TSTP Solution File: ITP181^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP181^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:35 EDT 2024
% Result : Theorem 19.11s 5.64s
% Output : Refutation 20.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 288
% Syntax : Number of formulae : 495 ( 232 unt; 83 typ; 0 def)
% Number of atoms : 1218 ( 430 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 5309 ( 260 ~; 8 |; 116 &;4271 @)
% ( 0 <=>; 654 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Number of types : 36 ( 35 usr)
% Number of type conns : 184 ( 184 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 10 con; 0-5 aty)
% Number of variables : 1902 ( 8 ^1830 !; 64 ?;1902 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc1217648014ion_pi_type,type,
produc1217648014ion_pi: $tType ).
thf(produc1961110975reeRes_type,type,
produc1961110975reeRes: $tType ).
thf(set_Pr100209225_pi_pi_type,type,
set_Pr100209225_pi_pi: $tType ).
thf(produc1443308494i_name_type,type,
produc1443308494i_name: $tType ).
thf(produc1559976732_pi_pi_type,type,
produc1559976732_pi_pi: $tType ).
thf(produc53907987_pi_pi_type,type,
produc53907987_pi_pi: $tType ).
thf(set_Pr1569510577ion_pi_type,type,
set_Pr1569510577ion_pi: $tType ).
thf(produc1462499409ion_pi_type,type,
produc1462499409ion_pi: $tType ).
thf(set_Pr305743074reeRes_type,type,
set_Pr305743074reeRes: $tType ).
thf(noptio1575811931_pi_pi_type,type,
noptio1575811931_pi_pi: $tType ).
thf(set_Pr1294453099i_name_type,type,
set_Pr1294453099i_name: $tType ).
thf(produc1834551554reeRes_type,type,
produc1834551554reeRes: $tType ).
thf(set_Pr1694908217_pi_pi_type,type,
set_Pr1694908217_pi_pi: $tType ).
thf(set_Pr1654044726_pi_pi_type,type,
set_Pr1654044726_pi_pi: $tType ).
thf(produc405342261i_name_type,type,
produc405342261i_name: $tType ).
thf(produc629157763_pi_pi_type,type,
produc629157763_pi_pi: $tType ).
thf(produc1141751126_pi_pi_type,type,
produc1141751126_pi_pi: $tType ).
thf(produc1357834675reeRes_type,type,
produc1357834675reeRes: $tType ).
thf(produc2052722628s_name_type,type,
produc2052722628s_name: $tType ).
thf(produc2008547984reeRes_type,type,
produc2008547984reeRes: $tType ).
thf(produc992857746Res_pi_type,type,
produc992857746Res_pi: $tType ).
thf(produc649380958reeRes_type,type,
produc649380958reeRes: $tType ).
thf(set_Pr1834926343_pi_pi_type,type,
set_Pr1834926343_pi_pi: $tType ).
thf(produc367475239e_name_type,type,
produc367475239e_name: $tType ).
thf(product_prod_pi_name_type,type,
product_prod_pi_name: $tType ).
thf(product_prod_name_pi_type,type,
product_prod_name_pi: $tType ).
thf(product_prod_pi_pi_type,type,
product_prod_pi_pi: $tType ).
thf(noption_Late_freeRes_type,type,
noption_Late_freeRes: $tType ).
thf(noption_name_type,type,
noption_name: $tType ).
thf(noption_pi_type,type,
noption_pi: $tType ).
thf(late_residual_type,type,
late_residual: $tType ).
thf(late_subject_type,type,
late_subject: $tType ).
thf(late_freeRes_type,type,
late_freeRes: $tType ).
thf(name_type,type,
name: $tType ).
thf(pi_type,type,
pi: $tType ).
thf(input_type,type,
input: name > name > pi > pi ).
thf(output_type,type,
output: name > name > pi > pi ).
thf(par_type,type,
par: pi > pi > pi ).
thf(piNil_type,type,
piNil: pi ).
thf(res_type,type,
res: name > pi > pi ).
