94, type, strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o).
% 4.08/2.19 thf(func_def_95, type, member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o).
% 4.08/2.19 thf(func_def_96, type, p: pi).
% 4.08/2.19 thf(func_def_97, type, pqr: pi).
% 4.08/2.19 thf(func_def_98, type, p2: pi).
% 4.08/2.19 thf(func_def_99, type, q: pi).
% 4.08/2.19 thf(func_def_100, type, qr: pi).
% 4.08/2.19 thf(func_def_101, type, q2: pi).
% 4.08/2.19 thf(func_def_102, type, r: pi).
% 4.08/2.19 thf(func_def_103, type, rel: set_Pr1834926343_pi_pi).
% 4.08/2.19 thf(func_def_104, type, alpha: late_freeRes).
% 4.08/2.19 thf(func_def_105, type, a: name).
% 4.08/2.19 thf(func_def_106, type, x: name).
% 4.08/2.19 thf(func_def_107, type, y: name).
% 4.08/2.19 thf(func_def_125, type, sK0: (late_freeRes > $o) > name).
% 4.08/2.19 thf(func_def_126, type, sK1: (late_freeRes > $o) > name).
% 4.08/2.19 thf(func_def_127, type, sK2: late_residual > pi > pi).
% 4.08/2.19 thf(func_def_128, type, sK3: (late_freeRes > late_residual > $o) > name).
% 4.08/2.19 thf(func_def_129, type, sK4: (late_freeRes > late_residual > $o) > pi).
% 4.08/2.19 thf(func_def_130, type, sK5: (late_freeRes > late_residual > $o) > late_freeRes).
% 4.08/2.19 thf(func_def_131, type, sK6: (late_freeRes > late_residual > $o) > late_subject).
% 4.08/2.19 thf(func_def_132, type, sK7: (late_freeRes > late_residual > $o) > pi).
% 4.08/2.19 thf(func_def_133, type, sK8: (late_freeRes > late_residual > $o) > late_freeRes).
% 4.08/2.19 thf(func_def_134, type, sK9: (late_freeRes > late_residual > $o) > late_freeRes).
% 4.08/2.19 thf(func_def_135, type, sK10: late_freeRes > name).
% 4.08/2.19 thf(func_def_136, type, sK11: (late_freeRes > late_residual > $o) > late_subject).
% 4.08/2.19 thf(func_def_137, type, sK12: (late_freeRes > late_residual > $o) > pi).
% 4.08/2.19 thf(func_def_138, type, sK13: (late_freeRes > late_residual > $o) > name).
% 4.08/2.19 thf(func_def_139, type, sK14: (late_freeRes > late_residual > $o) > late_freeRes).
% 4.08/2.19 thf(func_def_140, type, sK15: (late_freeRes > late_residual > $o) > late_freeRes).
% 4.08/2.19 thf(func_def_141, type, sK16: (late_freeRes > late_residual > $o) > late_freeRes).
% 4.08/2.19 thf(func_def_142, type, sK17: (late_freeRes > late_residual > $o) > pi).
% 4.08/2.19 thf(func_def_143, type, sK18: (product_prod_pi_pi > $o) > pi).
% 4.08/2.19 thf(func_def_144, type, sK19: (product_prod_pi_pi > $o) > pi).
% 4.08/2.19 thf(func_def_145, type, sK20: pi > name).
% 4.08/2.19 thf(func_def_146, type, sK21: product_prod_pi_pi > pi).
% 4.08/2.19 thf(func_def_147, type, sK22: product_prod_pi_pi > pi).
% 4.08/2.19 thf(func_def_148, type, sK23: product_prod_pi_pi > pi).
% 4.08/2.19 thf(func_def_149, type, sK24: product_prod_pi_pi > pi).
% 4.08/2.19 thf(func_def_150, type, sK25: (product_prod_pi_pi > $o) > pi).
