%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP188^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:24:41 AM UTC 2026
% Result : Theorem 6.54s 1.39s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 59
% Syntax : Number of formulae : 934 ( 413 unt; 0 typ; 0 def)
% Number of atoms : 6348 (2949 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 7502 (1388 ~;1519 |; 12 &;4526 @)
% ( 0 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 26 ( 25 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 100 ( 97 usr; 13 con; 0-5 aty)
% Number of variables : 2343 ( 4 ^;2333 !; 6 ?;2343 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_late_freeRes,type,
late_freeRes: $tType ).
thf(tp_late_residual,type,
late_residual: $tType ).
thf(tp_late_subject,type,
late_subject: $tType ).
thf(tp_name,type,
name: $tType ).
thf(tp_noptio1575811931_pi_pi,type,
noptio1575811931_pi_pi: $tType ).
thf(tp_noption_Late_freeRes,type,
noption_Late_freeRes: $tType ).
thf(tp_noption_name,type,
noption_name: $tType ).
thf(tp_noption_pi,type,
noption_pi: $tType ).
thf(tp_pi,type,
pi: $tType ).
thf(tp_produc1141751126_pi_pi,type,
produc1141751126_pi_pi: $tType ).
thf(tp_produc1357834675reeRes,type,
produc1357834675reeRes: $tType ).
thf(tp_produc1462499409ion_pi,type,
produc1462499409ion_pi: $tType ).
thf(tp_produc1834551554reeRes,type,
produc1834551554reeRes: $tType ).
thf(tp_produc2008547984reeRes,type,
produc2008547984reeRes: $tType ).
thf(tp_produc2052722628s_name,type,
produc2052722628s_name: $tType ).
thf(tp_produc367475239e_name,type,
produc367475239e_name: $tType ).
thf(tp_produc405342261i_name,type,
produc405342261i_name: $tType ).
thf(tp_produc53907987_pi_pi,type,
produc53907987_pi_pi: $tType ).
thf(tp_produc629157763_pi_pi,type,
produc629157763_pi_pi: $tType ).
thf(tp_produc649380958reeRes,type,
produc649380958reeRes: $tType ).
thf(tp_produc992857746Res_pi,type,
produc992857746Res_pi: $tType ).
thf(tp_product_prod_name_pi,type,
product_prod_name_pi: $tType ).
thf(tp_product_prod_pi_name,type,
product_prod_pi_name: $tType ).
thf(tp_product_prod_pi_pi,type,
product_prod_pi_pi: $tType ).
thf(tp_set_Pr1834926343_pi_pi,type,
set_Pr1834926343_pi_pi: $tType ).
thf(tp_aa,type,
aa: late_subject ).
thf(tp_abs_fu385186459_pi_pi,type,
abs_fu385186459_pi_pi: name > produc1141751126_pi_pi > name > noptio1575811931_pi_pi ).
thf(tp_abs_fu681348580reeRes,type,
abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
thf(tp_abs_fun_name_name,type,
abs_fun_name_name: name > name > name > noption_name ).
thf(tp_abs_fun_name_pi,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(tp_bang,type,
bang: pi > pi ).
thf(tp_collec1051790738_pi_pi,type,
collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
thf(tp_eqvt_pi,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(tp_fresh_1093033124n_name,type,
fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
thf(tp_fresh_1376661020_pi_pi,type,
fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o ).
thf(tp_fresh_1504024600reeRes,type,
fresh_1504024600reeRes: name > produc649380958reeRes > $o ).
thf(tp_fresh_1627595501_pi_pi,type,
fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
thf(tp_fresh_1641682979reeRes,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(tp_fresh_1711070152reeRes,type,
fresh_1711070152reeRes: name > produc1834551554reeRes > $o ).
thf(tp_fresh_1847501388Res_pi,type,
fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
thf(tp_fresh_1963366730reeRes,type,
fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
thf(tp_fresh_2007541374s_name,type,
fresh_2007541374s_name: name > produc2052722628s_name > $o ).
thf(tp_fresh_2065563522_pi_pi,type,
fresh_2065563522_pi_pi: name > ( name > noptio1575811931_pi_pi ) > $o ).
thf(tp_fresh_225680151ion_pi,type,
fresh_225680151ion_pi: name > produc1462499409ion_pi > $o ).
thf(tp_fresh_253309757_pi_pi,type,
fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o ).
thf(tp_fresh_261416607i_name,type,
fresh_261416607i_name: name > product_prod_pi_name > $o ).
thf(tp_fresh_441084397e_name,type,
fresh_441084397e_name: name > produc367475239e_name > $o ).
thf(tp_fresh_453496559i_name,type,
fresh_453496559i_name: name > produc405342261i_name > $o ).
thf(tp_fresh_493808761reeRes,type,
fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
thf(tp_fresh_543891186ion_pi,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
thf(tp_fresh_717452603ubject,type,
fresh_717452603ubject: name > late_subject > $o ).
thf(tp_fresh_785364841reeRes,type,
fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
thf(tp_fresh_81631222sidual,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(tp_fresh_93646139ame_pi,type,
fresh_93646139ame_pi: name > product_prod_name_pi > $o ).
thf(tp_fresh_975559885_pi_pi,type,
fresh_975559885_pi_pi: name > produc53907987_pi_pi > $o ).
thf(tp_fresh_name_name,type,
fresh_name_name: name > name > $o ).
thf(tp_fresh_name_pi,type,
fresh_name_pi: name > pi > $o ).
thf(tp_if_name,type,
if_name: $o > name > name > name ).
thf(tp_input,type,
input: name > name > pi > pi ).
thf(tp_late_BoundOutputS,type,
late_BoundOutputS: name > late_subject ).
thf(tp_late_BoundR,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(tp_late_FreeR,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(tp_late_InputS,type,
late_InputS: name > late_subject ).
thf(tp_late_OutputR,type,
late_OutputR: name > name > late_freeRes ).
thf(tp_late_TauR,type,
late_TauR: late_freeRes ).
thf(tp_late_transitions,type,
late_transitions: pi > late_residual > $o ).
thf(tp_match,type,
match: name > name > pi > pi ).
thf(tp_member558706512_pi_pi,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(tp_mismatch,type,
mismatch: name > name > pi > pi ).
thf(tp_output,type,
output: name > name > pi > pi ).
thf(tp_p,type,
p: pi ).
thf(tp_p2,type,
p2: pi ).
thf(tp_par,type,
par: pi > pi > pi ).
thf(tp_piNil,type,
piNil: pi ).
thf(tp_produc1177552196Res_pi,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(tp_produc1244821099reeRes,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(tp_produc1275980869_pi_pi,type,
produc1275980869_pi_pi: ( name > noption_pi ) > produc1141751126_pi_pi > produc53907987_pi_pi ).
thf(tp_produc1342893193ion_pi,type,
produc1342893193ion_pi: ( name > noption_pi ) > ( name > noption_pi ) > produc1462499409ion_pi ).
thf(tp_produc1505598906reeRes,type,
produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
thf(tp_produc1531804426reeRes,type,
produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
thf(tp_produc1570949143e_name,type,
produc1570949143e_name: name > name > produc367475239e_name ).
thf(tp_produc1638681944reeRes,type,
produc1638681944reeRes: pi > late_freeRes > produc649380958reeRes ).
thf(tp_produc1701355766s_name,type,
produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
thf(tp_produc1820286517_pi_pi,type,
produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).
thf(tp_produc235456326_pi_pi,type,
produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
thf(tp_produc540578151i_name,type,
produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).
thf(tp_product_Pair_name_pi,type,
product_Pair_name_pi: name > pi > product_prod_name_pi ).
thf(tp_product_Pair_pi_name,type,
product_Pair_pi_name: pi > name > product_prod_pi_name ).
thf(tp_product_Pair_pi_pi,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(tp_pxQ,type,
pxQ: pi ).
thf(tp_q,type,
q: pi ).
thf(tp_rel,type,
rel: set_Pr1834926343_pi_pi ).
thf(tp_res,type,
res: name > pi > pi ).
thf(tp_sK10_SY234,type,
sK10_SY234: pi > pi > set_Pr1834926343_pi_pi > pi ).
thf(tp_sK11_SY432,type,
sK11_SY432: product_prod_pi_pi > ( product_prod_pi_pi > $o ) > pi ).
thf(tp_sK12_SY433,type,
sK12_SY433: produc1141751126_pi_pi > ( produc1141751126_pi_pi > $o ) > pi ).
thf(tp_sK13_SY417,type,
sK13_SY417: product_prod_pi_pi > pi ).
thf(tp_sK14_SY435,type,
sK14_SY435: product_prod_pi_pi > ( product_prod_pi_pi > $o ) > pi ).
thf(tp_sK15_SY436,type,
sK15_SY436: set_Pr1834926343_pi_pi > pi > pi > pi ).
thf(tp_sK16_SY437,type,
sK16_SY437: produc1141751126_pi_pi > ( produc1141751126_pi_pi > $o ) > pi ).
thf(tp_sK17_SV159,type,
sK17_SV159: pi > name > pi > name > name ).
thf(tp_sK18_SY236,type,
sK18_SY236: pi > pi > set_Pr1834926343_pi_pi > pi ).
thf(tp_sK19_SY438,type,
sK19_SY438: set_Pr1834926343_pi_pi > pi > pi > pi ).
thf(tp_sK1_SY250,type,
sK1_SY250: produc1141751126_pi_pi > name ).
thf(tp_sK20_SY440,type,
sK20_SY440: set_Pr1834926343_pi_pi > pi > pi > name ).
thf(tp_sK2_SY290,type,
sK2_SY290: product_prod_pi_pi > pi ).
thf(tp_sK3_SY305,type,
sK3_SY305: product_prod_pi_pi > pi ).
thf(tp_sK4_SY406,type,
sK4_SY406: produc1141751126_pi_pi > pi ).
thf(tp_sK5_SY422,type,
sK5_SY422: product_prod_pi_pi > pi ).
thf(tp_sK6_SY427,type,
sK6_SY427: produc1141751126_pi_pi > pi ).
thf(tp_sK7_SY254,type,
sK7_SY254: product_prod_pi_pi > ( product_prod_pi_pi > $o ) > pi ).
thf(tp_sK8_SY257,type,
sK8_SY257: produc1141751126_pi_pi > ( produc1141751126_pi_pi > $o ) > name ).
thf(tp_sK9_SY293,type,
sK9_SY293: product_prod_pi_pi > ( product_prod_pi_pi > $o ) > pi ).
thf(tp_strong2129052853vative,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(tp_strong743114133lation,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(tp_subs,type,
subs: pi > name > name > pi ).
thf(tp_subst_name,type,
subst_name: name > name > name > name ).
thf(tp_sum,type,
sum: pi > pi > pi ).
thf(tp_tau,type,
tau: pi > pi ).
thf(tp_u,type,
u: name ).
thf(tp_x,type,
x: name ).
thf(tp_y,type,
y: name ).
thf(3,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Agent__Oname_T) ).
thf(8,axiom,
! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( par @ Pi12 @ Pi22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_pi_Odistinct_I79_J) ).
thf(9,axiom,
! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_pi_Odistinct_I81_J) ).
thf(17,axiom,
! [Pi1: pi,Pi2: pi,Pi: pi] :
( ( par @ Pi1 @ Pi2 )
!= ( bang @ Pi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_pi_Odistinct_I87_J) ).
thf(18,axiom,
! [Name3: name,Pi3: pi,Pi: pi] :
( ( res @ Name3 @ Pi3 )
!= ( bang @ Pi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_pi_Odistinct_I89_J) ).
thf(25,axiom,
! [P: pi,Q: pi,C: name,D: name] :
( ( subs @ ( sum @ P @ Q ) @ C @ D )
= ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_simps_I7_J) ).
thf(26,axiom,
! [P: pi,C: name,D: name] :
( ( subs @ ( bang @ P ) @ C @ D )
= ( bang @ ( subs @ P @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_simps_I10_J) ).
thf(50,axiom,
! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( mismatch @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_pi_Odistinct_I73_J) ).
thf(51,axiom,
! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( match @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_pi_Odistinct_I65_J) ).
thf(52,axiom,
! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( mismatch @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_pi_Odistinct_I75_J) ).
thf(53,axiom,
! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( match @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_pi_Odistinct_I67_J) ).
thf(83,axiom,
! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( output @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_pi_Odistinct_I29_J) ).
thf(84,axiom,
! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( output @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_pi_Odistinct_I31_J) ).
thf(127,axiom,
! [X1: name,X2: pi,Y1: name,Y2: pi] :
( ( ( res @ X1 @ X2 )
= ( res @ Y1 @ Y2 ) )
= ( ( abs_fun_name_pi @ X1 @ X2 )
= ( abs_fun_name_pi @ Y1 @ Y2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_pi_Oinject_I8_J) ).
thf(172,axiom,
! [Pi12: pi,Pi22: pi] :
( piNil
!= ( par @ Pi12 @ Pi22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_pi_Odistinct_I13_J) ).
thf(173,axiom,
! [Name: name,Pi: pi] :
( piNil
!= ( res @ Name @ Pi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_pi_Odistinct_I15_J) ).
thf(176,axiom,
! [Pi3: pi,Pi12: pi,Pi22: pi] :
( ( tau @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_pi_Odistinct_I43_J) ).
thf(177,axiom,
! [Pi3: pi,Name: name,Pi: pi] :
( ( tau @ Pi3 )
!= ( res @ Name @ Pi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_pi_Odistinct_I45_J) ).
thf(178,axiom,
! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( input @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_pi_Odistinct_I55_J) ).
thf(179,axiom,
! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( input @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_pi_Odistinct_I57_J) ).
thf(192,axiom,
! [P: pi,C: name,D: name] :
( ( subs @ ( tau @ P ) @ C @ D )
= ( tau @ ( subs @ P @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_simps_I2_J) ).
thf(193,axiom,
! [C: name,D: name] :
( ( subs @ piNil @ C @ D )
= piNil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_simps_I1_J) ).
thf(234,axiom,
! [B: name,P: pi,A: name,C: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
= ( subs @ P @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_substTrans) ).
thf(245,axiom,
! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
( ( ( par @ X2 @ X1 )
= ( par @ Y2 @ Y1 ) )
= ( ( X2 = Y2 )
& ( X1 = Y1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_pi_Oinject_I7_J) ).
thf(247,axiom,
! [P2: product_prod_pi_pi] :
? [X3: pi,Y3: pi] :
( P2
= ( product_Pair_pi_pi @ X3 @ Y3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_surj__pair) ).
thf(254,axiom,
! [P: product_prod_pi_pi > $o,P2: product_prod_pi_pi] :
( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
=> ( P @ P2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_prod__cases) ).
thf(261,axiom,
! [A: pi,B: pi,A2: pi,B2: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Pair__inject) ).
thf(267,axiom,
! [Y: produc1141751126_pi_pi] :
~ ! [A3: name,B3: pi,C2: pi] :
( Y
!= ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_prod__cases3) ).
thf(270,axiom,
! [A4: set_Pr1834926343_pi_pi] :
( ( collec1051790738_pi_pi
@ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A4 ) )
= A4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Collect__mem__eq) ).
thf(271,axiom,
! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
= ( P @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mem__Collect__eq) ).
thf(273,axiom,
! [P: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
( ! [A3: name,B3: pi,C2: pi] : ( P @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) )
=> ( P @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_prod__induct3) ).
thf(277,axiom,
! [Y: product_prod_pi_pi] :
~ ! [A3: pi,B3: pi] :
( Y
!= ( product_Pair_pi_pi @ A3 @ B3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_old_Oprod_Oexhaust) ).
thf(284,axiom,
! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
=> ( P @ Prod ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_old_Oprod_Oinducts) ).
thf(291,axiom,
! [A: name,P: pi,B: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( subs @ P @ A @ B )
= P ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_forget) ).
thf(292,axiom,
! [A: name,P: pi,C: name,B: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( A != C )
=> ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_fresh__fact1) ).
thf(293,axiom,
! [A: name,B: name,P: pi] :
( ( A != B )
=> ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_fresh__fact2) ).
thf(294,axiom,
! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_freshRes) ).
thf(299,axiom,
! [A: name,X2: pi,X1: pi] :
( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
= ( ( fresh_name_pi @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_pi_Ofresh_I8_J) ).
thf(302,axiom,
! [B: name,P: pi,A: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( subs @ ( res @ A @ P ) @ A @ B )
= ( res @ B @ ( subs @ P @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Agent_OsubstRes3) ).
thf(303,axiom,
! [B: name,P: pi,A: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( res @ A @ P )
= ( res @ B @ ( subs @ P @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_substRes2) ).
thf(304,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
( ! [R2: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
=> ( ! [R2: pi,S2: pi,X3: name] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ R2 ) @ ( res @ X3 @ S2 ) ) @ Rel ) )
=> ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_parSym) ).
thf(307,axiom,
! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
( ( par @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_pi_Odistinct_I85_J) ).
thf(309,axiom,
! [A: pi,B: pi,A2: pi,B2: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_old_Oprod_Oinject) ).
thf(316,axiom,
! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
( ( ( product_Pair_pi_pi @ X1 @ X2 )
= ( product_Pair_pi_pi @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_prod_Oinject) ).
thf(322,axiom,
! [P: pi,A: name] :
( ( subs @ P @ A @ A )
= P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_subst__identity) ).