thf(sum_type,type,
sum: pi > pi > pi ).
thf(tau_type,type,
tau: pi > pi ).
thf(subs_type,type,
subs: pi > name > name > pi ).
thf(late_OutputR_type,type,
late_OutputR: name > name > late_freeRes ).
thf(late_TauR_type,type,
late_TauR: late_freeRes ).
thf(late_BoundR_type,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(late_FreeR_type,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(late_BoundOutputS_type,type,
late_BoundOutputS: name > late_subject ).
thf(late_InputS_type,type,
late_InputS: name > late_subject ).
thf(late_transitions_type,type,
late_transitions: pi > late_residual > $o ).
thf(abs_fun_name_pi_type,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(abs_fu385186459_pi_pi_type,type,
abs_fu385186459_pi_pi: name > produc1141751126_pi_pi > name > noptio1575811931_pi_pi ).
thf(fresh_2065563522_pi_pi_type,type,
fresh_2065563522_pi_pi: name > ( name > noptio1575811931_pi_pi ) > $o ).
thf(fresh_name_name_type,type,
fresh_name_name: name > name > $o ).
thf(fresh_name_pi_type,type,
fresh_name_pi: name > pi > $o ).
thf(fresh_1641682979reeRes_type,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(fresh_81631222sidual_type,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(fresh_717452603ubject_type,type,
fresh_717452603ubject: name > late_subject > $o ).
thf(fresh_93646139ame_pi_type,type,
fresh_93646139ame_pi: name > product_prod_name_pi > $o ).
thf(fresh_1376661020_pi_pi_type,type,
fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o ).
thf(fresh_261416607i_name_type,type,
fresh_261416607i_name: name > product_prod_pi_name > $o ).
thf(fresh_1627595501_pi_pi_type,type,
fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
thf(fresh_1504024600reeRes_type,type,
fresh_1504024600reeRes: name > produc649380958reeRes > $o ).
thf(fresh_1847501388Res_pi_type,type,
fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
thf(ord_le797229014_pi_pi_type,type,
ord_le797229014_pi_pi: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > $o ).
thf(produc1275980869_pi_pi_type,type,
produc1275980869_pi_pi: ( name > noption_pi ) > produc1141751126_pi_pi > produc53907987_pi_pi ).
thf(product_Pair_name_pi_type,type,
product_Pair_name_pi: name > pi > product_prod_name_pi ).
thf(produc235456326_pi_pi_type,type,
produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
thf(product_Pair_pi_name_type,type,
product_Pair_pi_name: pi > name > product_prod_pi_name ).
thf(product_Pair_pi_pi_type,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(produc1638681944reeRes_type,type,
produc1638681944reeRes: pi > late_freeRes > produc649380958reeRes ).
thf(produc1177552196Res_pi_type,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(eqvt_pi_type,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(strong2129052853vative_type,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(strong743114133lation_type,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(member540268543_pi_pi_type,type,
member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o ).
thf(member558706512_pi_pi_type,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(p_type,type,
p: pi ).
thf(pq_type,type,
pq: pi ).
thf(q_type,type,
q: pi ).
thf(a_type,type,
a: late_subject ).
thf(x_type,type,
x: name ).
thf(y_type,type,
y: name ).
thf(125,axiom,
! [A: produc53907987_pi_pi > $o,B: produc53907987_pi_pi] :
( ! [C: name > noption_pi,D: produc1141751126_pi_pi] : ( A @ ( produc1275980869_pi_pi @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_prod__cases) ).
thf(794,plain,
! [A: produc53907987_pi_pi > $o,B: produc53907987_pi_pi] :
( ! [C: name > noption_pi,D: produc1141751126_pi_pi] : ( A @ ( produc1275980869_pi_pi @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(119,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: late_freeRes] :
( ( eqvt_pi @ A )
=> ( ! [F: pi,G: name] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
=> ( ( G != C )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
=> ( ! [F: pi,G: late_subject,H: name] :
( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
=> ( ( fresh_717452603ubject @ C @ G )
=> ( ( C != H )
=> ( ( fresh_1641682979reeRes @ H @ E )
=> ? [I: pi] :
( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
& ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
=> ( ! [F: pi,G: late_freeRes] :
( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
=> ( ( fresh_1641682979reeRes @ C @ G )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
=> ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_resSimCases) ).