% 4.08/2.19 thf(func_def_151, type, sK26: (product_prod_pi_pi > $o) > pi).
% 4.08/2.19 thf(func_def_152, type, sK27: (pi > $o) > pi > pi > name > late_subject > pi).
% 4.08/2.19 thf(func_def_153, type, sK28: (pi > $o) > pi > pi > name > late_subject > pi).
% 4.08/2.19 thf(func_def_154, type, sK29: (late_residual > $o) > late_freeRes).
% 4.08/2.19 thf(func_def_155, type, sK30: (late_residual > $o) > pi).
% 4.08/2.19 thf(func_def_156, type, sK31: (late_residual > $o) > name).
% 4.08/2.19 thf(func_def_157, type, sK32: (late_residual > $o) > pi).
% 4.08/2.19 thf(func_def_158, type, sK33: (late_residual > $o) > late_subject).
% 4.08/2.19 thf(func_def_159, type, sK34: late_freeRes > name).
% 4.08/2.19 thf(func_def_160, type, sK35: late_freeRes > name).
% 4.08/2.19 thf(func_def_161, type, sK36: name > pi > name > late_residual > name).
% 4.08/2.19 thf(func_def_162, type, sK37: name > pi > name > late_residual > name).
% 4.08/2.19 thf(func_def_163, type, sK38: name > pi > name > late_residual > pi).
% 4.08/2.19 thf(func_def_164, type, sK39: pi > pi > name > late_freeRes > late_freeRes).
% 4.08/2.19 thf(func_def_165, type, sK40: pi > pi > name > late_freeRes > pi).
% 4.08/2.19 thf(func_def_166, type, sK41: pi > pi > name > late_freeRes > name).
% 4.08/2.19 thf(func_def_167, type, sK42: pi > pi > name > late_freeRes > pi).
% 4.08/2.19 thf(func_def_168, type, sK43: pi > name > late_freeRes > (pi > $o) > pi).
% 4.08/2.19 thf(func_def_170, type, ph45: !>[X0: $tType]:(X0)).
% 4.08/2.19 thf(f1106,plain,(
% 4.08/2.19 $false),
% 4.08/2.19 inference(subsumption_resolution,[status(thm)],[f1105,f1034])).
% 4.08/2.19 thf(f1034,plain,(
% 4.08/2.19 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r))) = $true)),
% 4.08/2.19 inference(cnf_transformation,[status(thm)],[f638])).
% 4.08/2.19 thf(f638,plain,(
% 4.08/2.19 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r))) = $true)),
% 4.08/2.19 inference(fool_elimination,[status(thm)],[f637])).
% 4.08/2.19 thf(f637,plain,(
% 4.08/2.19 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r)))),
% 4.08/2.19 inference(rectify,[status(thm)],[f8])).
% 4.08/2.19 thf(f8,axiom,(
% 4.08/2.19 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r)))),
% 4.08/2.19 file('/export/starexec/sandbox/tmp/tmp.OawlmjC21l/DTF2THF_8720.p',fact_7__092_060open_062_IP_A_092_060parallel_062_AQ_J_A_092_060parallel_062_AR_A_092_060longmapsto_062_A_092_060tau_062_A_092_060prec_062_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_092_060close_062)).
% 4.08/2.19 thf(f1105,plain,(
% 4.08/2.19 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r))) != $true)),
% 4.08/2.19 inference(trivial_inequality_removal,[status(thm)],[f1102])).
% 4.08/2.19 thf(f1102,plain,(
% 4.08/2.19 ($true != $true) | ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r))) != $true)),
% 4.08/2.19 inference(superposition,[status(thm)],[f973,f981])).
% 4.08/2.19 thf(f981,plain,(
% 4.08/2.19 ((member558706512_pi_pi @ (product_Pair_pi_pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel) = $true)),
% 4.08/2.19 inference(cnf_transformation,[status(thm)],[f418])).