thf(323,axiom,
! [X: name,C: name,D: name,P: pi] :
( ( X != C )
=> ( ( X != D )
=> ( ( subs @ ( res @ X @ P ) @ C @ D )
= ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_simps_I9_J) ).
thf(324,axiom,
! [P: pi,Q: pi,C: name,D: name] :
( ( subs @ ( par @ P @ Q ) @ C @ D )
= ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_simps_I8_J) ).
thf(328,axiom,
fresh_name_pi @ y @ ( res @ x @ q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062y_A_092_060sharp_062_A_060_092_060nu_062x_062Q_092_060close_062) ).
thf(329,axiom,
! [Y: name,R: pi,Z: name,S: pi] :
( ( fresh_name_pi @ Y @ R )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) ) @ rel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_ScopeExt) ).
thf(330,axiom,
! [Y: name,R: pi,S: pi] :
( ( fresh_name_pi @ Y @ R )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( par @ R @ S ) ) @ ( par @ R @ ( res @ Y @ S ) ) ) @ rel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Res) ).
thf(331,axiom,
fresh_name_pi @ x @ p2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__092_060open_062x_A_092_060sharp_062_AP_H_092_060close_062) ).
thf(332,axiom,
fresh_name_pi @ y @ q,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062) ).
thf(333,axiom,
( ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u )
= ( res @ x @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ q @ y @ u ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062_060_092_060nu_062x_062_IP_H_A_092_060parallel_062_AQ_J_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062_IP_H_091y_058_058_061u_093_A_092_060parallel_062_AQ_091y_058_058_061u_093_J_092_060close_062) ).
thf(334,axiom,
eqvt_pi @ rel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_EqvtRel) ).
thf(335,axiom,
fresh_name_pi @ x @ ( subs @ p2 @ y @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062x_A_092_060sharp_062_AP_H_091y_058_058_061u_093_092_060close_062) ).
thf(336,axiom,
y != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062) ).
thf(337,axiom,
( ( subs @ ( res @ x @ q ) @ y @ u )
= ( res @ x @ ( subs @ q @ y @ u ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062_060_092_060nu_062x_062Q_091y_058_058_061u_093_A_061_A_060_092_060nu_062x_062Q_091y_058_058_061u_093_092_060close_062) ).
thf(338,axiom,
x != u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_False) ).
thf(339,conjecture,
member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(340,negated_conjecture,
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel )
= $false ),
inference(negate_conjecture,[status(cth)],[339]) ).
thf(341,plain,
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel )
= $false ),
inference(unfold_def,[status(thm)],[340]) ).
thf(342,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(343,plain,
( ( ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(344,plain,
( ( ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(345,plain,
( ( ! [Pi1: pi,Pi2: pi,Pi: pi] :
( ( par @ Pi1 @ Pi2 )
!= ( bang @ Pi ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(346,plain,
( ( ! [Name3: name,Pi3: pi,Pi: pi] :
( ( res @ Name3 @ Pi3 )
!= ( bang @ Pi ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(347,plain,
( ( ! [P: pi,Q: pi,C: name,D: name] :
( ( subs @ ( sum @ P @ Q ) @ C @ D )
= ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(348,plain,
( ( ! [P: pi,C: name,D: name] :
( ( subs @ ( bang @ P ) @ C @ D )
= ( bang @ ( subs @ P @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(349,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( mismatch @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(350,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( match @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(351,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( mismatch @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(352,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( match @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(353,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( output @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(354,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( output @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(355,plain,
( ( ! [X1: name,X2: pi,Y1: name,Y2: pi] :
( ( ( res @ X1 @ X2 )
= ( res @ Y1 @ Y2 ) )
= ( ( abs_fun_name_pi @ X1 @ X2 )
= ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(356,plain,
( ( ! [Pi12: pi,Pi22: pi] :
( piNil
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(357,plain,
( ( ! [Name: name,Pi: pi] :
( piNil
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(358,plain,
( ( ! [Pi3: pi,Pi12: pi,Pi22: pi] :
( ( tau @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(359,plain,
( ( ! [Pi3: pi,Name: name,Pi: pi] :
( ( tau @ Pi3 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(360,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( input @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(361,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( input @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(362,plain,
( ( ! [P: pi,C: name,D: name] :
( ( subs @ ( tau @ P ) @ C @ D )
= ( tau @ ( subs @ P @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(363,plain,
( ( ! [C: name,D: name] :
( ( subs @ piNil @ C @ D )
= piNil ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(364,plain,
( ( ! [B: name,P: pi,A: name,C: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
= ( subs @ P @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(365,plain,
( ( ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
( ( ( par @ X2 @ X1 )
= ( par @ Y2 @ Y1 ) )
= ( ( X2 = Y2 )
& ( X1 = Y1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(366,plain,
( ( ! [P2: product_prod_pi_pi] :
? [X3: pi,Y3: pi] :
( P2
= ( product_Pair_pi_pi @ X3 @ Y3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(367,plain,
( ( ! [P: product_prod_pi_pi > $o,P2: product_prod_pi_pi] :
( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
=> ( P @ P2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(368,plain,
( ( ! [A: pi,B: pi,A2: pi,B2: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(369,plain,
( ( ! [Y: produc1141751126_pi_pi] :
~ ! [A3: name,B3: pi,C2: pi] :
( Y
!= ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(370,plain,
( ( ! [A4: set_Pr1834926343_pi_pi] :
( ( collec1051790738_pi_pi
@ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A4 ) )
= A4 ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(371,plain,
( ( ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
= ( P @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(372,plain,
( ( ! [P: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
( ! [A3: name,B3: pi,C2: pi] : ( P @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) )
=> ( P @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(373,plain,
( ( ! [Y: product_prod_pi_pi] :
~ ! [A3: pi,B3: pi] :
( Y
!= ( product_Pair_pi_pi @ A3 @ B3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(374,plain,
( ( ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
=> ( P @ Prod ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(375,plain,
( ( ! [A: name,P: pi,B: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( subs @ P @ A @ B )
= P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(376,plain,
( ( ! [A: name,P: pi,C: name,B: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( A != C )
=> ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(377,plain,
( ( ! [A: name,B: name,P: pi] :
( ( A != B )
=> ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(378,plain,
( ( ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(379,plain,
( ( ! [A: name,X2: pi,X1: pi] :
( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
= ( ( fresh_name_pi @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(380,plain,
( ( ! [B: name,P: pi,A: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( subs @ ( res @ A @ P ) @ A @ B )
= ( res @ B @ ( subs @ P @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(381,plain,
( ( ! [B: name,P: pi,A: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( res @ A @ P )
= ( res @ B @ ( subs @ P @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(382,plain,
( ( ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
( ! [R2: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
=> ( ! [R2: pi,S2: pi,X3: name] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ R2 ) @ ( res @ X3 @ S2 ) ) @ Rel ) )
=> ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(383,plain,
( ( ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
( ( par @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(384,plain,
( ( ! [A: pi,B: pi,A2: pi,B2: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(385,plain,
( ( ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
( ( ( product_Pair_pi_pi @ X1 @ X2 )
= ( product_Pair_pi_pi @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(386,plain,
( ( ! [P: pi,A: name] :
( ( subs @ P @ A @ A )
= P ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(387,plain,
( ( ! [X: name,C: name,D: name,P: pi] :
( ( X != C )
=> ( ( X != D )
=> ( ( subs @ ( res @ X @ P ) @ C @ D )
= ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(388,plain,
( ( ! [P: pi,Q: pi,C: name,D: name] :
( ( subs @ ( par @ P @ Q ) @ C @ D )
= ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(389,plain,
( ( fresh_name_pi @ y @ ( res @ x @ q ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(390,plain,
( ( ! [Y: name,R: pi,Z: name,S: pi] :
( ( fresh_name_pi @ Y @ R )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) ) @ rel ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(391,plain,
( ( ! [Y: name,R: pi,S: pi] :
( ( fresh_name_pi @ Y @ R )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( par @ R @ S ) ) @ ( par @ R @ ( res @ Y @ S ) ) ) @ rel ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(392,plain,
( ( fresh_name_pi @ x @ p2 )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(393,plain,
( ( fresh_name_pi @ y @ q )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(394,plain,
( ( ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u )
= ( res @ x @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ q @ y @ u ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(395,plain,
( ( eqvt_pi @ rel )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(396,plain,
( ( fresh_name_pi @ x @ ( subs @ p2 @ y @ u ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(397,plain,
( ( y != x )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(398,plain,
( ( ( subs @ ( res @ x @ q ) @ y @ u )
= ( res @ x @ ( subs @ q @ y @ u ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(399,plain,
( ( x != u )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(400,plain,
( ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel ) )
= $true ),
inference(polarity_switch,[status(thm)],[341]) ).
thf(401,plain,
( ( x != u )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(402,plain,
( ( ( subs @ ( res @ x @ q ) @ y @ u )
= ( res @ x @ ( subs @ q @ y @ u ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(403,plain,
( ( y != x )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(404,plain,
( ( fresh_name_pi @ x @ ( subs @ p2 @ y @ u ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(405,plain,
( ( eqvt_pi @ rel )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(406,plain,
( ( ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u )
= ( res @ x @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ q @ y @ u ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(407,plain,
( ( fresh_name_pi @ y @ q )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(408,plain,
( ( fresh_name_pi @ x @ p2 )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(409,plain,
( ( ! [Y: name,R: pi,S: pi] :
( ( fresh_name_pi @ Y @ R )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( par @ R @ S ) ) @ ( par @ R @ ( res @ Y @ S ) ) ) @ rel ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(410,plain,
( ( ! [Y: name,R: pi,Z: name,S: pi] :
( ( fresh_name_pi @ Y @ R )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) ) @ rel ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(411,plain,
( ( fresh_name_pi @ y @ ( res @ x @ q ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(412,plain,
( ( ! [P: pi,Q: pi,C: name,D: name] :
( ( subs @ ( par @ P @ Q ) @ C @ D )
= ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(413,plain,
( ( ! [X: name,C: name,D: name,P: pi] :
( ( X != C )
=> ( ( X != D )
=> ( ( subs @ ( res @ X @ P ) @ C @ D )
= ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(414,plain,
( ( ! [P: pi,A: name] :
( ( subs @ P @ A @ A )
= P ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(415,plain,
( ( ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
( ( ( product_Pair_pi_pi @ X1 @ X2 )
= ( product_Pair_pi_pi @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(416,plain,
( ( ! [A: pi,B: pi,A2: pi,B2: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(417,plain,
( ( ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
( ( par @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(418,plain,
( ( ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
( ! [R2: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
=> ( ! [R2: pi,S2: pi,X3: name] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X3 @ R2 ) @ ( res @ X3 @ S2 ) ) @ Rel ) )
=> ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(419,plain,
( ( ! [B: name,P: pi,A: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( res @ A @ P )
= ( res @ B @ ( subs @ P @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(420,plain,
( ( ! [B: name,P: pi,A: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( subs @ ( res @ A @ P ) @ A @ B )
= ( res @ B @ ( subs @ P @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(421,plain,
( ( ! [A: name,X2: pi,X1: pi] :
( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
= ( ( fresh_name_pi @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(422,plain,
( ( ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(423,plain,
( ( ! [A: name,B: name,P: pi] :
( ( A != B )
=> ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(424,plain,
( ( ! [A: name,P: pi,C: name,B: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( A != C )
=> ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(425,plain,
( ( ! [A: name,P: pi,B: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( subs @ P @ A @ B )
= P ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(426,plain,
( ( ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
=> ( P @ Prod ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(427,plain,
( ( ! [Y: product_prod_pi_pi] :
~ ! [A3: pi,B3: pi] :
( Y
!= ( product_Pair_pi_pi @ A3 @ B3 ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(428,plain,
( ( ! [P: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
( ! [A3: name,B3: pi,C2: pi] : ( P @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) )
=> ( P @ X ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(429,plain,
( ( ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
= ( P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(430,plain,
( ( ! [A4: set_Pr1834926343_pi_pi] :
( ( collec1051790738_pi_pi
@ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A4 ) )
= A4 ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(431,plain,
( ( ! [Y: produc1141751126_pi_pi] :
~ ! [A3: name,B3: pi,C2: pi] :
( Y
!= ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(432,plain,
( ( ! [A: pi,B: pi,A2: pi,B2: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(433,plain,
( ( ! [P: product_prod_pi_pi > $o,P2: product_prod_pi_pi] :
( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
=> ( P @ P2 ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(434,plain,
( ( ! [P2: product_prod_pi_pi] :
? [X3: pi,Y3: pi] :
( P2
= ( product_Pair_pi_pi @ X3 @ Y3 ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(435,plain,
( ( ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
( ( ( par @ X2 @ X1 )
= ( par @ Y2 @ Y1 ) )
= ( ( X2 = Y2 )
& ( X1 = Y1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(436,plain,
( ( ! [B: name,P: pi,A: name,C: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
= ( subs @ P @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(437,plain,
( ( ! [C: name,D: name] :
( ( subs @ piNil @ C @ D )
= piNil ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(438,plain,