thf(760,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: late_freeRes] :
( ( eqvt_pi @ A )
=> ( ! [F: pi,G: name] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
=> ( ( G != C )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
=> ( ! [F: pi,G: late_subject,H: name] :
( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
=> ( ( fresh_717452603ubject @ C @ G )
=> ( ( C != H )
=> ( ( fresh_1641682979reeRes @ H @ E )
=> ? [I: pi] :
( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
& ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
=> ( ! [F: pi,G: late_freeRes] :
( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
=> ( ( fresh_1641682979reeRes @ C @ G )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
=> ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(166,axiom,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_old_Oprod_Oinject) ).
thf(1031,plain,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(9,axiom,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( tau @ A ) @ B )
=> ~ ! [C: pi] :
( ( ( tau @ A )
= ( tau @ C ) )
=> ( B
!= ( late_FreeR @ late_TauR @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_tauCases_H) ).
thf(234,plain,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( tau @ A ) @ B )
=> ~ ! [C: pi] :
( ( ( tau @ A )
= ( tau @ C ) )
=> ( B
!= ( late_FreeR @ late_TauR @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(153,axiom,
! [A: pi,B: late_subject,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_BoundR @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_tauBoundTrans) ).
thf(941,plain,
! [A: pi,B: late_subject,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_BoundR @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(120,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( F != B )
=> ( ( F != C )
=> ( ( fresh_name_pi @ F @ D )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_transitions_OComm2) ).
thf(777,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( F != B )
=> ( ( F != C )
=> ( ( fresh_name_pi @ F @ D )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(188,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_717452603ubject @ E @ B )
=> ( ( E != C )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_transitions_OResB) ).
thf(1110,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_717452603ubject @ E @ B )
=> ( ( E != C )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(41,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( A != B )
=> ( ( A != C )
=> ( ( subs @ ( res @ A @ D ) @ B @ C )
= ( res @ A @ ( subs @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_simps_I9_J) ).
thf(352,plain,
! [A: name,B: name,C: name,D: pi] :
( ( A != B )
=> ( ( A != C )
=> ( ( subs @ ( res @ A @ D ) @ B @ C )
= ( res @ A @ ( subs @ D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(182,axiom,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_sumCases_H) ).
thf(1083,plain,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(68,axiom,
! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_residual_Ostrong__inducts) ).
thf(468,plain,
! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(205,axiom,
fresh_717452603ubject @ y @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Bound_Ohyps_I4_J) ).
thf(1158,plain,
fresh_717452603ubject @ y @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(4,axiom,
! [A: late_freeRes > $o,B: late_freeRes] :
( ! [C: name,D: name] : ( A @ ( late_OutputR @ C @ D ) )
=> ( ( A @ late_TauR )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_freeRes_Oinducts) ).
thf(217,plain,
! [A: late_freeRes > $o,B: late_freeRes] :
( ! [C: name,D: name] : ( A @ ( late_OutputR @ C @ D ) )
=> ( ( A @ late_TauR )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,axiom,
! [A: name > noption_pi,B: produc1141751126_pi_pi,C: name > noption_pi,D: produc1141751126_pi_pi] :
( ( ( produc1275980869_pi_pi @ A @ B )
= ( produc1275980869_pi_pi @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Pair__inject) ).
thf(308,plain,
! [A: name > noption_pi,B: produc1141751126_pi_pi,C: name > noption_pi,D: produc1141751126_pi_pi] :
( ( ( produc1275980869_pi_pi @ A @ B )
= ( produc1275980869_pi_pi @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(149,axiom,
! [A: set_Pr1654044726_pi_pi,B: set_Pr1654044726_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] :
( ( member540268543_pi_pi @ ( produc235456326_pi_pi @ C @ D ) @ A )
=> ( member540268543_pi_pi @ ( produc235456326_pi_pi @ C @ D ) @ B ) )
=> ( ord_le797229014_pi_pi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_subrelI) ).