% 4.08/2.19 thf(f418,plain,(
% 4.08/2.19 ((member558706512_pi_pi @ (product_Pair_pi_pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel) = $true)),
% 4.08/2.19 inference(fool_elimination,[status(thm)],[f417])).
% 4.08/2.19 thf(f417,plain,(
% 4.08/2.19 (member558706512_pi_pi @ (product_Pair_pi_pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)),
% 4.08/2.19 inference(rectify,[status(thm)],[f7])).
% 4.08/2.19 thf(f7,axiom,(
% 4.08/2.19 (member558706512_pi_pi @ (product_Pair_pi_pi @ (par @ (res @ y @ (par @ p2 @ (subs @ q2 @ x @ y))) @ r) @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)),
% 4.08/2.19 file('/export/starexec/sandbox/tmp/tmp.OawlmjC21l/DTF2THF_8720.p',fact_6__092_060open_062_I_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_AQ_H_091x_058_058_061y_093_J_A_092_060parallel_062_AR_M_A_060_092_060nu_062y_062_IP_H_A_092_060parallel_062_A_IQ_H_A_092_060parallel_062_AR_J_091x_058_058_061y_093_J_J_A_092_060in_062_ARel_092_060close_062)).
% 4.08/2.19 thf(f973,plain,(
% 4.08/2.19 ( ! [X0 : pi] : (($true != (member558706512_pi_pi @ (product_Pair_pi_pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)) | ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0)) != $true)) )),
% 4.08/2.19 inference(cnf_transformation,[status(thm)],[f836])).
% 4.08/2.19 thf(f836,plain,(
% 4.08/2.19 ! [X0 : pi] : (($true != (member558706512_pi_pi @ (product_Pair_pi_pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)) | ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0)) != $true))),
% 4.08/2.19 inference(ennf_transformation,[status(thm)],[f668])).
% 4.08/2.19 thf(f668,plain,(
% 4.08/2.19 ~? [X0 : pi] : (((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0)) = $true) & ($true = (member558706512_pi_pi @ (product_Pair_pi_pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel)))),
% 4.08/2.19 inference(fool_elimination,[status(thm)],[f667])).
% 4.08/2.19 thf(f667,plain,(
% 4.08/2.19 ~? [X0 : pi] : ((member558706512_pi_pi @ (product_Pair_pi_pi @ X0 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X0)))),
% 4.08/2.19 inference(rectify,[status(thm)],[f325])).
% 4.08/2.19 thf(f325,negated_conjecture,(
% 4.08/2.19 ~? [X80 : pi] : ((member558706512_pi_pi @ (product_Pair_pi_pi @ X80 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X80)))),
% 4.08/2.19 inference(negated_conjecture,[status(cth)],[f324])).
% 4.08/2.19 thf(f324,conjecture,(
% 4.08/2.19 ? [X80 : pi] : ((member558706512_pi_pi @ (product_Pair_pi_pi @ X80 @ (res @ y @ (par @ p2 @ (subs @ (par @ q2 @ r) @ x @ y)))) @ rel) & (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ X80)))),
% 4.08/2.19 file('/export/starexec/sandbox/tmp/tmp.OawlmjC21l/DTF2THF_8720.p',conj_0)).
% 4.08/2.19 % SZS output end Proof for DTF2THF_8720
% 4.08/2.19 % (8825)------------------------------
% 4.08/2.19 % (8825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.08/2.19 % (8825)Termination reason: Refutation
% 4.08/2.19
% 4.08/2.19 % (8825)Memory used [KB]: 7164
% 4.08/2.19 % (8825)Time elapsed: 0.060 s
% 4.08/2.19 % (8825)Instructions burned: 98 (million)
% 4.08/2.19 % (8825)------------------------------
% 4.08/2.19 % (8825)------------------------------
% 4.08/2.19 % (8819)Success in time 0.105 s
%------------------------------------------------------------------------------