( ( ! [P: pi,C: name,D: name] :
( ( subs @ ( tau @ P ) @ C @ D )
= ( tau @ ( subs @ P @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(439,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( input @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(440,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( input @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(441,plain,
( ( ! [Pi3: pi,Name: name,Pi: pi] :
( ( tau @ Pi3 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(442,plain,
( ( ! [Pi3: pi,Pi12: pi,Pi22: pi] :
( ( tau @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(443,plain,
( ( ! [Name: name,Pi: pi] :
( piNil
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(444,plain,
( ( ! [Pi12: pi,Pi22: pi] :
( piNil
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(445,plain,
( ( ! [X1: name,X2: pi,Y1: name,Y2: pi] :
( ( ( res @ X1 @ X2 )
= ( res @ Y1 @ Y2 ) )
= ( ( abs_fun_name_pi @ X1 @ X2 )
= ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(446,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( output @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(447,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( output @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(448,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( match @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(449,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
( ( mismatch @ Name12 @ Name22 @ Pi3 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(450,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( match @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(451,plain,
( ( ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
( ( mismatch @ Name12 @ Name22 @ Pi3 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(452,plain,
( ( ! [P: pi,C: name,D: name] :
( ( subs @ ( bang @ P ) @ C @ D )
= ( bang @ ( subs @ P @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(453,plain,
( ( ! [P: pi,Q: pi,C: name,D: name] :
( ( subs @ ( sum @ P @ Q ) @ C @ D )
= ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(454,plain,
( ( ! [Name3: name,Pi3: pi,Pi: pi] :
( ( res @ Name3 @ Pi3 )
!= ( bang @ Pi ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(455,plain,
( ( ! [Pi1: pi,Pi2: pi,Pi: pi] :
( ( par @ Pi1 @ Pi2 )
!= ( bang @ Pi ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(456,plain,
( ( ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(457,plain,
( ( ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( par @ Pi12 @ Pi22 ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(458,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(459,plain,
( ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(460,plain,
( ( ! [SX0: name,SX1: name,SX2: pi,SX3: pi,SX4: pi] :
( ( mismatch @ SX0 @ SX1 @ SX2 )
!= ( par @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(461,plain,
( ( ! [SX0: pi,SX1: pi,SX2: pi] :
( ( par @ SX0 @ SX1 )
!= ( bang @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(462,plain,
( ( ! [SX0: pi,SX1: pi,SX2: pi] :
( ( tau @ SX0 )
!= ( par @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(463,plain,
( ( ! [SX0: name,SX1: pi,SX2: name,SX3: pi] :
( ~ ( fresh_name_pi @ SX0 @ SX1 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SX0 @ ( res @ SX2 @ ( par @ SX1 @ SX3 ) ) ) @ ( res @ SX2 @ ( par @ SX1 @ ( res @ SX0 @ SX3 ) ) ) ) @ rel ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(464,plain,
( ( x != u )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(465,plain,
( ( ! [SX0: name,SX1: name,SX2: pi,SX3: pi,SX4: pi] :
( ( match @ SX0 @ SX1 @ SX2 )
!= ( par @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(466,plain,
( ( ! [SX0: name,SX1: pi] :
( piNil
!= ( res @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(467,plain,
( ( ! [SX0: name,SX1: pi,SX2: name,SX3: name] :
( ~ ( fresh_name_pi @ SX0 @ SX1 )
| ( ( subs @ ( subs @ SX1 @ SX2 @ SX0 ) @ SX0 @ SX3 )
= ( subs @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(468,plain,
( ( ! [SX0: name,SX1: pi,SX2: pi] :
( ~ ( fresh_name_pi @ SX0 @ SX1 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SX0 @ ( par @ SX1 @ SX2 ) ) @ ( par @ SX1 @ ( res @ SX0 @ SX2 ) ) ) @ rel ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(469,plain,
( ( ! [SX0: pi,SX1: pi,SX2: name,SX3: pi] :
( ( sum @ SX0 @ SX1 )
!= ( res @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(470,plain,
( ( ! [SX0: name,SX1: pi,SX2: name,SX3: name] :
( ~ ( fresh_name_pi @ SX0 @ SX1 )
| ~ ( ( SX0 != SX2 ) )
| ( fresh_name_pi @ SX0 @ ( subs @ SX1 @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(471,plain,
( ( ! [SX0: name,SX1: name,SX2: pi] :
( ~ ( ( SX0 != SX1 ) )
| ( fresh_name_pi @ SX0 @ ( subs @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(472,plain,
( ( ! [SX0: name,SX1: name,SX2: pi,SX3: pi,SX4: pi] :
( ( input @ SX0 @ SX1 @ SX2 )
!= ( par @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(473,plain,
( ( ! [SX0: name,SX1: name,SX2: name,SX3: pi] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( ( SX0 != SX2 ) )
| ( ( subs @ ( res @ SX0 @ SX3 ) @ SX1 @ SX2 )
= ( res @ SX0 @ ( subs @ SX3 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(474,plain,
( ( ! [SX0: set_Pr1834926343_pi_pi,SX1: pi,SX2: pi] :
( ~ ! [SX3: pi,SX4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ SX3 @ SX4 ) @ ( par @ SX4 @ SX3 ) ) @ SX0 )
| ~ ! [SX3: pi,SX4: pi,SX5: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ SX3 @ SX4 ) @ SX0 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SX5 @ SX3 ) @ ( res @ SX5 @ SX4 ) ) @ SX0 ) )
| ( strong743114133lation @ ( par @ SX1 @ SX2 ) @ SX0 @ ( par @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(475,plain,
( ( ! [SX0: name,SX1: pi,SX2: pi] :
( ( res @ SX0 @ SX1 )
!= ( bang @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(476,plain,
( ( ! [SX0: pi,SX1: pi,SX2: pi,SX3: pi] :
( ( ( par @ SX0 @ SX1 )
= ( par @ SX2 @ SX3 ) )
= ( ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(477,plain,
( ( ! [SX0: name,SX1: pi,SX2: name] :
( ~ ( fresh_name_pi @ SX0 @ SX1 )
| ( ( res @ SX2 @ SX1 )
= ( res @ SX0 @ ( subs @ SX1 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(478,plain,
( ( ! [SX0: name,SX1: name,SX2: pi,SX3: name,SX4: pi] :
( ( match @ SX0 @ SX1 @ SX2 )
!= ( res @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(479,plain,
( ( ! [SX0: produc1141751126_pi_pi] :
~ ! [SX1: name,SX2: pi,SX3: pi] :
( SX0
!= ( produc235456326_pi_pi @ SX1 @ ( product_Pair_pi_pi @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(480,plain,
( ( ! [SX0: product_prod_pi_pi > $o,SX1: product_prod_pi_pi] :
( ~ ! [SX2: pi,SX3: pi] : ( SX0 @ ( product_Pair_pi_pi @ SX2 @ SX3 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(481,plain,
( ( ! [SX0: produc1141751126_pi_pi > $o,SX1: produc1141751126_pi_pi] :
( ~ ! [SX2: name,SX3: pi,SX4: pi] : ( SX0 @ ( produc235456326_pi_pi @ SX2 @ ( product_Pair_pi_pi @ SX3 @ SX4 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(482,plain,
( ( ! [SX0: pi,SX1: pi] :
( piNil
!= ( par @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(483,plain,
( ( ! [SX0: name,SX1: name,SX2: pi,SX3: pi,SX4: pi] :
( ( output @ SX0 @ SX1 @ SX2 )
!= ( par @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(484,plain,
( ( ! [SX0: pi,SX1: pi,SX2: pi,SX3: pi] :
( ( sum @ SX0 @ SX1 )
!= ( par @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(485,plain,
( ( ! [SX0: name,SX1: pi,SX2: name] :
( ~ ( fresh_name_pi @ SX0 @ SX1 )
| ( ( subs @ ( res @ SX2 @ SX1 ) @ SX2 @ SX0 )
= ( res @ SX0 @ ( subs @ SX1 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(486,plain,
( ( ! [SX0: name,SX1: pi,SX2: pi] :
( ( fresh_name_pi @ SX0 @ ( par @ SX1 @ SX2 ) )
= ( ~ ( ~ ( fresh_name_pi @ SX0 @ SX1 )
| ~ ( fresh_name_pi @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(487,plain,
( ( ! [SX0: pi,SX1: pi,SX2: pi,SX3: pi] :
( ( ( product_Pair_pi_pi @ SX0 @ SX1 )
= ( product_Pair_pi_pi @ SX2 @ SX3 ) )
= ( ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(488,plain,
( ( ! [SX0: name,SX1: name,SX2: pi,SX3: name,SX4: pi] :
( ( output @ SX0 @ SX1 @ SX2 )
!= ( res @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(489,plain,
( ( ! [SX0: pi,SX1: pi,SX2: name,SX3: pi] :
( ( par @ SX0 @ SX1 )
!= ( res @ SX2 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(490,plain,
( ( ! [SX0: pi,SX1: name,SX2: pi] :
( ( tau @ SX0 )
!= ( res @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(491,plain,
( ( ! [SX0: pi,SX1: pi,SX2: pi,SX3: pi] :
( ( ( product_Pair_pi_pi @ SX0 @ SX1 )
!= ( product_Pair_pi_pi @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(492,plain,
( ( ! [SX0: pi,SX1: pi,SX2: pi,SX3: pi] :
( ( ( product_Pair_pi_pi @ SX0 @ SX1 )
= ( product_Pair_pi_pi @ SX2 @ SX3 ) )
= ( ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(493,plain,
( ( ! [SX0: product_prod_pi_pi] :
~ ! [SX1: pi] :
~ ~ ! [SX2: pi] :
( SX0
!= ( product_Pair_pi_pi @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(494,plain,
( ( ! [SX0: product_prod_pi_pi > $o,SX1: product_prod_pi_pi] :
( ~ ! [SX2: pi,SX3: pi] : ( SX0 @ ( product_Pair_pi_pi @ SX2 @ SX3 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(495,plain,
( ( ! [SX0: name,SX1: name,SX2: pi,SX3: name,SX4: pi] :
( ( mismatch @ SX0 @ SX1 @ SX2 )
!= ( res @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(496,plain,
( ( y != x )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(497,plain,
( ( ! [SX0: name,SX1: pi,SX2: name] :
( ~ ( fresh_name_pi @ SX0 @ SX1 )
| ( ( subs @ SX1 @ SX0 @ SX2 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(498,plain,
( ( ! [SX0: name,SX1: name,SX2: pi,SX3: name,SX4: pi] :
( ( input @ SX0 @ SX1 @ SX2 )
!= ( res @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(499,plain,
( ( ! [SX0: product_prod_pi_pi] :
~ ! [SX1: pi,SX2: pi] :
( SX0
!= ( product_Pair_pi_pi @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(500,plain,
! [SV1: pi] :
( ( ! [SY178: pi,SY179: name,SY180: name] :
( ( subs @ ( par @ SV1 @ SY178 ) @ SY179 @ SY180 )
= ( par @ ( subs @ SV1 @ SY179 @ SY180 ) @ ( subs @ SY178 @ SY179 @ SY180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(501,plain,
! [SV2: pi] :
( ( ! [SY181: name] :
( ( subs @ SV2 @ SY181 @ SY181 )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(502,plain,
! [SV3: name] :
( ( ! [SY182: pi] : ( fresh_name_pi @ SV3 @ ( res @ SV3 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(503,plain,
! [SV4: product_prod_pi_pi] :
( ( ! [SY183: product_prod_pi_pi > $o] :
( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SY183 ) )
= ( SY183 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(504,plain,
! [SV5: set_Pr1834926343_pi_pi] :
( ( ( collec1051790738_pi_pi
@ ^ [SY184: product_prod_pi_pi] : ( member558706512_pi_pi @ SY184 @ SV5 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(505,plain,
! [SV6: name] :
( ( ! [SY185: name] :
( ( subs @ piNil @ SV6 @ SY185 )
= piNil ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(506,plain,
! [SV7: pi] :
( ( ! [SY186: name,SY187: name] :
( ( subs @ ( tau @ SV7 ) @ SY186 @ SY187 )
= ( tau @ ( subs @ SV7 @ SY186 @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(507,plain,
! [SV8: name] :
( ( ! [SY188: pi,SY189: name,SY190: pi] :
( ( ( res @ SV8 @ SY188 )
= ( res @ SY189 @ SY190 ) )
= ( ( abs_fun_name_pi @ SV8 @ SY188 )
= ( abs_fun_name_pi @ SY189 @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(508,plain,
! [SV9: pi] :
( ( ! [SY191: name,SY192: name] :
( ( subs @ ( bang @ SV9 ) @ SY191 @ SY192 )
= ( bang @ ( subs @ SV9 @ SY191 @ SY192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(509,plain,
! [SV10: pi] :
( ( ! [SY193: pi,SY194: name,SY195: name] :
( ( subs @ ( sum @ SV10 @ SY193 ) @ SY194 @ SY195 )
= ( sum @ ( subs @ SV10 @ SY194 @ SY195 ) @ ( subs @ SY193 @ SY194 @ SY195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(510,plain,
! [SV11: $o] :
( ( ( SV11 = $true )
| ( SV11 = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[458]) ).
thf(511,plain,
( ( ( $true = $true )
| ( $true = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[458]) ).
thf(512,plain,
( ( ( $false = $true )
| ( $false = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[458]) ).
thf(513,plain,
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( subs @ ( res @ x @ ( par @ p2 @ q ) ) @ y @ u ) @ ( par @ ( subs @ p2 @ y @ u ) @ ( subs @ ( res @ x @ q ) @ y @ u ) ) ) @ rel )
= $false ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(514,plain,
! [SV12: name] :
( ( ! [SY196: name,SY197: pi,SY198: pi,SY199: pi] :
( ( mismatch @ SV12 @ SY196 @ SY197 )
!= ( par @ SY198 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(515,plain,
! [SV13: pi] :
( ( ! [SY200: pi,SY201: pi] :
( ( par @ SV13 @ SY200 )
!= ( bang @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(516,plain,
! [SV14: pi] :
( ( ! [SY202: pi,SY203: pi] :
( ( tau @ SV14 )
!= ( par @ SY202 @ SY203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(517,plain,
! [SV15: name] :
( ( ! [SY204: pi,SY205: name,SY206: pi] :
( ~ ( fresh_name_pi @ SV15 @ SY204 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SV15 @ ( res @ SY205 @ ( par @ SY204 @ SY206 ) ) ) @ ( res @ SY205 @ ( par @ SY204 @ ( res @ SV15 @ SY206 ) ) ) ) @ rel ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(518,plain,
( ( x = u )
= $false ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(519,plain,
! [SV16: name] :
( ( ! [SY207: name,SY208: pi,SY209: pi,SY210: pi] :
( ( match @ SV16 @ SY207 @ SY208 )
!= ( par @ SY209 @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(520,plain,
! [SV17: name] :
( ( ! [SY211: pi] :
( piNil
!= ( res @ SV17 @ SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(521,plain,
! [SV18: name] :
( ( ! [SY212: pi,SY213: name,SY214: name] :
( ~ ( fresh_name_pi @ SV18 @ SY212 )
| ( ( subs @ ( subs @ SY212 @ SY213 @ SV18 ) @ SV18 @ SY214 )
= ( subs @ SY212 @ SY213 @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(522,plain,
! [SV19: name] :
( ( ! [SY215: pi,SY216: pi] :
( ~ ( fresh_name_pi @ SV19 @ SY215 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SV19 @ ( par @ SY215 @ SY216 ) ) @ ( par @ SY215 @ ( res @ SV19 @ SY216 ) ) ) @ rel ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(523,plain,
! [SV20: pi] :
( ( ! [SY217: pi,SY218: name,SY219: pi] :
( ( sum @ SV20 @ SY217 )
!= ( res @ SY218 @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(524,plain,
! [SV21: name] :
( ( ! [SY220: pi,SY221: name,SY222: name] :
( ~ ( fresh_name_pi @ SV21 @ SY220 )
| ~ ( ( SV21 != SY221 ) )
| ( fresh_name_pi @ SV21 @ ( subs @ SY220 @ SY222 @ SY221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(525,plain,
! [SV22: name] :
( ( ! [SY223: name,SY224: pi] :
( ~ ( ( SV22 != SY223 ) )
| ( fresh_name_pi @ SV22 @ ( subs @ SY224 @ SV22 @ SY223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(526,plain,
! [SV23: name] :
( ( ! [SY225: name,SY226: pi,SY227: pi,SY228: pi] :
( ( input @ SV23 @ SY225 @ SY226 )
!= ( par @ SY227 @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(527,plain,
! [SV24: name] :
( ( ! [SY229: name,SY230: name,SY231: pi] :
( ~ ( ( SV24 != SY229 ) )
| ~ ( ( SV24 != SY230 ) )
| ( ( subs @ ( res @ SV24 @ SY231 ) @ SY229 @ SY230 )
= ( res @ SV24 @ ( subs @ SY231 @ SY229 @ SY230 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(528,plain,
! [SV25: set_Pr1834926343_pi_pi] :
( ( ! [SY232: pi,SY233: pi] :
( ~ ! [SY234: pi,SY235: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ SY234 @ SY235 ) @ ( par @ SY235 @ SY234 ) ) @ SV25 )
| ~ ! [SY236: pi,SY237: pi,SY238: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ SY236 @ SY237 ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SY238 @ SY236 ) @ ( res @ SY238 @ SY237 ) ) @ SV25 ) )
| ( strong743114133lation @ ( par @ SY232 @ SY233 ) @ SV25 @ ( par @ SY233 @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(529,plain,
! [SV26: name] :
( ( ! [SY239: pi,SY240: pi] :
( ( res @ SV26 @ SY239 )
!= ( bang @ SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(530,plain,
! [SV27: pi] :
( ( ! [SY241: pi,SY242: pi,SY243: pi] :
( ( ( par @ SV27 @ SY241 )
= ( par @ SY242 @ SY243 ) )
= ( ~ ( ( SV27 != SY242 )
| ( SY241 != SY243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(531,plain,
! [SV28: name] :
( ( ! [SY244: pi,SY245: name] :
( ~ ( fresh_name_pi @ SV28 @ SY244 )
| ( ( res @ SY245 @ SY244 )
= ( res @ SV28 @ ( subs @ SY244 @ SY245 @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(532,plain,
! [SV29: name] :