thf(873,plain,
! [A: set_Pr1654044726_pi_pi,B: set_Pr1654044726_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] :
( ( member540268543_pi_pi @ ( produc235456326_pi_pi @ C @ D ) @ A )
=> ( member540268543_pi_pi @ ( produc235456326_pi_pi @ C @ D ) @ B ) )
=> ( ord_le797229014_pi_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(169,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Late__Semantics_OPar2B) ).
thf(1041,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(196,axiom,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_freshRes) ).
thf(1137,plain,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(126,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_Late__Semantics_OfreeRes_Oinject) ).
thf(797,plain,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(176,axiom,
! [A: produc1141751126_pi_pi] :
? [B: name,C: product_prod_pi_pi] :
( A
= ( produc235456326_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_surj__pair) ).
thf(1063,plain,
! [A: produc1141751126_pi_pi] :
? [B: name,C: product_prod_pi_pi] :
( A
= ( produc235456326_pi_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(136,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_resTrans_I1_J) ).
thf(829,plain,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(193,axiom,
! [A: produc53907987_pi_pi] :
~ ! [B: name > noption_pi,C: name,D: pi,E: pi] :
( A
!= ( produc1275980869_pi_pi @ B @ ( produc235456326_pi_pi @ C @ ( product_Pair_pi_pi @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_prod__cases4) ).
thf(1127,plain,
! [A: produc53907987_pi_pi] :
~ ! [B: name > noption_pi,C: name,D: pi,E: pi] :
( A
!= ( produc1275980869_pi_pi @ B @ ( produc235456326_pi_pi @ C @ ( product_Pair_pi_pi @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(28,axiom,
! [A: name,B: pi,C: name,D: name,E: pi] :
~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_resTauOutputTrans) ).
thf(301,plain,
! [A: name,B: pi,C: name,D: name,E: pi] :
~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(93,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( output @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_pi_Odistinct_I31_J) ).
thf(565,plain,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( output @ A @ B @ C )
!= ( res @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(60,axiom,
! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
~ ( strong743114133lation @ piNil @ A @ ( input @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_nilSim_I2_J) ).
thf(436,plain,
! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
~ ( strong743114133lation @ piNil @ A @ ( input @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(122,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_Late__Semantics_OComm1) ).
thf(785,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(47,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: produc1141751126_pi_pi] :
( ( eqvt_pi @ A )
=> ( ! [E: late_subject,F: name,G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_name_pi @ F @ C )
=> ( ( fresh_name_pi @ F @ B )
=> ( ( fresh_717452603ubject @ F @ E )
=> ( ( fresh_1376661020_pi_pi @ F @ D )
=> ? [H: pi] :
( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
& ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
=> ( ! [E: late_freeRes,F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
=> ? [G: pi] :
( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
=> ( strong743114133lation @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_simCasesCont) ).
thf(372,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: produc1141751126_pi_pi] :
( ( eqvt_pi @ A )
=> ( ! [E: late_subject,F: name,G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_name_pi @ F @ C )
=> ( ( fresh_name_pi @ F @ B )
=> ( ( fresh_717452603ubject @ F @ E )
=> ( ( fresh_1376661020_pi_pi @ F @ D )
=> ? [H: pi] :
( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
& ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
=> ( ! [E: late_freeRes,F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
=> ? [G: pi] :
( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
=> ( strong743114133lation @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(143,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh_name_pi @ A @ ( sum @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_pi_Ofresh_I7_J) ).
thf(853,plain,
! [A: name,B: pi,C: pi] :
( ( fresh_name_pi @ A @ ( sum @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(200,axiom,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_Sum2) ).