( ( ! [SY246: name,SY247: pi,SY248: name,SY249: pi] :
( ( match @ SV29 @ SY246 @ SY247 )
!= ( res @ SY248 @ SY249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(533,plain,
! [SV30: produc1141751126_pi_pi] :
( ( ~ ! [SY250: name,SY251: pi,SY252: pi] :
( SV30
!= ( produc235456326_pi_pi @ SY250 @ ( product_Pair_pi_pi @ SY251 @ SY252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(534,plain,
! [SV31: product_prod_pi_pi > $o] :
( ( ! [SY253: product_prod_pi_pi] :
( ~ ! [SY254: pi,SY255: pi] : ( SV31 @ ( product_Pair_pi_pi @ SY254 @ SY255 ) )
| ( SV31 @ SY253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(535,plain,
! [SV32: produc1141751126_pi_pi > $o] :
( ( ! [SY256: produc1141751126_pi_pi] :
( ~ ! [SY257: name,SY258: pi,SY259: pi] : ( SV32 @ ( produc235456326_pi_pi @ SY257 @ ( product_Pair_pi_pi @ SY258 @ SY259 ) ) )
| ( SV32 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(536,plain,
! [SV33: pi] :
( ( ! [SY260: pi] :
( piNil
!= ( par @ SV33 @ SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(537,plain,
! [SV34: name] :
( ( ! [SY261: name,SY262: pi,SY263: pi,SY264: pi] :
( ( output @ SV34 @ SY261 @ SY262 )
!= ( par @ SY263 @ SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(538,plain,
! [SV35: pi] :
( ( ! [SY265: pi,SY266: pi,SY267: pi] :
( ( sum @ SV35 @ SY265 )
!= ( par @ SY266 @ SY267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(539,plain,
! [SV36: name] :
( ( ! [SY268: pi,SY269: name] :
( ~ ( fresh_name_pi @ SV36 @ SY268 )
| ( ( subs @ ( res @ SY269 @ SY268 ) @ SY269 @ SV36 )
= ( res @ SV36 @ ( subs @ SY268 @ SY269 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(540,plain,
! [SV37: name] :
( ( ! [SY270: pi,SY271: pi] :
( ( fresh_name_pi @ SV37 @ ( par @ SY270 @ SY271 ) )
= ( ~ ( ~ ( fresh_name_pi @ SV37 @ SY270 )
| ~ ( fresh_name_pi @ SV37 @ SY271 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(541,plain,
! [SV38: pi] :
( ( ! [SY272: pi,SY273: pi,SY274: pi] :
( ( ( product_Pair_pi_pi @ SV38 @ SY272 )
= ( product_Pair_pi_pi @ SY273 @ SY274 ) )
= ( ~ ( ( SV38 != SY273 )
| ( SY272 != SY274 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(542,plain,
! [SV39: name] :
( ( ! [SY275: name,SY276: pi,SY277: name,SY278: pi] :
( ( output @ SV39 @ SY275 @ SY276 )
!= ( res @ SY277 @ SY278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(543,plain,
! [SV40: pi] :
( ( ! [SY279: pi,SY280: name,SY281: pi] :
( ( par @ SV40 @ SY279 )
!= ( res @ SY280 @ SY281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(544,plain,
! [SV41: pi] :
( ( ! [SY282: name,SY283: pi] :
( ( tau @ SV41 )
!= ( res @ SY282 @ SY283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(545,plain,
! [SV42: pi] :
( ( ! [SY284: pi,SY285: pi,SY286: pi] :
( ( ( product_Pair_pi_pi @ SV42 @ SY284 )
!= ( product_Pair_pi_pi @ SY285 @ SY286 ) )
| ~ ( ( SV42 != SY285 )
| ( SY284 != SY286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(546,plain,
! [SV43: pi] :
( ( ! [SY287: pi,SY288: pi,SY289: pi] :
( ( ( product_Pair_pi_pi @ SV43 @ SY287 )
= ( product_Pair_pi_pi @ SY288 @ SY289 ) )
= ( ~ ( ( SV43 != SY288 )
| ( SY287 != SY289 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(547,plain,
! [SV44: product_prod_pi_pi] :
( ( ~ ! [SY290: pi] :
~ ~ ! [SY291: pi] :
( SV44
!= ( product_Pair_pi_pi @ SY290 @ SY291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(548,plain,
! [SV45: product_prod_pi_pi > $o] :
( ( ! [SY292: product_prod_pi_pi] :
( ~ ! [SY293: pi,SY294: pi] : ( SV45 @ ( product_Pair_pi_pi @ SY293 @ SY294 ) )
| ( SV45 @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(549,plain,
! [SV46: name] :
( ( ! [SY295: name,SY296: pi,SY297: name,SY298: pi] :
( ( mismatch @ SV46 @ SY295 @ SY296 )
!= ( res @ SY297 @ SY298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(550,plain,
( ( y = x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(551,plain,
! [SV47: name] :
( ( ! [SY299: pi,SY300: name] :
( ~ ( fresh_name_pi @ SV47 @ SY299 )
| ( ( subs @ SY299 @ SV47 @ SY300 )
= SY299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(552,plain,
! [SV48: name] :
( ( ! [SY301: name,SY302: pi,SY303: name,SY304: pi] :
( ( input @ SV48 @ SY301 @ SY302 )
!= ( res @ SY303 @ SY304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(553,plain,
! [SV49: product_prod_pi_pi] :
( ( ~ ! [SY305: pi,SY306: pi] :
( SV49
!= ( product_Pair_pi_pi @ SY305 @ SY306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(554,plain,
! [SV50: pi,SV1: pi] :
( ( ! [SY307: name,SY308: name] :
( ( subs @ ( par @ SV1 @ SV50 ) @ SY307 @ SY308 )
= ( par @ ( subs @ SV1 @ SY307 @ SY308 ) @ ( subs @ SV50 @ SY307 @ SY308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(555,plain,
! [SV51: name,SV2: pi] :
( ( ( subs @ SV2 @ SV51 @ SV51 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(556,plain,
! [SV52: pi,SV3: name] :
( ( fresh_name_pi @ SV3 @ ( res @ SV3 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(557,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
= ( SV53 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(558,plain,
! [SV54: name,SV6: name] :
( ( ( subs @ piNil @ SV6 @ SV54 )
= piNil )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(559,plain,
! [SV55: name,SV7: pi] :
( ( ! [SY309: name] :
( ( subs @ ( tau @ SV7 ) @ SV55 @ SY309 )
= ( tau @ ( subs @ SV7 @ SV55 @ SY309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(560,plain,
! [SV56: pi,SV8: name] :
( ( ! [SY310: name,SY311: pi] :
( ( ( res @ SV8 @ SV56 )
= ( res @ SY310 @ SY311 ) )
= ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SY310 @ SY311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(561,plain,
! [SV57: name,SV9: pi] :
( ( ! [SY312: name] :
( ( subs @ ( bang @ SV9 ) @ SV57 @ SY312 )
= ( bang @ ( subs @ SV9 @ SV57 @ SY312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(562,plain,
! [SV58: pi,SV10: pi] :
( ( ! [SY313: name,SY314: name] :
( ( subs @ ( sum @ SV10 @ SV58 ) @ SY313 @ SY314 )
= ( sum @ ( subs @ SV10 @ SY313 @ SY314 ) @ ( subs @ SV58 @ SY313 @ SY314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(563,plain,
! [SV11: $o] :
( ( ( SV11 = $true )
= $true )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(564,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(565,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(566,plain,
! [SV59: name,SV12: name] :
( ( ! [SY315: pi,SY316: pi,SY317: pi] :
( ( mismatch @ SV12 @ SV59 @ SY315 )
!= ( par @ SY316 @ SY317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(567,plain,
! [SV60: pi,SV13: pi] :
( ( ! [SY318: pi] :
( ( par @ SV13 @ SV60 )
!= ( bang @ SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(568,plain,
! [SV61: pi,SV14: pi] :
( ( ! [SY319: pi] :
( ( tau @ SV14 )
!= ( par @ SV61 @ SY319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(569,plain,
! [SV62: pi,SV15: name] :
( ( ! [SY320: name,SY321: pi] :
( ~ ( fresh_name_pi @ SV15 @ SV62 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SV15 @ ( res @ SY320 @ ( par @ SV62 @ SY321 ) ) ) @ ( res @ SY320 @ ( par @ SV62 @ ( res @ SV15 @ SY321 ) ) ) ) @ rel ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(570,plain,
! [SV63: name,SV16: name] :
( ( ! [SY322: pi,SY323: pi,SY324: pi] :
( ( match @ SV16 @ SV63 @ SY322 )
!= ( par @ SY323 @ SY324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(571,plain,
! [SV64: pi,SV17: name] :
( ( piNil
!= ( res @ SV17 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(572,plain,
! [SV65: pi,SV18: name] :
( ( ! [SY325: name,SY326: name] :
( ~ ( fresh_name_pi @ SV18 @ SV65 )
| ( ( subs @ ( subs @ SV65 @ SY325 @ SV18 ) @ SV18 @ SY326 )
= ( subs @ SV65 @ SY325 @ SY326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(573,plain,
! [SV66: pi,SV19: name] :
( ( ! [SY327: pi] :
( ~ ( fresh_name_pi @ SV19 @ SV66 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SV19 @ ( par @ SV66 @ SY327 ) ) @ ( par @ SV66 @ ( res @ SV19 @ SY327 ) ) ) @ rel ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(574,plain,
! [SV67: pi,SV20: pi] :
( ( ! [SY328: name,SY329: pi] :
( ( sum @ SV20 @ SV67 )
!= ( res @ SY328 @ SY329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(575,plain,
! [SV68: pi,SV21: name] :
( ( ! [SY330: name,SY331: name] :
( ~ ( fresh_name_pi @ SV21 @ SV68 )
| ~ ( ( SV21 != SY330 ) )
| ( fresh_name_pi @ SV21 @ ( subs @ SV68 @ SY331 @ SY330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(576,plain,
! [SV69: name,SV22: name] :
( ( ! [SY332: pi] :
( ~ ( ( SV22 != SV69 ) )
| ( fresh_name_pi @ SV22 @ ( subs @ SY332 @ SV22 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(577,plain,
! [SV70: name,SV23: name] :
( ( ! [SY333: pi,SY334: pi,SY335: pi] :
( ( input @ SV23 @ SV70 @ SY333 )
!= ( par @ SY334 @ SY335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(578,plain,
! [SV71: name,SV24: name] :
( ( ! [SY336: name,SY337: pi] :
( ~ ( ( SV24 != SV71 ) )
| ~ ( ( SV24 != SY336 ) )
| ( ( subs @ ( res @ SV24 @ SY337 ) @ SV71 @ SY336 )
= ( res @ SV24 @ ( subs @ SY337 @ SV71 @ SY336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(579,plain,
! [SV72: pi,SV25: set_Pr1834926343_pi_pi] :
( ( ! [SY338: pi] :
( ~ ! [SY234: pi,SY235: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ SY234 @ SY235 ) @ ( par @ SY235 @ SY234 ) ) @ SV25 )
| ~ ! [SY236: pi,SY237: pi,SY238: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ SY236 @ SY237 ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SY238 @ SY236 ) @ ( res @ SY238 @ SY237 ) ) @ SV25 ) )
| ( strong743114133lation @ ( par @ SV72 @ SY338 ) @ SV25 @ ( par @ SY338 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(580,plain,
! [SV73: pi,SV26: name] :
( ( ! [SY344: pi] :
( ( res @ SV26 @ SV73 )
!= ( bang @ SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(581,plain,
! [SV74: pi,SV27: pi] :
( ( ! [SY345: pi,SY346: pi] :
( ( ( par @ SV27 @ SV74 )
= ( par @ SY345 @ SY346 ) )
= ( ~ ( ( SV27 != SY345 )
| ( SV74 != SY346 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(582,plain,
! [SV75: pi,SV28: name] :
( ( ! [SY347: name] :
( ~ ( fresh_name_pi @ SV28 @ SV75 )
| ( ( res @ SY347 @ SV75 )
= ( res @ SV28 @ ( subs @ SV75 @ SY347 @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(583,plain,
! [SV76: name,SV29: name] :
( ( ! [SY348: pi,SY349: name,SY350: pi] :
( ( match @ SV29 @ SV76 @ SY348 )
!= ( res @ SY349 @ SY350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(584,plain,
! [SV30: produc1141751126_pi_pi] :
( ( ! [SY250: name,SY251: pi,SY252: pi] :
( SV30
!= ( produc235456326_pi_pi @ SY250 @ ( product_Pair_pi_pi @ SY251 @ SY252 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(585,plain,
! [SV77: product_prod_pi_pi,SV31: product_prod_pi_pi > $o] :
( ( ~ ! [SY254: pi,SY255: pi] : ( SV31 @ ( product_Pair_pi_pi @ SY254 @ SY255 ) )
| ( SV31 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(586,plain,
! [SV78: produc1141751126_pi_pi,SV32: produc1141751126_pi_pi > $o] :
( ( ~ ! [SY257: name,SY258: pi,SY259: pi] : ( SV32 @ ( produc235456326_pi_pi @ SY257 @ ( product_Pair_pi_pi @ SY258 @ SY259 ) ) )
| ( SV32 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(587,plain,
! [SV79: pi,SV33: pi] :
( ( piNil
!= ( par @ SV33 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(588,plain,
! [SV80: name,SV34: name] :
( ( ! [SY356: pi,SY357: pi,SY358: pi] :
( ( output @ SV34 @ SV80 @ SY356 )
!= ( par @ SY357 @ SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(589,plain,
! [SV81: pi,SV35: pi] :
( ( ! [SY359: pi,SY360: pi] :
( ( sum @ SV35 @ SV81 )
!= ( par @ SY359 @ SY360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(590,plain,
! [SV82: pi,SV36: name] :
( ( ! [SY361: name] :
( ~ ( fresh_name_pi @ SV36 @ SV82 )
| ( ( subs @ ( res @ SY361 @ SV82 ) @ SY361 @ SV36 )
= ( res @ SV36 @ ( subs @ SV82 @ SY361 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(591,plain,
! [SV83: pi,SV37: name] :
( ( ! [SY362: pi] :
( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SY362 ) )
= ( ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SY362 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(592,plain,
! [SV84: pi,SV38: pi] :
( ( ! [SY363: pi,SY364: pi] :
( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SY363 @ SY364 ) )
= ( ~ ( ( SV38 != SY363 )
| ( SV84 != SY364 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(593,plain,
! [SV85: name,SV39: name] :
( ( ! [SY365: pi,SY366: name,SY367: pi] :
( ( output @ SV39 @ SV85 @ SY365 )
!= ( res @ SY366 @ SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(594,plain,
! [SV86: pi,SV40: pi] :
( ( ! [SY368: name,SY369: pi] :
( ( par @ SV40 @ SV86 )
!= ( res @ SY368 @ SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(595,plain,
! [SV87: name,SV41: pi] :
( ( ! [SY370: pi] :
( ( tau @ SV41 )
!= ( res @ SV87 @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(596,plain,
! [SV88: pi,SV42: pi] :
( ( ! [SY371: pi,SY372: pi] :
( ( ( product_Pair_pi_pi @ SV42 @ SV88 )
!= ( product_Pair_pi_pi @ SY371 @ SY372 ) )
| ~ ( ( SV42 != SY371 )
| ( SV88 != SY372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(597,plain,
! [SV89: pi,SV43: pi] :
( ( ! [SY373: pi,SY374: pi] :
( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SY373 @ SY374 ) )
= ( ~ ( ( SV43 != SY373 )
| ( SV89 != SY374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(598,plain,
! [SV44: product_prod_pi_pi] :
( ( ! [SY290: pi] :
~ ~ ! [SY291: pi] :
( SV44
!= ( product_Pair_pi_pi @ SY290 @ SY291 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(599,plain,
! [SV90: product_prod_pi_pi,SV45: product_prod_pi_pi > $o] :
( ( ~ ! [SY293: pi,SY294: pi] : ( SV45 @ ( product_Pair_pi_pi @ SY293 @ SY294 ) )
| ( SV45 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(600,plain,
! [SV91: name,SV46: name] :
( ( ! [SY377: pi,SY378: name,SY379: pi] :
( ( mismatch @ SV46 @ SV91 @ SY377 )
!= ( res @ SY378 @ SY379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(601,plain,
! [SV92: pi,SV47: name] :
( ( ! [SY380: name] :
( ~ ( fresh_name_pi @ SV47 @ SV92 )
| ( ( subs @ SV92 @ SV47 @ SY380 )
= SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(602,plain,
! [SV93: name,SV48: name] :
( ( ! [SY381: pi,SY382: name,SY383: pi] :
( ( input @ SV48 @ SV93 @ SY381 )
!= ( res @ SY382 @ SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(603,plain,
! [SV49: product_prod_pi_pi] :
( ( ! [SY305: pi,SY306: pi] :
( SV49
!= ( product_Pair_pi_pi @ SY305 @ SY306 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(604,plain,
! [SV94: name,SV50: pi,SV1: pi] :
( ( ! [SY384: name] :
( ( subs @ ( par @ SV1 @ SV50 ) @ SV94 @ SY384 )
= ( par @ ( subs @ SV1 @ SV94 @ SY384 ) @ ( subs @ SV50 @ SV94 @ SY384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(605,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ~ ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
| ( SV53 @ SV4 ) )
| ~ ( ~ ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
| ~ ( SV53 @ SV4 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[557]) ).
thf(606,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
= ( SV53 @ SV4 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[557]) ).
thf(607,plain,
! [SV95: name,SV55: name,SV7: pi] :
( ( ( subs @ ( tau @ SV7 ) @ SV55 @ SV95 )
= ( tau @ ( subs @ SV7 @ SV55 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(608,plain,
! [SV96: name,SV56: pi,SV8: name] :
( ( ! [SY385: pi] :
( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SY385 ) )
= ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SY385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(609,plain,
! [SV97: name,SV57: name,SV9: pi] :
( ( ( subs @ ( bang @ SV9 ) @ SV57 @ SV97 )
= ( bang @ ( subs @ SV9 @ SV57 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(610,plain,
! [SV98: name,SV58: pi,SV10: pi] :
( ( ! [SY386: name] :
( ( subs @ ( sum @ SV10 @ SV58 ) @ SV98 @ SY386 )
= ( sum @ ( subs @ SV10 @ SV98 @ SY386 ) @ ( subs @ SV58 @ SV98 @ SY386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(611,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $true )
| ~ ( ~ SV11
| ~ $true ) )
= $true )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[563]) ).
thf(612,plain,
! [SV11: $o] :
( ( ( SV11 = $true )
= $true )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[563]) ).
thf(613,plain,
( ( ( ~ ( $true
| $true )
| ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[564]) ).
thf(614,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[564]) ).
thf(615,plain,
( ( ( ~ ( $false
| $true )
| ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[565]) ).
thf(616,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[565]) ).