thf(1147,plain,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(57,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( input @ A @ B @ C ) @ D )
=> ~ ! [E: name,F: name,G: pi] :
( ( ( A = F )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ G ) ) )
=> ( ( D
= ( late_BoundR @ ( late_InputS @ F ) @ E @ G ) )
=> ( E = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_inputCases_H) ).
thf(416,plain,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( input @ A @ B @ C ) @ D )
=> ~ ! [E: name,F: name,G: pi] :
( ( ( A = F )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ G ) ) )
=> ( ( D
= ( late_BoundR @ ( late_InputS @ F ) @ E @ G ) )
=> ( E = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(7,axiom,
! [A: name,B: name,C: pi,D: pi] :
~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ late_TauR @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_outputTauTrans) ).
thf(228,plain,
! [A: name,B: name,C: pi,D: pi] :
~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ late_TauR @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,axiom,
! [A: late_residual > $o,B: late_residual] :
( ! [C: late_subject,D: name,E: pi] : ( A @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [C: late_freeRes,D: pi] : ( A @ ( late_FreeR @ C @ D ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_residual_Oinducts) ).
thf(289,plain,
! [A: late_residual > $o,B: late_residual] :
( ! [C: late_subject,D: name,E: pi] : ( A @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [C: late_freeRes,D: pi] : ( A @ ( late_FreeR @ C @ D ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(70,axiom,
! [A: name > late_residual > $o,B: name,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_residual_Ostrong__inducts) ).
thf(475,plain,
! [A: name > late_residual > $o,B: name,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(62,axiom,
( fresh_name_name
= ( != @ name ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_name__fresh) ).
thf(443,plain,
( fresh_name_name
= ( ^ [A: name,B: name] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(72,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_nilSim_I1_J) ).
thf(485,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(81,axiom,
! [A: name,B: pi,C: late_freeRes,D: pi,E: pi > $o] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
=> ( ! [F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ C @ F ) )
=> ( ( fresh_1641682979reeRes @ A @ C )
=> ( E @ ( res @ A @ F ) ) ) )
=> ( E @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_resCasesF) ).
thf(514,plain,
! [A: name,B: pi,C: late_freeRes,D: pi,E: pi > $o] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
=> ( ! [F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ C @ F ) )
=> ( ( fresh_1641682979reeRes @ A @ C )
=> ( E @ ( res @ A @ F ) ) ) )
=> ( E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(129,axiom,
! [A: name] : ( fresh_name_pi @ A @ piNil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_pi_Ofresh_I1_J) ).
thf(806,plain,
! [A: name] : ( fresh_name_pi @ A @ piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(71,axiom,
! [A: name > late_residual > $o,B: name,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_residual_Ostrong__induct) ).
thf(480,plain,
! [A: name > late_residual > $o,B: name,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: name] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(51,axiom,
! [A: pi,B: pi,C: name,D: name] :
( ( subs @ ( par @ A @ B ) @ C @ D )
= ( par @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_simps_I8_J) ).
thf(396,plain,
! [A: pi,B: pi,C: name,D: name] :
( ( subs @ ( par @ A @ B ) @ C @ D )
= ( par @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(79,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh_name_pi @ A @ ( par @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_pi_Ofresh_I8_J) ).
thf(507,plain,
! [A: name,B: pi,C: pi] :
( ( fresh_name_pi @ A @ ( par @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(179,axiom,
! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_BoundR @ ( late_InputS @ E ) @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_resOutputInputTrans) ).
thf(1072,plain,
! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_BoundR @ ( late_InputS @ E ) @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(64,axiom,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_pi_Oinject_I2_J) ).
thf(453,plain,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(25,axiom,
! [A: name,B: late_freeRes,C: pi] :
( ( fresh_81631222sidual @ A @ ( late_FreeR @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_residual_Ofresh_I2_J) ).
thf(292,plain,
! [A: name,B: late_freeRes,C: pi] :
( ( fresh_81631222sidual @ A @ ( late_FreeR @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(61,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_pi_Odistinct_I29_J) ).