thf(617,plain,
! [SV99: pi,SV59: name,SV12: name] :
( ( ! [SY387: pi,SY388: pi] :
( ( mismatch @ SV12 @ SV59 @ SV99 )
!= ( par @ SY387 @ SY388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(618,plain,
! [SV100: pi,SV60: pi,SV13: pi] :
( ( ( par @ SV13 @ SV60 )
!= ( bang @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(619,plain,
! [SV101: pi,SV61: pi,SV14: pi] :
( ( ( tau @ SV14 )
!= ( par @ SV61 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(620,plain,
! [SV102: name,SV62: pi,SV15: name] :
( ( ! [SY389: pi] :
( ~ ( fresh_name_pi @ SV15 @ SV62 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SV15 @ ( res @ SV102 @ ( par @ SV62 @ SY389 ) ) ) @ ( res @ SV102 @ ( par @ SV62 @ ( res @ SV15 @ SY389 ) ) ) ) @ rel ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(621,plain,
! [SV103: pi,SV63: name,SV16: name] :
( ( ! [SY390: pi,SY391: pi] :
( ( match @ SV16 @ SV63 @ SV103 )
!= ( par @ SY390 @ SY391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(622,plain,
! [SV64: pi,SV17: name] :
( ( piNil
= ( res @ SV17 @ SV64 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(623,plain,
! [SV104: name,SV65: pi,SV18: name] :
( ( ! [SY392: name] :
( ~ ( fresh_name_pi @ SV18 @ SV65 )
| ( ( subs @ ( subs @ SV65 @ SV104 @ SV18 ) @ SV18 @ SY392 )
= ( subs @ SV65 @ SV104 @ SY392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(624,plain,
! [SV105: pi,SV66: pi,SV19: name] :
( ( ~ ( fresh_name_pi @ SV19 @ SV66 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SV19 @ ( par @ SV66 @ SV105 ) ) @ ( par @ SV66 @ ( res @ SV19 @ SV105 ) ) ) @ rel ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(625,plain,
! [SV106: name,SV67: pi,SV20: pi] :
( ( ! [SY393: pi] :
( ( sum @ SV20 @ SV67 )
!= ( res @ SV106 @ SY393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(626,plain,
! [SV107: name,SV68: pi,SV21: name] :
( ( ! [SY394: name] :
( ~ ( fresh_name_pi @ SV21 @ SV68 )
| ~ ( ( SV21 != SV107 ) )
| ( fresh_name_pi @ SV21 @ ( subs @ SV68 @ SY394 @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(627,plain,
! [SV108: pi,SV69: name,SV22: name] :
( ( ~ ( ( SV22 != SV69 ) )
| ( fresh_name_pi @ SV22 @ ( subs @ SV108 @ SV22 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(628,plain,
! [SV109: pi,SV70: name,SV23: name] :
( ( ! [SY395: pi,SY396: pi] :
( ( input @ SV23 @ SV70 @ SV109 )
!= ( par @ SY395 @ SY396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(629,plain,
! [SV110: name,SV71: name,SV24: name] :
( ( ! [SY397: pi] :
( ~ ( ( SV24 != SV71 ) )
| ~ ( ( SV24 != SV110 ) )
| ( ( subs @ ( res @ SV24 @ SY397 ) @ SV71 @ SV110 )
= ( res @ SV24 @ ( subs @ SY397 @ SV71 @ SV110 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(630,plain,
! [SV111: pi,SV72: pi,SV25: set_Pr1834926343_pi_pi] :
( ( ~ ! [SY234: pi,SY235: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ SY234 @ SY235 ) @ ( par @ SY235 @ SY234 ) ) @ SV25 )
| ~ ! [SY236: pi,SY237: pi,SY238: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ SY236 @ SY237 ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SY238 @ SY236 ) @ ( res @ SY238 @ SY237 ) ) @ SV25 ) )
| ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(631,plain,
! [SV112: pi,SV73: pi,SV26: name] :
( ( ( res @ SV26 @ SV73 )
!= ( bang @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(632,plain,
! [SV113: pi,SV74: pi,SV27: pi] :
( ( ! [SY403: pi] :
( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SY403 ) )
= ( ~ ( ( SV27 != SV113 )
| ( SV74 != SY403 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(633,plain,
! [SV114: name,SV75: pi,SV28: name] :
( ( ~ ( fresh_name_pi @ SV28 @ SV75 )
| ( ( res @ SV114 @ SV75 )
= ( res @ SV28 @ ( subs @ SV75 @ SV114 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(634,plain,
! [SV115: pi,SV76: name,SV29: name] :
( ( ! [SY404: name,SY405: pi] :
( ( match @ SV29 @ SV76 @ SV115 )
!= ( res @ SY404 @ SY405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(635,plain,
! [SV30: produc1141751126_pi_pi] :
( ( ! [SY406: pi,SY407: pi] :
( SV30
!= ( produc235456326_pi_pi @ ( sK1_SY250 @ SV30 ) @ ( product_Pair_pi_pi @ SY406 @ SY407 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[584]) ).
thf(636,plain,
! [SV77: product_prod_pi_pi,SV31: product_prod_pi_pi > $o] :
( ( ( ~ ! [SY254: pi,SY255: pi] : ( SV31 @ ( product_Pair_pi_pi @ SY254 @ SY255 ) ) )
= $true )
| ( ( SV31 @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(637,plain,
! [SV78: produc1141751126_pi_pi,SV32: produc1141751126_pi_pi > $o] :
( ( ( ~ ! [SY257: name,SY258: pi,SY259: pi] : ( SV32 @ ( produc235456326_pi_pi @ SY257 @ ( product_Pair_pi_pi @ SY258 @ SY259 ) ) ) )
= $true )
| ( ( SV32 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(638,plain,
! [SV79: pi,SV33: pi] :
( ( piNil
= ( par @ SV33 @ SV79 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(639,plain,
! [SV116: pi,SV80: name,SV34: name] :
( ( ! [SY408: pi,SY409: pi] :
( ( output @ SV34 @ SV80 @ SV116 )
!= ( par @ SY408 @ SY409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(640,plain,
! [SV117: pi,SV81: pi,SV35: pi] :
( ( ! [SY410: pi] :
( ( sum @ SV35 @ SV81 )
!= ( par @ SV117 @ SY410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(641,plain,
! [SV118: name,SV82: pi,SV36: name] :
( ( ~ ( fresh_name_pi @ SV36 @ SV82 )
| ( ( subs @ ( res @ SV118 @ SV82 ) @ SV118 @ SV36 )
= ( res @ SV36 @ ( subs @ SV82 @ SV118 @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(642,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= ( ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(643,plain,
! [SV120: pi,SV84: pi,SV38: pi] :
( ( ! [SY411: pi] :
( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SY411 ) )
= ( ~ ( ( SV38 != SV120 )
| ( SV84 != SY411 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(644,plain,
! [SV121: pi,SV85: name,SV39: name] :
( ( ! [SY412: name,SY413: pi] :
( ( output @ SV39 @ SV85 @ SV121 )
!= ( res @ SY412 @ SY413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(645,plain,
! [SV122: name,SV86: pi,SV40: pi] :
( ( ! [SY414: pi] :
( ( par @ SV40 @ SV86 )
!= ( res @ SV122 @ SY414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(646,plain,
! [SV123: pi,SV87: name,SV41: pi] :
( ( ( tau @ SV41 )
!= ( res @ SV87 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(647,plain,
! [SV124: pi,SV88: pi,SV42: pi] :
( ( ! [SY415: pi] :
( ( ( product_Pair_pi_pi @ SV42 @ SV88 )
!= ( product_Pair_pi_pi @ SV124 @ SY415 ) )
| ~ ( ( SV42 != SV124 )
| ( SV88 != SY415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(648,plain,
! [SV125: pi,SV89: pi,SV43: pi] :
( ( ! [SY416: pi] :
( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SY416 ) )
= ( ~ ( ( SV43 != SV125 )
| ( SV89 != SY416 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(649,plain,
! [SV44: product_prod_pi_pi] :
( ( ~ ~ ! [SY417: pi] :
( SV44
!= ( product_Pair_pi_pi @ ( sK2_SY290 @ SV44 ) @ SY417 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[598]) ).
thf(650,plain,
! [SV90: product_prod_pi_pi,SV45: product_prod_pi_pi > $o] :
( ( ( ~ ! [SY293: pi,SY294: pi] : ( SV45 @ ( product_Pair_pi_pi @ SY293 @ SY294 ) ) )
= $true )
| ( ( SV45 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(651,plain,
! [SV126: pi,SV91: name,SV46: name] :
( ( ! [SY418: name,SY419: pi] :
( ( mismatch @ SV46 @ SV91 @ SV126 )
!= ( res @ SY418 @ SY419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(652,plain,
! [SV127: name,SV92: pi,SV47: name] :
( ( ~ ( fresh_name_pi @ SV47 @ SV92 )
| ( ( subs @ SV92 @ SV47 @ SV127 )
= SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(653,plain,
! [SV128: pi,SV93: name,SV48: name] :
( ( ! [SY420: name,SY421: pi] :
( ( input @ SV48 @ SV93 @ SV128 )
!= ( res @ SY420 @ SY421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(654,plain,
! [SV49: product_prod_pi_pi] :
( ( ! [SY422: pi] :
( SV49
!= ( product_Pair_pi_pi @ ( sK3_SY305 @ SV49 ) @ SY422 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[603]) ).
thf(655,plain,
! [SV129: name,SV94: name,SV50: pi,SV1: pi] :
( ( ( subs @ ( par @ SV1 @ SV50 ) @ SV94 @ SV129 )
= ( par @ ( subs @ SV1 @ SV94 @ SV129 ) @ ( subs @ SV50 @ SV94 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(656,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ( ~ ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
| ( SV53 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
| ~ ( SV53 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(657,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(658,plain,
! [SV131: name,SV98: name,SV58: pi,SV10: pi] :
( ( ( subs @ ( sum @ SV10 @ SV58 ) @ SV98 @ SV131 )
= ( sum @ ( subs @ SV10 @ SV98 @ SV131 ) @ ( subs @ SV58 @ SV98 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(659,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $true ) )
= $true )
| ( ( ~ ( ~ SV11
| ~ $true ) )
= $true )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(660,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $false )
| ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[612]) ).
thf(661,plain,
! [SV11: $o] :
( ( ( SV11 = $false )
= $true )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[612]) ).
thf(662,plain,
( ( ( ~ ( $true
| $true ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(663,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[614]) ).
thf(664,plain,
( ( ( $true = $false )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[614]) ).
thf(665,plain,
( ( ( ~ ( $false
| $true ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(666,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[616]) ).
thf(667,plain,
( ( ( $false = $false )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[616]) ).
thf(668,plain,
! [SV132: pi,SV99: pi,SV59: name,SV12: name] :
( ( ! [SY423: pi] :
( ( mismatch @ SV12 @ SV59 @ SV99 )
!= ( par @ SV132 @ SY423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(669,plain,
! [SV100: pi,SV60: pi,SV13: pi] :
( ( ( par @ SV13 @ SV60 )
= ( bang @ SV100 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(670,plain,
! [SV101: pi,SV61: pi,SV14: pi] :
( ( ( tau @ SV14 )
= ( par @ SV61 @ SV101 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(671,plain,
! [SV133: pi,SV102: name,SV62: pi,SV15: name] :
( ( ~ ( fresh_name_pi @ SV15 @ SV62 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SV15 @ ( res @ SV102 @ ( par @ SV62 @ SV133 ) ) ) @ ( res @ SV102 @ ( par @ SV62 @ ( res @ SV15 @ SV133 ) ) ) ) @ rel ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(672,plain,
! [SV134: pi,SV103: pi,SV63: name,SV16: name] :
( ( ! [SY424: pi] :
( ( match @ SV16 @ SV63 @ SV103 )
!= ( par @ SV134 @ SY424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(673,plain,
! [SV135: name,SV104: name,SV65: pi,SV18: name] :
( ( ~ ( fresh_name_pi @ SV18 @ SV65 )
| ( ( subs @ ( subs @ SV65 @ SV104 @ SV18 ) @ SV18 @ SV135 )
= ( subs @ SV65 @ SV104 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(674,plain,
! [SV105: pi,SV66: pi,SV19: name] :
( ( ( ~ ( fresh_name_pi @ SV19 @ SV66 ) )
= $true )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SV19 @ ( par @ SV66 @ SV105 ) ) @ ( par @ SV66 @ ( res @ SV19 @ SV105 ) ) ) @ rel )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(675,plain,
! [SV136: pi,SV106: name,SV67: pi,SV20: pi] :
( ( ( sum @ SV20 @ SV67 )
!= ( res @ SV106 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(676,plain,
! [SV137: name,SV107: name,SV68: pi,SV21: name] :
( ( ~ ( fresh_name_pi @ SV21 @ SV68 )
| ~ ( ( SV21 != SV107 ) )
| ( fresh_name_pi @ SV21 @ ( subs @ SV68 @ SV137 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(677,plain,
! [SV108: pi,SV69: name,SV22: name] :
( ( ( ~ ( ( SV22 != SV69 ) ) )
= $true )
| ( ( fresh_name_pi @ SV22 @ ( subs @ SV108 @ SV22 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(678,plain,
! [SV138: pi,SV109: pi,SV70: name,SV23: name] :
( ( ! [SY425: pi] :
( ( input @ SV23 @ SV70 @ SV109 )
!= ( par @ SV138 @ SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(679,plain,
! [SV139: pi,SV110: name,SV71: name,SV24: name] :
( ( ~ ( ( SV24 != SV71 ) )
| ~ ( ( SV24 != SV110 ) )
| ( ( subs @ ( res @ SV24 @ SV139 ) @ SV71 @ SV110 )
= ( res @ SV24 @ ( subs @ SV139 @ SV71 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(680,plain,
! [SV111: pi,SV72: pi,SV25: set_Pr1834926343_pi_pi] :
( ( ( ~ ! [SY234: pi,SY235: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ SY234 @ SY235 ) @ ( par @ SY235 @ SY234 ) ) @ SV25 ) )
= $true )
| ( ( ~ ! [SY236: pi,SY237: pi,SY238: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ SY236 @ SY237 ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SY238 @ SY236 ) @ ( res @ SY238 @ SY237 ) ) @ SV25 ) )
| ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(681,plain,
! [SV112: pi,SV73: pi,SV26: name] :
( ( ( res @ SV26 @ SV73 )
= ( bang @ SV112 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(682,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= ( ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(683,plain,
! [SV114: name,SV75: pi,SV28: name] :
( ( ( ~ ( fresh_name_pi @ SV28 @ SV75 ) )
= $true )
| ( ( ( res @ SV114 @ SV75 )
= ( res @ SV28 @ ( subs @ SV75 @ SV114 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(684,plain,
! [SV141: name,SV115: pi,SV76: name,SV29: name] :
( ( ! [SY426: pi] :
( ( match @ SV29 @ SV76 @ SV115 )
!= ( res @ SV141 @ SY426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(685,plain,
! [SV30: produc1141751126_pi_pi] :
( ( ! [SY427: pi] :
( SV30
!= ( produc235456326_pi_pi @ ( sK1_SY250 @ SV30 ) @ ( product_Pair_pi_pi @ ( sK4_SY406 @ SV30 ) @ SY427 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[635]) ).
thf(686,plain,
! [SV77: product_prod_pi_pi,SV31: product_prod_pi_pi > $o] :
( ( ( ! [SY254: pi,SY255: pi] : ( SV31 @ ( product_Pair_pi_pi @ SY254 @ SY255 ) ) )
= $false )
| ( ( SV31 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(687,plain,
! [SV78: produc1141751126_pi_pi,SV32: produc1141751126_pi_pi > $o] :
( ( ( ! [SY257: name,SY258: pi,SY259: pi] : ( SV32 @ ( produc235456326_pi_pi @ SY257 @ ( product_Pair_pi_pi @ SY258 @ SY259 ) ) ) )
= $false )
| ( ( SV32 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(688,plain,
! [SV142: pi,SV116: pi,SV80: name,SV34: name] :
( ( ! [SY428: pi] :
( ( output @ SV34 @ SV80 @ SV116 )
!= ( par @ SV142 @ SY428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(689,plain,
! [SV143: pi,SV117: pi,SV81: pi,SV35: pi] :
( ( ( sum @ SV35 @ SV81 )
!= ( par @ SV117 @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(690,plain,
! [SV118: name,SV82: pi,SV36: name] :
( ( ( ~ ( fresh_name_pi @ SV36 @ SV82 ) )
= $true )
| ( ( ( subs @ ( res @ SV118 @ SV82 ) @ SV118 @ SV36 )
= ( res @ SV36 @ ( subs @ SV82 @ SV118 @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(691,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ~ ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) )
| ~ ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[642]) ).
thf(692,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= ( ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[642]) ).
thf(693,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= ( ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(694,plain,
! [SV145: name,SV121: pi,SV85: name,SV39: name] :
( ( ! [SY429: pi] :
( ( output @ SV39 @ SV85 @ SV121 )
!= ( res @ SV145 @ SY429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(695,plain,
! [SV146: pi,SV122: name,SV86: pi,SV40: pi] :
( ( ( par @ SV40 @ SV86 )
!= ( res @ SV122 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(696,plain,
! [SV123: pi,SV87: name,SV41: pi] :
( ( ( tau @ SV41 )
= ( res @ SV87 @ SV123 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(697,plain,
! [SV147: pi,SV124: pi,SV88: pi,SV42: pi] :
( ( ( ( product_Pair_pi_pi @ SV42 @ SV88 )
!= ( product_Pair_pi_pi @ SV124 @ SV147 ) )
| ~ ( ( SV42 != SV124 )
| ( SV88 != SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(698,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= ( ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(699,plain,
! [SV44: product_prod_pi_pi] :
( ( ~ ! [SY417: pi] :
( SV44
!= ( product_Pair_pi_pi @ ( sK2_SY290 @ SV44 ) @ SY417 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[649]) ).
thf(700,plain,
! [SV90: product_prod_pi_pi,SV45: product_prod_pi_pi > $o] :
( ( ( ! [SY293: pi,SY294: pi] : ( SV45 @ ( product_Pair_pi_pi @ SY293 @ SY294 ) ) )
= $false )
| ( ( SV45 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(701,plain,
! [SV149: name,SV126: pi,SV91: name,SV46: name] :
( ( ! [SY430: pi] :
( ( mismatch @ SV46 @ SV91 @ SV126 )
!= ( res @ SV149 @ SY430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(702,plain,
! [SV127: name,SV92: pi,SV47: name] :
( ( ( ~ ( fresh_name_pi @ SV47 @ SV92 ) )
= $true )
| ( ( ( subs @ SV92 @ SV47 @ SV127 )
= SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(703,plain,
! [SV150: name,SV128: pi,SV93: name,SV48: name] :
( ( ! [SY431: pi] :
( ( input @ SV48 @ SV93 @ SV128 )
!= ( res @ SV150 @ SY431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(704,plain,
! [SV49: product_prod_pi_pi] :
( ( SV49
!= ( product_Pair_pi_pi @ ( sK3_SY305 @ SV49 ) @ ( sK5_SY422 @ SV49 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[654]) ).
thf(705,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
| ( SV53 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
| ~ ( SV53 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(706,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ~ ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) ) )
| ~ ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[657]) ).
thf(707,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[657]) ).
thf(708,plain,
! [SV11: $o] :
( ( ( SV11
| $true )
= $false )
| ( ( ~ ( ~ SV11
| ~ $true ) )
= $true )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(709,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $false ) )
= $true )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(710,plain,
( ( ( $true
| $true )
= $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(711,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(712,plain,
( ( ( $false
| $true )
= $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(713,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(714,plain,
! [SV151: pi,SV132: pi,SV99: pi,SV59: name,SV12: name] :
( ( ( mismatch @ SV12 @ SV59 @ SV99 )
!= ( par @ SV132 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(715,plain,
! [SV133: pi,SV102: name,SV62: pi,SV15: name] :
( ( ( ~ ( fresh_name_pi @ SV15 @ SV62 ) )
= $true )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SV15 @ ( res @ SV102 @ ( par @ SV62 @ SV133 ) ) ) @ ( res @ SV102 @ ( par @ SV62 @ ( res @ SV15 @ SV133 ) ) ) ) @ rel )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(716,plain,
! [SV152: pi,SV134: pi,SV103: pi,SV63: name,SV16: name] :
( ( ( match @ SV16 @ SV63 @ SV103 )
!= ( par @ SV134 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(717,plain,
! [SV135: name,SV104: name,SV65: pi,SV18: name] :
( ( ( ~ ( fresh_name_pi @ SV18 @ SV65 ) )
= $true )
| ( ( ( subs @ ( subs @ SV65 @ SV104 @ SV18 ) @ SV18 @ SV135 )
= ( subs @ SV65 @ SV104 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(718,plain,
! [SV105: pi,SV66: pi,SV19: name] :
( ( ( fresh_name_pi @ SV19 @ SV66 )
= $false )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SV19 @ ( par @ SV66 @ SV105 ) ) @ ( par @ SV66 @ ( res @ SV19 @ SV105 ) ) ) @ rel )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(719,plain,
! [SV136: pi,SV106: name,SV67: pi,SV20: pi] :
( ( ( sum @ SV20 @ SV67 )
= ( res @ SV106 @ SV136 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(720,plain,
! [SV137: name,SV107: name,SV68: pi,SV21: name] :
( ( ( ~ ( fresh_name_pi @ SV21 @ SV68 ) )
= $true )
| ( ( ~ ( ( SV21 != SV107 ) )
| ( fresh_name_pi @ SV21 @ ( subs @ SV68 @ SV137 @ SV107 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(721,plain,
! [SV108: pi,SV69: name,SV22: name] :
( ( ( SV22 != SV69 )
= $false )
| ( ( fresh_name_pi @ SV22 @ ( subs @ SV108 @ SV22 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(722,plain,
! [SV153: pi,SV138: pi,SV109: pi,SV70: name,SV23: name] :
( ( ( input @ SV23 @ SV70 @ SV109 )
!= ( par @ SV138 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(723,plain,
! [SV139: pi,SV110: name,SV71: name,SV24: name] :
( ( ( ~ ( ( SV24 != SV71 ) ) )
= $true )
| ( ( ~ ( ( SV24 != SV110 ) )
| ( ( subs @ ( res @ SV24 @ SV139 ) @ SV71 @ SV110 )
= ( res @ SV24 @ ( subs @ SV139 @ SV71 @ SV110 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(724,plain,
! [SV111: pi,SV72: pi,SV25: set_Pr1834926343_pi_pi] :
( ( ( ! [SY234: pi,SY235: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ SY234 @ SY235 ) @ ( par @ SY235 @ SY234 ) ) @ SV25 ) )
= $false )
| ( ( ~ ! [SY236: pi,SY237: pi,SY238: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ SY236 @ SY237 ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SY238 @ SY236 ) @ ( res @ SY238 @ SY237 ) ) @ SV25 ) )
| ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(725,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ~ ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
| ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) )
| ~ ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
| ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[682]) ).
thf(726,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= ( ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[682]) ).
thf(727,plain,
! [SV114: name,SV75: pi,SV28: name] :
( ( ( fresh_name_pi @ SV28 @ SV75 )
= $false )
| ( ( ( res @ SV114 @ SV75 )
= ( res @ SV28 @ ( subs @ SV75 @ SV114 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(728,plain,
! [SV154: pi,SV141: name,SV115: pi,SV76: name,SV29: name] :
( ( ( match @ SV29 @ SV76 @ SV115 )
!= ( res @ SV141 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(729,plain,
! [SV30: produc1141751126_pi_pi] :
( ( SV30
!= ( produc235456326_pi_pi @ ( sK1_SY250 @ SV30 ) @ ( product_Pair_pi_pi @ ( sK4_SY406 @ SV30 ) @ ( sK6_SY427 @ SV30 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[685]) ).
thf(730,plain,
! [SV77: product_prod_pi_pi,SV31: product_prod_pi_pi > $o] :
( ( ( ! [SY432: pi] : ( SV31 @ ( product_Pair_pi_pi @ ( sK7_SY254 @ SV77 @ SV31 ) @ SY432 ) ) )
= $false )
| ( ( SV31 @ SV77 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[686]) ).
thf(731,plain,
! [SV78: produc1141751126_pi_pi,SV32: produc1141751126_pi_pi > $o] :
( ( ( ! [SY433: pi,SY434: pi] : ( SV32 @ ( produc235456326_pi_pi @ ( sK8_SY257 @ SV78 @ SV32 ) @ ( product_Pair_pi_pi @ SY433 @ SY434 ) ) ) )
= $false )
| ( ( SV32 @ SV78 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[687]) ).
thf(732,plain,
! [SV155: pi,SV142: pi,SV116: pi,SV80: name,SV34: name] :
( ( ( output @ SV34 @ SV80 @ SV116 )
!= ( par @ SV142 @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(733,plain,
! [SV143: pi,SV117: pi,SV81: pi,SV35: pi] :
( ( ( sum @ SV35 @ SV81 )
= ( par @ SV117 @ SV143 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(734,plain,
! [SV118: name,SV82: pi,SV36: name] :
( ( ( fresh_name_pi @ SV36 @ SV82 )
= $false )
| ( ( ( subs @ ( res @ SV118 @ SV82 ) @ SV118 @ SV36 )
= ( res @ SV36 @ ( subs @ SV82 @ SV118 @ SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(735,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true )
| ( ( ~ ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(736,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ~ ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) )
| ~ ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[693]) ).
thf(737,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= ( ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[693]) ).
thf(738,plain,
! [SV156: pi,SV145: name,SV121: pi,SV85: name,SV39: name] :
( ( ( output @ SV39 @ SV85 @ SV121 )
!= ( res @ SV145 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(739,plain,
! [SV146: pi,SV122: name,SV86: pi,SV40: pi] :
( ( ( par @ SV40 @ SV86 )
= ( res @ SV122 @ SV146 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(740,plain,
! [SV147: pi,SV124: pi,SV88: pi,SV42: pi] :
( ( ( ( product_Pair_pi_pi @ SV42 @ SV88 )
!= ( product_Pair_pi_pi @ SV124 @ SV147 ) )
= $true )
| ( ( ~ ( ( SV42 != SV124 )
| ( SV88 != SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(741,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ~ ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) )
| ~ ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[698]) ).
thf(742,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= ( ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[698]) ).
thf(743,plain,
! [SV44: product_prod_pi_pi] :
( ( ! [SY417: pi] :
( SV44
!= ( product_Pair_pi_pi @ ( sK2_SY290 @ SV44 ) @ SY417 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(744,plain,
! [SV90: product_prod_pi_pi,SV45: product_prod_pi_pi > $o] :
( ( ( ! [SY435: pi] : ( SV45 @ ( product_Pair_pi_pi @ ( sK9_SY293 @ SV90 @ SV45 ) @ SY435 ) ) )
= $false )
| ( ( SV45 @ SV90 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[700]) ).
thf(745,plain,
! [SV157: pi,SV149: name,SV126: pi,SV91: name,SV46: name] :
( ( ( mismatch @ SV46 @ SV91 @ SV126 )
!= ( res @ SV149 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(746,plain,
! [SV127: name,SV92: pi,SV47: name] :
( ( ( fresh_name_pi @ SV47 @ SV92 )
= $false )
| ( ( ( subs @ SV92 @ SV47 @ SV127 )
= SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(747,plain,
! [SV158: pi,SV150: name,SV128: pi,SV93: name,SV48: name] :
( ( ( input @ SV48 @ SV93 @ SV128 )
!= ( res @ SV150 @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(748,plain,
! [SV49: product_prod_pi_pi] :
( ( SV49
= ( product_Pair_pi_pi @ ( sK3_SY305 @ SV49 ) @ ( sK5_SY422 @ SV49 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[704]) ).
thf(749,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
= $false )
| ( ( ~ ( ~ ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
| ~ ( SV53 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(750,plain,
! [SV4: product_prod_pi_pi,SV53: product_prod_pi_pi > $o] :
( ( ( SV53 @ SV4 )
= $false )
| ( ( ~ ( ~ ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
| ~ ( SV53 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(751,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ~ ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) ) ) )
= $true )
| ( ( ~ ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(752,plain,
! [SV11: $o] :
( ( SV11 = $false )
| ( ( ~ ( ~ SV11
| ~ $true ) )
= $true )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(753,plain,
! [SV11: $o] :
( ( $true = $false )
| ( ( ~ ( ~ SV11
| ~ $true ) )
= $true )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(754,plain,
! [SV11: $o] :
( ( ( SV11
| $false )
= $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(755,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(756,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[710]) ).
thf(757,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(758,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(759,plain,
( ( $true = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(760,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(761,plain,
! [SV151: pi,SV132: pi,SV99: pi,SV59: name,SV12: name] :
( ( ( mismatch @ SV12 @ SV59 @ SV99 )
= ( par @ SV132 @ SV151 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(762,plain,
! [SV133: pi,SV102: name,SV62: pi,SV15: name] :
( ( ( fresh_name_pi @ SV15 @ SV62 )
= $false )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SV15 @ ( res @ SV102 @ ( par @ SV62 @ SV133 ) ) ) @ ( res @ SV102 @ ( par @ SV62 @ ( res @ SV15 @ SV133 ) ) ) ) @ rel )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(763,plain,
! [SV152: pi,SV134: pi,SV103: pi,SV63: name,SV16: name] :
( ( ( match @ SV16 @ SV63 @ SV103 )
= ( par @ SV134 @ SV152 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(764,plain,
! [SV135: name,SV104: name,SV65: pi,SV18: name] :
( ( ( fresh_name_pi @ SV18 @ SV65 )
= $false )
| ( ( ( subs @ ( subs @ SV65 @ SV104 @ SV18 ) @ SV18 @ SV135 )
= ( subs @ SV65 @ SV104 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(765,plain,
! [SV137: name,SV107: name,SV68: pi,SV21: name] :
( ( ( fresh_name_pi @ SV21 @ SV68 )
= $false )
| ( ( ~ ( ( SV21 != SV107 ) )
| ( fresh_name_pi @ SV21 @ ( subs @ SV68 @ SV137 @ SV107 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(766,plain,
! [SV108: pi,SV69: name,SV22: name] :
( ( ( SV22 = SV69 )
= $true )
| ( ( fresh_name_pi @ SV22 @ ( subs @ SV108 @ SV22 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(767,plain,
! [SV153: pi,SV138: pi,SV109: pi,SV70: name,SV23: name] :
( ( ( input @ SV23 @ SV70 @ SV109 )
= ( par @ SV138 @ SV153 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(768,plain,
! [SV139: pi,SV110: name,SV71: name,SV24: name] :
( ( ( SV24 != SV71 )
= $false )
| ( ( ~ ( ( SV24 != SV110 ) )
| ( ( subs @ ( res @ SV24 @ SV139 ) @ SV71 @ SV110 )
= ( res @ SV24 @ ( subs @ SV139 @ SV71 @ SV110 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(769,plain,
! [SV25: set_Pr1834926343_pi_pi,SV72: pi,SV111: pi] :
( ( ( ! [SY436: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) @ SY436 ) @ ( par @ SY436 @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) ) ) @ SV25 ) )
= $false )
| ( ( ~ ! [SY236: pi,SY237: pi,SY238: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ SY236 @ SY237 ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SY238 @ SY236 ) @ ( res @ SY238 @ SY237 ) ) @ SV25 ) )
| ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[724]) ).
thf(770,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ( ~ ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
| ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true )
| ( ( ~ ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
| ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(771,plain,
! [SV154: pi,SV141: name,SV115: pi,SV76: name,SV29: name] :
( ( ( match @ SV29 @ SV76 @ SV115 )
= ( res @ SV141 @ SV154 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(772,plain,
! [SV30: produc1141751126_pi_pi] :
( ( SV30
= ( produc235456326_pi_pi @ ( sK1_SY250 @ SV30 ) @ ( product_Pair_pi_pi @ ( sK4_SY406 @ SV30 ) @ ( sK6_SY427 @ SV30 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(773,plain,
! [SV77: product_prod_pi_pi,SV31: product_prod_pi_pi > $o] :
( ( ( SV31 @ ( product_Pair_pi_pi @ ( sK7_SY254 @ SV77 @ SV31 ) @ ( sK11_SY432 @ SV77 @ SV31 ) ) )
= $false )
| ( ( SV31 @ SV77 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[730]) ).
thf(774,plain,
! [SV78: produc1141751126_pi_pi,SV32: produc1141751126_pi_pi > $o] :
( ( ( ! [SY437: pi] : ( SV32 @ ( produc235456326_pi_pi @ ( sK8_SY257 @ SV78 @ SV32 ) @ ( product_Pair_pi_pi @ ( sK12_SY433 @ SV78 @ SV32 ) @ SY437 ) ) ) )
= $false )
| ( ( SV32 @ SV78 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[731]) ).
thf(775,plain,
! [SV155: pi,SV142: pi,SV116: pi,SV80: name,SV34: name] :
( ( ( output @ SV34 @ SV80 @ SV116 )
= ( par @ SV142 @ SV155 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(776,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) )
= $false )
| ( ( ~ ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(777,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ( ~ ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(778,plain,
! [SV156: pi,SV145: name,SV121: pi,SV85: name,SV39: name] :
( ( ( output @ SV39 @ SV85 @ SV121 )
= ( res @ SV145 @ SV156 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(779,plain,
! [SV147: pi,SV124: pi,SV88: pi,SV42: pi] :
( ( ( ( product_Pair_pi_pi @ SV42 @ SV88 )
= ( product_Pair_pi_pi @ SV124 @ SV147 ) )
= $false )
| ( ( ~ ( ( SV42 != SV124 )
| ( SV88 != SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(780,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ( ~ ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(781,plain,
! [SV44: product_prod_pi_pi] :
( ( SV44
!= ( product_Pair_pi_pi @ ( sK2_SY290 @ SV44 ) @ ( sK13_SY417 @ SV44 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[743]) ).
thf(782,plain,
! [SV90: product_prod_pi_pi,SV45: product_prod_pi_pi > $o] :
( ( ( SV45 @ ( product_Pair_pi_pi @ ( sK9_SY293 @ SV90 @ SV45 ) @ ( sK14_SY435 @ SV90 @ SV45 ) ) )
= $false )
| ( ( SV45 @ SV90 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[744]) ).
thf(783,plain,
! [SV157: pi,SV149: name,SV126: pi,SV91: name,SV46: name] :
( ( ( mismatch @ SV46 @ SV91 @ SV126 )
= ( res @ SV149 @ SV157 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(784,plain,
! [SV158: pi,SV150: name,SV128: pi,SV93: name,SV48: name] :
( ( ( input @ SV48 @ SV93 @ SV128 )
= ( res @ SV150 @ SV158 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(785,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ( ~ ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
| ~ ( SV53 @ SV4 ) )
= $false )
| ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(786,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ( ~ ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
| ~ ( SV53 @ SV4 ) )
= $false )
| ( ( SV53 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(787,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) ) )
= $false )
| ( ( ~ ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(788,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $true )
= $false )
| ( SV11 = $false )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(789,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $true )
= $false )
| ( $true = $false )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(790,plain,
! [SV11: $o] :
( ( SV11 = $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(791,plain,
! [SV11: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(792,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(793,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(794,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(795,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(796,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(797,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(798,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[760]) ).
thf(799,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[760]) ).
thf(800,plain,
! [SV137: name,SV68: pi,SV107: name,SV21: name] :
( ( ( ~ ( ( SV21 != SV107 ) ) )
= $true )
| ( ( fresh_name_pi @ SV21 @ ( subs @ SV68 @ SV137 @ SV107 ) )
= $true )
| ( ( fresh_name_pi @ SV21 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(801,plain,
! [SV139: pi,SV110: name,SV71: name,SV24: name] :
( ( ( SV24 = SV71 )
= $true )
| ( ( ~ ( ( SV24 != SV110 ) )
| ( ( subs @ ( res @ SV24 @ SV139 ) @ SV71 @ SV110 )
= ( res @ SV24 @ ( subs @ SV139 @ SV71 @ SV110 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[768]) ).
thf(802,plain,
! [SV25: set_Pr1834926343_pi_pi,SV72: pi,SV111: pi] :
( ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) ) @ ( par @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) ) ) @ SV25 )
= $false )
| ( ( ~ ! [SY236: pi,SY237: pi,SY238: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ SY236 @ SY237 ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SY238 @ SY236 ) @ ( res @ SY238 @ SY237 ) ) @ SV25 ) )
| ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[769]) ).
thf(803,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
| ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) )
= $false )
| ( ( ~ ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
| ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(804,plain,
! [SV78: produc1141751126_pi_pi,SV32: produc1141751126_pi_pi > $o] :
( ( ( SV32 @ ( produc235456326_pi_pi @ ( sK8_SY257 @ SV78 @ SV32 ) @ ( product_Pair_pi_pi @ ( sK12_SY433 @ SV78 @ SV32 ) @ ( sK16_SY437 @ SV78 @ SV32 ) ) ) )
= $false )
| ( ( SV32 @ SV78 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[774]) ).
thf(805,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $false )
| ( ( ~ ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[776]) ).
thf(806,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) )
= $false )
| ( ( ~ ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[776]) ).
thf(807,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(808,plain,
! [SV147: pi,SV88: pi,SV124: pi,SV42: pi] :
( ( ( ( SV42 != SV124 )
| ( SV88 != SV147 ) )
= $false )
| ( ( ( product_Pair_pi_pi @ SV42 @ SV88 )
= ( product_Pair_pi_pi @ SV124 @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(809,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(810,plain,
! [SV44: product_prod_pi_pi] :
( ( SV44
= ( product_Pair_pi_pi @ ( sK2_SY290 @ SV44 ) @ ( sK13_SY417 @ SV44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(811,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ( ~ ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) ) )
= $false )
| ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(812,plain,
! [SV4: product_prod_pi_pi,SV53: product_prod_pi_pi > $o] :
( ( ( ~ ( SV53 @ SV4 ) )
= $false )
| ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(813,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ( ~ ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) ) )
= $false )
| ( ( SV53 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(814,plain,
! [SV4: product_prod_pi_pi,SV53: product_prod_pi_pi > $o] :
( ( ( ~ ( SV53 @ SV4 ) )
= $false )
| ( ( SV53 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(815,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $false )
| ( ( ~ ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(816,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false )
| ( ( ~ ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(817,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( SV11 = $false )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(818,plain,
! [SV11: $o] :
( ( ( ~ $true ) = $false )
| ( SV11 = $false )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[788]) ).
thf(819,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( $true = $false )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(820,plain,
! [SV11: $o] :
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(821,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $false )
= $false )
| ( SV11 = $false )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(822,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $false )
= $false )
| ( $false = $false )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(823,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(824,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(825,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(826,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(827,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(828,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(829,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(830,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(831,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[797]) ).
thf(832,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[797]) ).
thf(833,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(834,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(835,plain,
! [SV137: name,SV68: pi,SV107: name,SV21: name] :
( ( ( SV21 != SV107 )
= $false )
| ( ( fresh_name_pi @ SV21 @ ( subs @ SV68 @ SV137 @ SV107 ) )
= $true )
| ( ( fresh_name_pi @ SV21 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(836,plain,
! [SV71: name,SV139: pi,SV110: name,SV24: name] :
( ( ( ~ ( ( SV24 != SV110 ) ) )
= $true )
| ( ( ( subs @ ( res @ SV24 @ SV139 ) @ SV71 @ SV110 )
= ( res @ SV24 @ ( subs @ SV139 @ SV71 @ SV110 ) ) )
= $true )
| ( ( SV24 = SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(837,plain,
! [SV111: pi,SV72: pi,SV25: set_Pr1834926343_pi_pi] :
( ( ( ~ ! [SY236: pi,SY237: pi,SY238: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ SY236 @ SY237 ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SY238 @ SY236 ) @ ( res @ SY238 @ SY237 ) ) @ SV25 ) ) )
= $true )
| ( ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) )
= $true )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) ) @ ( par @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) ) ) @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(838,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $false )
| ( ( ~ ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
| ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[803]) ).
thf(839,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) )
= $false )
| ( ( ~ ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
| ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[803]) ).
thf(840,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(841,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) )
= $true )
| ( ( ~ ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(842,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(843,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(844,plain,
! [SV147: pi,SV88: pi,SV124: pi,SV42: pi] :
( ( ( SV42 != SV124 )
= $false )
| ( ( ( product_Pair_pi_pi @ SV42 @ SV88 )
= ( product_Pair_pi_pi @ SV124 @ SV147 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[808]) ).
thf(845,plain,
! [SV124: pi,SV42: pi,SV147: pi,SV88: pi] :
( ( ( SV88 != SV147 )
= $false )
| ( ( ( product_Pair_pi_pi @ SV42 @ SV88 )
= ( product_Pair_pi_pi @ SV124 @ SV147 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[808]) ).
thf(846,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(847,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(848,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
= $true )
| ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(849,plain,
! [SV4: product_prod_pi_pi,SV53: product_prod_pi_pi > $o] :
( ( ( SV53 @ SV4 )
= $true )
| ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(850,plain,
! [SV53: product_prod_pi_pi > $o,SV4: product_prod_pi_pi] :
( ( ( member558706512_pi_pi @ SV4 @ ( collec1051790738_pi_pi @ SV53 ) )
= $true )
| ( ( SV53 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(851,plain,
! [SV4: product_prod_pi_pi,SV53: product_prod_pi_pi > $o] :
( ( ( SV53 @ SV4 )
= $true )
| ( ( SV53 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(852,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) ) )
= $false )
| ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(853,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ! [SV159: name] :
( ( abs_fun_name_pi @ SV8 @ SV56 @ SV159 )
= ( abs_fun_name_pi @ SV96 @ SV130 @ SV159 ) ) )
= $false )
| ( ( ~ ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[816]) ).
thf(854,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false )
| ( ( ~ ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[816]) ).
thf(855,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( SV11 = $false )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(856,plain,
! [SV11: $o] :
( ( $true = $true )
| ( SV11 = $false )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(857,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( $true = $false )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(858,plain,
! [SV11: $o] :
( ( $true = $true )
| ( $true = $false )
| ( ( SV11 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(859,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( SV11 = $false )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[821]) ).
thf(860,plain,
! [SV11: $o] :
( ( ( ~ $false ) = $false )
| ( SV11 = $false )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[821]) ).
thf(861,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( $false = $false )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(862,plain,
! [SV11: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(863,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(864,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(865,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(866,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(867,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[827]) ).
thf(868,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[827]) ).
thf(869,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[828]) ).
thf(870,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[828]) ).
thf(871,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(872,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(873,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(874,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(875,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(876,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(877,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(878,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(879,plain,
! [SV137: name,SV68: pi,SV107: name,SV21: name] :
( ( ( SV21 = SV107 )
= $true )
| ( ( fresh_name_pi @ SV21 @ ( subs @ SV68 @ SV137 @ SV107 ) )
= $true )
| ( ( fresh_name_pi @ SV21 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(880,plain,
! [SV71: name,SV139: pi,SV110: name,SV24: name] :
( ( ( SV24 != SV110 )
= $false )
| ( ( ( subs @ ( res @ SV24 @ SV139 ) @ SV71 @ SV110 )
= ( res @ SV24 @ ( subs @ SV139 @ SV71 @ SV110 ) ) )
= $true )
| ( ( SV24 = SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(881,plain,
! [SV111: pi,SV72: pi,SV25: set_Pr1834926343_pi_pi] :
( ( ( ! [SY236: pi,SY237: pi,SY238: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ SY236 @ SY237 ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SY238 @ SY236 ) @ ( res @ SY238 @ SY237 ) ) @ SV25 ) ) )
= $false )
| ( ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) )
= $true )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) ) @ ( par @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) ) ) @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(882,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
| ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) )
= $false )
| ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(883,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( ( SV27 != SV113 )
| ( SV74 != SV140 ) )
= $true )
| ( ( ~ ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
| ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(884,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(885,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(886,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ SV83 ) )
= $true )
| ( ( ~ ( fresh_name_pi @ SV37 @ SV119 ) )
= $true )
| ( ( ~ ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(887,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) )
= $false )
| ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(888,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( ( SV38 != SV120 )
| ( SV84 != SV144 ) )
= $true )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[843]) ).
thf(889,plain,
! [SV147: pi,SV88: pi,SV124: pi,SV42: pi] :
( ( ( SV42 = SV124 )
= $true )
| ( ( ( product_Pair_pi_pi @ SV42 @ SV88 )
= ( product_Pair_pi_pi @ SV124 @ SV147 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[844]) ).
thf(890,plain,
! [SV124: pi,SV42: pi,SV147: pi,SV88: pi] :
( ( ( SV88 = SV147 )
= $true )
| ( ( ( product_Pair_pi_pi @ SV42 @ SV88 )
= ( product_Pair_pi_pi @ SV124 @ SV147 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(891,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) )
= $false )
| ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(892,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( ( SV43 != SV125 )
| ( SV89 != SV148 ) )
= $true )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(893,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
= $false )
| ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(894,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false )
| ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(895,plain,
! [SV96: name,SV130: pi,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) )
= ( abs_fun_name_pi @ SV96 @ SV130 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) ) )
= $false )
| ( ( ~ ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[853]) ).
thf(896,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) ) )
= $false )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(897,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $false )
| ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[855]) ).
thf(898,plain,
! [SV11: $o] :
( ( ( SV11 = $false )
= $true )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[855]) ).
thf(899,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $false )
| ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[856]) ).
thf(900,plain,
! [SV11: $o] :
( ( ( SV11 = $false )
= $true )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[856]) ).
thf(901,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $false )
| ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[857]) ).
thf(902,plain,
! [SV11: $o] :
( ( ( SV11 = $false )
= $true )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[857]) ).
thf(903,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $false )
| ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[858]) ).
thf(904,plain,
! [SV11: $o] :
( ( ( SV11 = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[858]) ).
thf(905,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( SV11 = $false )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[859]) ).
thf(906,plain,
! [SV11: $o] :
( ( $false = $true )
| ( SV11 = $false )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[860]) ).
thf(907,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( $false = $false )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(908,plain,
! [SV11: $o] :
( ( $false = $true )
| ( $false = $false )
| ( ( SV11 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(909,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[863]) ).
thf(910,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[863]) ).
thf(911,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[864]) ).
thf(912,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[864]) ).
thf(913,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[865]) ).
thf(914,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[865]) ).
thf(915,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[866]) ).
thf(916,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[866]) ).
thf(917,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(918,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(919,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(920,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[870]) ).
thf(921,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[871]) ).
thf(922,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[871]) ).
thf(923,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[872]) ).
thf(924,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[872]) ).
thf(925,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[873]) ).
thf(926,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[873]) ).
thf(927,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[874]) ).
thf(928,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[874]) ).
thf(929,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(930,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(931,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(932,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(933,plain,
! [SV71: name,SV139: pi,SV110: name,SV24: name] :
( ( ( SV24 = SV110 )
= $true )
| ( ( ( subs @ ( res @ SV24 @ SV139 ) @ SV71 @ SV110 )
= ( res @ SV24 @ ( subs @ SV139 @ SV71 @ SV110 ) ) )
= $true )
| ( ( SV24 = SV71 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[880]) ).
thf(934,plain,
! [SV25: set_Pr1834926343_pi_pi,SV72: pi,SV111: pi] :
( ( ( ! [SY438: pi,SY439: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( sK18_SY236 @ SV111 @ SV72 @ SV25 ) @ SY438 ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SY439 @ ( sK18_SY236 @ SV111 @ SV72 @ SV25 ) ) @ ( res @ SY439 @ SY438 ) ) @ SV25 ) ) )
= $false )
| ( ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) )
= $true )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) ) @ ( par @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) ) ) @ SV25 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[881]) ).
thf(935,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
= $false )
| ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[882]) ).
thf(936,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) )
= $false )
| ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[882]) ).
thf(937,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( SV27 != SV113 )
= $true )
| ( ( SV74 != SV140 )
= $true )
| ( ( ~ ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
| ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(938,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $true )
| ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[884]) ).
thf(939,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) )
= $true )
| ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(940,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( ~ ( fresh_name_pi @ SV37 @ SV119 ) )
= $true )
| ( ( ~ ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(941,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false )
| ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(942,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) )
= $false )
| ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(943,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( SV38 != SV120 )
= $true )
| ( ( SV84 != SV144 )
= $true )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(944,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false )
| ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[891]) ).
thf(945,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) )
= $false )
| ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[891]) ).
thf(946,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( SV43 != SV125 )
= $true )
| ( ( SV89 != SV148 )
= $true )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(947,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $true )
| ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(948,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $true )
| ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(949,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
| ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) ) )
= $false )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) )
= ( abs_fun_name_pi @ SV96 @ SV130 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(950,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
= $false )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(951,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(952,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $false ) )
= $true )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(953,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $false ) )
= $true )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(954,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $false ) )
= $true )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(955,plain,
! [SV11: $o] :
( ( ( ~ ( SV11
| $false ) )
= $true )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(956,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(957,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(958,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(959,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(960,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(961,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(962,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(963,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(964,plain,
! [SV25: set_Pr1834926343_pi_pi,SV72: pi,SV111: pi] :
( ( ( ! [SY440: name] :
( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( sK18_SY236 @ SV111 @ SV72 @ SV25 ) @ ( sK19_SY438 @ SV25 @ SV72 @ SV111 ) ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ SY440 @ ( sK18_SY236 @ SV111 @ SV72 @ SV25 ) ) @ ( res @ SY440 @ ( sK19_SY438 @ SV25 @ SV72 @ SV111 ) ) ) @ SV25 ) ) )
= $false )
| ( ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) )
= $true )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) ) @ ( par @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) ) ) @ SV25 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[934]) ).
thf(965,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $true )
| ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(966,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) )
= $true )
| ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[936]) ).
thf(967,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( SV27 = SV113 )
= $false )
| ( ( SV74 != SV140 )
= $true )
| ( ( ~ ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
| ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(968,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(969,plain,
! [SV83: pi,SV119: pi,SV37: name] :
( ( ( fresh_name_pi @ SV37 @ SV119 )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( ~ ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(970,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $true )
| ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(971,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) )
= $true )
| ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(972,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( SV38 = SV120 )
= $false )
| ( ( SV84 != SV144 )
= $true )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(973,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $true )
| ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(974,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) )
= $true )
| ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(975,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( SV43 = SV125 )
= $false )
| ( ( SV89 != SV148 )
= $true )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(976,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ! [SV160: name] :
( ( abs_fun_name_pi @ SV8 @ SV56 @ SV160 )
= ( abs_fun_name_pi @ SV96 @ SV130 @ SV160 ) ) )
= $true )
| ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[948]) ).
thf(977,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $true )
| ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[948]) ).
thf(978,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( res @ SV8 @ SV56 )
!= ( res @ SV96 @ SV130 ) )
= $false )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) )
= ( abs_fun_name_pi @ SV96 @ SV130 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(979,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
!= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) )
= ( abs_fun_name_pi @ SV96 @ SV130 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(980,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $true )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(981,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $true )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(982,plain,
! [SV11: $o] :
( ( ( SV11
| $false )
= $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(983,plain,
! [SV11: $o] :
( ( ( SV11
| $false )
= $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(984,plain,
! [SV11: $o] :
( ( ( SV11
| $false )
= $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(985,plain,
! [SV11: $o] :
( ( ( SV11
| $false )
= $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(986,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(987,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(988,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(989,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(990,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(991,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(992,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(993,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(994,plain,
! [SV25: set_Pr1834926343_pi_pi,SV72: pi,SV111: pi] :
( ( ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( sK18_SY236 @ SV111 @ SV72 @ SV25 ) @ ( sK19_SY438 @ SV25 @ SV72 @ SV111 ) ) @ SV25 )
| ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ ( sK20_SY440 @ SV25 @ SV72 @ SV111 ) @ ( sK18_SY236 @ SV111 @ SV72 @ SV25 ) ) @ ( res @ ( sK20_SY440 @ SV25 @ SV72 @ SV111 ) @ ( sK19_SY438 @ SV25 @ SV72 @ SV111 ) ) ) @ SV25 ) )
= $false )
| ( ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) )
= $true )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) ) @ ( par @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) ) ) @ SV25 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[964]) ).
thf(995,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( ( SV27 != SV113 )
| ( SV74 != SV140 ) )
= $false )
| ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(996,plain,
! [SV113: pi,SV27: pi,SV140: pi,SV74: pi] :
( ( ( SV74 = SV140 )
= $false )
| ( ( SV27 = SV113 )
= $false )
| ( ( ~ ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
| ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(997,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ SV83 ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[968]) ).
thf(998,plain,
! [SV83: pi,SV119: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ SV119 ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[968]) ).
thf(999,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
| ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(1000,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( ( SV38 != SV120 )
| ( SV84 != SV144 ) )
= $false )
| ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1001,plain,
! [SV120: pi,SV38: pi,SV144: pi,SV84: pi] :
( ( ( SV84 = SV144 )
= $false )
| ( ( SV38 = SV120 )
= $false )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1002,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( ( SV43 != SV125 )
| ( SV89 != SV148 ) )
= $false )
| ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1003,plain,
! [SV125: pi,SV43: pi,SV148: pi,SV89: pi] :
( ( ( SV89 = SV148 )
= $false )
| ( ( SV43 = SV125 )
= $false )
| ( ( ~ ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1004,plain,
! [SV130: pi,SV96: name,SV161: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ SV161 )
= ( abs_fun_name_pi @ SV96 @ SV130 @ SV161 ) )
= $true )
| ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1005,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( res @ SV8 @ SV56 )
= ( res @ SV96 @ SV130 ) )
= $true )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) )
= ( abs_fun_name_pi @ SV96 @ SV130 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(1006,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $true )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) )
= ( abs_fun_name_pi @ SV96 @ SV130 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[979]) ).
thf(1007,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ! [SV162: name] :
( ( abs_fun_name_pi @ SV8 @ SV56 @ SV162 )
= ( abs_fun_name_pi @ SV96 @ SV130 @ SV162 ) ) )
= $true )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[981]) ).
thf(1008,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $true )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[981]) ).
thf(1009,plain,
! [SV11: $o] :
( ( SV11 = $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1010,plain,
! [SV11: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1011,plain,
! [SV11: $o] :
( ( SV11 = $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1012,plain,
! [SV11: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1013,plain,
! [SV11: $o] :
( ( SV11 = $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[984]) ).
thf(1014,plain,
! [SV11: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[984]) ).
thf(1015,plain,
! [SV11: $o] :
( ( SV11 = $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1016,plain,
! [SV11: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV11
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1017,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1018,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1019,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[987]) ).
thf(1020,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[987]) ).
thf(1021,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1022,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1023,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1024,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1025,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1026,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1027,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[991]) ).
thf(1028,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[991]) ).
thf(1029,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1030,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1031,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1032,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1033,plain,
! [SV25: set_Pr1834926343_pi_pi,SV72: pi,SV111: pi] :
( ( ( ~ ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( sK18_SY236 @ SV111 @ SV72 @ SV25 ) @ ( sK19_SY438 @ SV25 @ SV72 @ SV111 ) ) @ SV25 ) )
= $false )
| ( ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) )
= $true )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) ) @ ( par @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) ) ) @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1034,plain,
! [SV111: pi,SV72: pi,SV25: set_Pr1834926343_pi_pi] :
( ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ ( sK20_SY440 @ SV25 @ SV72 @ SV111 ) @ ( sK18_SY236 @ SV111 @ SV72 @ SV25 ) ) @ ( res @ ( sK20_SY440 @ SV25 @ SV72 @ SV111 ) @ ( sK19_SY438 @ SV25 @ SV72 @ SV111 ) ) ) @ SV25 )
= $false )
| ( ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) )
= $true )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) ) @ ( par @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) ) ) @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1035,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( SV27 != SV113 )
= $false )
| ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[995]) ).
thf(1036,plain,
! [SV113: pi,SV27: pi,SV140: pi,SV74: pi] :
( ( ( SV74 != SV140 )
= $false )
| ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[995]) ).
thf(1037,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
| ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) )
= $false )
| ( ( SV27 = SV113 )
= $false )
| ( ( SV74 = SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1038,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( fresh_name_pi @ SV37 @ SV83 )
= $true )
| ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1039,plain,
! [SV83: pi,SV119: pi,SV37: name] :
( ( ( fresh_name_pi @ SV37 @ SV119 )
= $true )
| ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1040,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1041,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1042,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( SV38 != SV120 )
= $false )
| ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1000]) ).
thf(1043,plain,
! [SV120: pi,SV38: pi,SV144: pi,SV84: pi] :
( ( ( SV84 != SV144 )
= $false )
| ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1000]) ).
thf(1044,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
| ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) )
= $false )
| ( ( SV38 = SV120 )
= $false )
| ( ( SV84 = SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1045,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( SV43 != SV125 )
= $false )
| ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1046,plain,
! [SV125: pi,SV43: pi,SV148: pi,SV89: pi] :
( ( ( SV89 != SV148 )
= $false )
| ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1047,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
| ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) )
= $false )
| ( ( SV43 = SV125 )
= $false )
| ( ( SV89 = SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1048,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ! [SV163: name] :
( ( abs_fun_name_pi @ SV8 @ SV56 @ SV163 )
= ( abs_fun_name_pi @ SV96 @ SV130 @ SV163 ) ) )
= $true )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) )
= ( abs_fun_name_pi @ SV96 @ SV130 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1006]) ).
thf(1049,plain,
! [SV130: pi,SV96: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $true )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) )
= ( abs_fun_name_pi @ SV96 @ SV130 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1006]) ).
thf(1050,plain,
! [SV130: pi,SV96: name,SV164: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ SV164 )
= ( abs_fun_name_pi @ SV96 @ SV130 @ SV164 ) )
= $true )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 )
= ( abs_fun_name_pi @ SV96 @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1051,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $false )
= $false )
| ( SV11 = $false )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1052,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $false )
= $false )
| ( $false = $false )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1053,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $false )
= $false )
| ( SV11 = $false )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1054,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $false )
= $false )
| ( $false = $false )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1055,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $false )
= $false )
| ( SV11 = $false )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1056,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1057,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $false )
= $false )
| ( SV11 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1058,plain,
! [SV11: $o] :
( ( ( ~ SV11
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1059,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1060,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1061,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1062,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1063,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1064,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1065,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1066,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1067,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1068,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1069,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1070,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1071,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1072,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1073,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1074,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1075,plain,
! [SV25: set_Pr1834926343_pi_pi,SV72: pi,SV111: pi] :
( ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( sK18_SY236 @ SV111 @ SV72 @ SV25 ) @ ( sK19_SY438 @ SV25 @ SV72 @ SV111 ) ) @ SV25 )
= $true )
| ( ( strong743114133lation @ ( par @ SV72 @ SV111 ) @ SV25 @ ( par @ SV111 @ SV72 ) )
= $true )
| ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) ) @ ( par @ ( sK15_SY436 @ SV25 @ SV72 @ SV111 ) @ ( sK10_SY234 @ SV111 @ SV72 @ SV25 ) ) ) @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1076,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( SV27 = SV113 )
= $true )
| ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1035]) ).
thf(1077,plain,
! [SV113: pi,SV27: pi,SV140: pi,SV74: pi] :
( ( ( SV74 = SV140 )
= $true )
| ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1078,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ( ( par @ SV27 @ SV74 )
!= ( par @ SV113 @ SV140 ) )
= $false )
| ( ( SV27 = SV113 )
= $false )
| ( ( SV74 = SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1037]) ).
thf(1079,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( ~ ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) )
= $false )
| ( ( SV27 = SV113 )
= $false )
| ( ( SV74 = SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1037]) ).
thf(1080,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( fresh_name_pi @ SV37 @ ( par @ SV83 @ SV119 ) )
= $true )
| ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1081,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) ) )
= $true )
| ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1082,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( SV38 = SV120 )
= $true )
| ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1083,plain,
! [SV120: pi,SV38: pi,SV144: pi,SV84: pi] :
( ( ( SV84 = SV144 )
= $true )
| ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1084,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
!= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $false )
| ( ( SV38 = SV120 )
= $false )
| ( ( SV84 = SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1085,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( ~ ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) )
= $false )
| ( ( SV38 = SV120 )
= $false )
| ( ( SV84 = SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1086,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( SV43 = SV125 )
= $true )
| ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1087,plain,
! [SV125: pi,SV43: pi,SV148: pi,SV89: pi] :
( ( ( SV89 = SV148 )
= $true )
| ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1046]) ).
thf(1088,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
!= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $false )
| ( ( SV43 = SV125 )
= $false )
| ( ( SV89 = SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1089,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( ~ ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) )
= $false )
| ( ( SV43 = SV125 )
= $false )
| ( ( SV89 = SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1090,plain,
! [SV130: pi,SV96: name,SV165: name,SV56: pi,SV8: name] :
( ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ SV165 )
= ( abs_fun_name_pi @ SV96 @ SV130 @ SV165 ) )
= $true )
| ( ( ( abs_fun_name_pi @ SV8 @ SV56 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) )
= ( abs_fun_name_pi @ SV96 @ SV130 @ ( sK17_SV159 @ SV130 @ SV96 @ SV56 @ SV8 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1091,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( SV11 = $false )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1092,plain,
! [SV11: $o] :
( ( ( ~ $false ) = $false )
| ( SV11 = $false )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1093,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( $false = $false )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1094,plain,
! [SV11: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1095,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( SV11 = $false )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1096,plain,
! [SV11: $o] :
( ( ( ~ $false ) = $false )
| ( SV11 = $false )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1097,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( $false = $false )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1098,plain,
! [SV11: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1099,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( SV11 = $false )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1100,plain,
! [SV11: $o] :
( ( ( ~ $false ) = $false )
| ( SV11 = $false )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1101,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1102,plain,
! [SV11: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1103,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( SV11 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1104,plain,
! [SV11: $o] :
( ( ( ~ $false ) = $false )
| ( SV11 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1105,plain,
! [SV11: $o] :
( ( ( ~ SV11 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1106,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1107,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1108,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1109,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1110,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1111,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1112,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1113,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1114,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1115,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1116,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1063]) ).
thf(1117,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1118,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1064]) ).
thf(1119,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1120,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1121,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1122,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1123,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1124,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1125,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1126,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1127,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1128,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1069]) ).
thf(1129,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1130,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1131,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1132,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1133,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1072]) ).
thf(1134,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1072]) ).
thf(1135,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1136,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1137,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1074]) ).
thf(1138,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1074]) ).
thf(1139,plain,
! [SV140: pi,SV113: pi,SV74: pi,SV27: pi] :
( ( ( ( par @ SV27 @ SV74 )
= ( par @ SV113 @ SV140 ) )
= $true )
| ( ( SV27 = SV113 )
= $false )
| ( ( SV74 = SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1140,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( ~ ( ( SV27 != SV113 )
| ( SV74 != SV140 ) ) )
= $true )
| ( ( SV27 = SV113 )
= $false )
| ( ( SV74 = SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1141,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ SV83 )
| ~ ( fresh_name_pi @ SV37 @ SV119 ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1142,plain,
! [SV144: pi,SV120: pi,SV84: pi,SV38: pi] :
( ( ( ( product_Pair_pi_pi @ SV38 @ SV84 )
= ( product_Pair_pi_pi @ SV120 @ SV144 ) )
= $true )
| ( ( SV38 = SV120 )
= $false )
| ( ( SV84 = SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1143,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( ~ ( ( SV38 != SV120 )
| ( SV84 != SV144 ) ) )
= $true )
| ( ( SV38 = SV120 )
= $false )
| ( ( SV84 = SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1144,plain,
! [SV148: pi,SV125: pi,SV89: pi,SV43: pi] :
( ( ( ( product_Pair_pi_pi @ SV43 @ SV89 )
= ( product_Pair_pi_pi @ SV125 @ SV148 ) )
= $true )
| ( ( SV43 = SV125 )
= $false )
| ( ( SV89 = SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1088]) ).
thf(1145,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( ~ ( ( SV43 != SV125 )
| ( SV89 != SV148 ) ) )
= $true )
| ( ( SV43 = SV125 )
= $false )
| ( ( SV89 = SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1089]) ).
thf(1146,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( SV11 = $false )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1147,plain,
! [SV11: $o] :
( ( $false = $true )
| ( SV11 = $false )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1148,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( $false = $false )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1149,plain,
! [SV11: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV11 = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1150,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( SV11 = $false )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1151,plain,
! [SV11: $o] :
( ( $false = $true )
| ( SV11 = $false )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1096]) ).
thf(1152,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( $false = $false )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1153,plain,
! [SV11: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV11 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1154,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( SV11 = $false )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1155,plain,
! [SV11: $o] :
( ( $false = $true )
| ( SV11 = $false )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1100]) ).
thf(1156,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1101]) ).
thf(1157,plain,
! [SV11: $o] :
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV11 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1158,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( SV11 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1159,plain,
! [SV11: $o] :
( ( $false = $true )
| ( SV11 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1160,plain,
! [SV11: $o] :
( ( SV11 = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1161,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1162,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1163,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1164,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1165,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1166,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1167,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1168,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1169,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1170,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1115]) ).
thf(1171,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1116]) ).
thf(1172,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1117]) ).
thf(1173,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1174,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1175,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1176,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1177,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1178,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1179,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1180,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1181,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1182,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1183,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1184,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1185,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1186,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1131]) ).
thf(1187,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1132]) ).
thf(1188,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1133]) ).
thf(1189,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1190,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1135]) ).
thf(1191,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1136]) ).
thf(1192,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1193,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1138]) ).
thf(1194,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( ( SV27 != SV113 )
| ( SV74 != SV140 ) )
= $false )
| ( ( SV27 = SV113 )
= $false )
| ( ( SV74 = SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1195,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ SV83 ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1141]) ).
thf(1196,plain,
! [SV83: pi,SV119: pi,SV37: name] :
( ( ( ~ ( fresh_name_pi @ SV37 @ SV119 ) )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1141]) ).
thf(1197,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( ( SV38 != SV120 )
| ( SV84 != SV144 ) )
= $false )
| ( ( SV38 = SV120 )
= $false )
| ( ( SV84 = SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1198,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( ( SV43 != SV125 )
| ( SV89 != SV148 ) )
= $false )
| ( ( SV43 = SV125 )
= $false )
| ( ( SV89 = SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1199,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( SV27 != SV113 )
= $false )
| ( ( SV27 = SV113 )
= $false )
| ( ( SV74 = SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1194]) ).
thf(1200,plain,
! [SV113: pi,SV27: pi,SV140: pi,SV74: pi] :
( ( ( SV74 != SV140 )
= $false )
| ( ( SV27 = SV113 )
= $false )
| ( ( SV74 = SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1194]) ).
thf(1201,plain,
! [SV119: pi,SV83: pi,SV37: name] :
( ( ( fresh_name_pi @ SV37 @ SV83 )
= $true )
| ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1195]) ).
thf(1202,plain,
! [SV83: pi,SV119: pi,SV37: name] :
( ( ( fresh_name_pi @ SV37 @ SV119 )
= $true )
| ( ( fresh_name_pi @ SV37 @ SV83 )
= $false )
| ( ( fresh_name_pi @ SV37 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1196]) ).
thf(1203,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( SV38 != SV120 )
= $false )
| ( ( SV38 = SV120 )
= $false )
| ( ( SV84 = SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1197]) ).
thf(1204,plain,
! [SV120: pi,SV38: pi,SV144: pi,SV84: pi] :
( ( ( SV84 != SV144 )
= $false )
| ( ( SV38 = SV120 )
= $false )
| ( ( SV84 = SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1197]) ).
thf(1205,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( SV43 != SV125 )
= $false )
| ( ( SV43 = SV125 )
= $false )
| ( ( SV89 = SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1206,plain,
! [SV125: pi,SV43: pi,SV148: pi,SV89: pi] :
( ( ( SV89 != SV148 )
= $false )
| ( ( SV43 = SV125 )
= $false )
| ( ( SV89 = SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1207,plain,
! [SV140: pi,SV74: pi,SV113: pi,SV27: pi] :
( ( ( SV27 = SV113 )
= $true )
| ( ( SV27 = SV113 )
= $false )
| ( ( SV74 = SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1208,plain,
! [SV113: pi,SV27: pi,SV140: pi,SV74: pi] :
( ( ( SV74 = SV140 )
= $true )
| ( ( SV27 = SV113 )
= $false )
| ( ( SV74 = SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1209,plain,
! [SV144: pi,SV84: pi,SV120: pi,SV38: pi] :
( ( ( SV38 = SV120 )
= $true )
| ( ( SV38 = SV120 )
= $false )
| ( ( SV84 = SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1210,plain,
! [SV120: pi,SV38: pi,SV144: pi,SV84: pi] :
( ( ( SV84 = SV144 )
= $true )
| ( ( SV38 = SV120 )
= $false )
| ( ( SV84 = SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1204]) ).
thf(1211,plain,
! [SV148: pi,SV89: pi,SV125: pi,SV43: pi] :
( ( ( SV43 = SV125 )
= $true )
| ( ( SV43 = SV125 )
= $false )
| ( ( SV89 = SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1205]) ).
thf(1212,plain,
! [SV125: pi,SV43: pi,SV148: pi,SV89: pi] :
( ( ( SV89 = SV148 )
= $true )
| ( ( SV43 = SV125 )
= $false )
| ( ( SV89 = SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1206]) ).
thf(1213,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[402,1212,1211,1210,1209,1208,1207,1202,1201,1193,1192,1191,1190,1189,1188,1187,1186,1185,1184,1183,1182,1181,1180,1179,1178,1177,1176,1175,1174,1173,1172,1171,1170,1169,1168,1167,1166,1165,1164,1163,1162,1161,1160,1159,1158,1157,1156,1155,1154,1153,1152,1151,1150,1149,1148,1147,1146,1144,1142,1139,1090,1087,1086,1083,1082,1080,1077,1076,1075,1050,1049,1039,1038,1034,1008,1005,1004,980,977,973,970,965,947,938,933,932,931,930,929,928,926,924,922,920,919,918,917,916,914,912,910,908,907,906,905,904,902,900,898,890,889,879,851,850,849,848,810,804,784,783,782,778,775,773,772,771,767,766,764,763,762,761,748,746,742,739,737,734,733,727,726,719,718,707,696,692,681,670,669,667,664,661,658,655,638,622,609,607,606,558,556,555,550,518,513,504,411,408,407,406,405,404]) ).
thf(1214,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP188^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n011.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 11:19:36 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.54/1.39 ...
% 6.54/1.39
% 6.54/1.39 No.of.Axioms: 58
% 6.54/1.39
% 6.54/1.39 Length.of.Defs: 0
% 6.54/1.39
% 6.54/1.39 Contains.Choice.Funs: false
% 6.54/1.39 ........................
% 6.54/1.39
% 6.54/1.39 ********************************
% 6.54/1.39 * All subproblems solved! *
% 6.54/1.39 ********************************
% 6.54/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:58,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1213,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.54/1.39
% 6.54/1.39 %**** Beginning of derivation protocol ****
% 6.54/1.39 % SZS output start CNFRefutation
% See solution above
% 1.36/1.40
% 1.36/1.40 %**** End of derivation protocol ****
% 1.36/1.40 %**** no. of clauses in derivation: 934 ****
% 1.36/1.40 %**** clause counter: 1213 ****
% 1.36/1.40
% 1.36/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:58,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1213,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------