thf(439,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( par @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(88,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_Late__Semantics_OClose1) ).
thf(546,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(45,axiom,
! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
~ ( strong743114133lation @ piNil @ A @ ( output @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_nilSim_I3_J) ).
thf(366,plain,
! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
~ ( strong743114133lation @ piNil @ A @ ( output @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(171,axiom,
! [A: produc1141751126_pi_pi] :
~ ! [B: name] :
~ ( fresh_1376661020_pi_pi @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_name__exists__fresh) ).
thf(1047,plain,
! [A: produc1141751126_pi_pi] :
~ ! [B: name] :
~ ( fresh_1376661020_pi_pi @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(174,axiom,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Sum1) ).
thf(1057,plain,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(135,axiom,
! [A: product_prod_pi_pi] :
~ ! [B: pi,C: pi] :
( A
!= ( product_Pair_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_old_Oprod_Oexhaust) ).
thf(825,plain,
! [A: product_prod_pi_pi] :
~ ! [B: pi,C: pi] :
( A
!= ( product_Pair_pi_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(40,axiom,
! [A: name,B: name,C: name,D: pi,E: late_freeRes,F: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_FreeR @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_resInputFreeTrans) ).
thf(349,plain,
! [A: name,B: name,C: name,D: pi,E: late_freeRes,F: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_FreeR @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(97,axiom,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_FreeR @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_inputFreeTrans) ).
thf(598,plain,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_FreeR @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(92,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_pi_Odistinct_I79_J) ).
thf(561,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(20,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( sum @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_pi_Odistinct_I41_J) ).
thf(275,plain,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( sum @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(123,axiom,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_simps_I1_J) ).
thf(788,plain,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(151,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: pi] :
( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
( ( ( par @ A @ B )
= ( par @ F @ J ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( par @ I @ J ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_name_pi @ H @ F )
=> ( ( fresh_name_pi @ H @ J )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) )
=> ~ ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
( ( ( par @ A @ B )
= ( par @ J @ F ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( par @ J @ I ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_name_pi @ H @ J )
=> ( ( fresh_name_pi @ H @ F )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_parCasesB_H) ).
thf(879,plain,
! [A: pi,B: pi,C: late_subject,D: name,E: pi] :
( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
( ( ( par @ A @ B )
= ( par @ F @ J ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( par @ I @ J ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_name_pi @ H @ F )
=> ( ( fresh_name_pi @ H @ J )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) )
=> ~ ! [F: pi,G: late_subject,H: name,I: pi,J: pi] :
( ( ( par @ A @ B )
= ( par @ J @ F ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( par @ J @ I ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_name_pi @ H @ J )
=> ( ( fresh_name_pi @ H @ F )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(35,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_Late__Semantics_Osubject_Oinject_I2_J) ).
thf(329,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(181,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_pi_Odistinct_I81_J) ).
thf(1079,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(118,axiom,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( fresh_1641682979reeRes @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_freshFreeDerivative_I1_J) ).
thf(757,plain,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( fresh_1641682979reeRes @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(107,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( C != B )
=> ( ( fresh_name_pi @ C @ G )
=> ( ( F != B )
=> ( ( fresh_name_pi @ F @ D )
=> ( ( C != F )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_transitions_OClose1) ).
thf(682,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( C != B )
=> ( ( fresh_name_pi @ C @ G )
=> ( ( F != B )
=> ( ( fresh_name_pi @ F @ D )
=> ( ( C != F )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(206,axiom,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ a @ y @ pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Bound_Ohyps_I1_J) ).
thf(1159,plain,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ a @ y @ pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(67,axiom,
! [A: pi,B: pi,C: set_Pr1834926343_pi_pi] :
( ! [D: late_subject,E: name,F: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ F ) )
=> ( ( fresh_name_pi @ E @ B )
=> ? [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ C ) ) ) )
=> ( ! [D: late_freeRes,E: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ C ) ) )
=> ( strong743114133lation @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_simCases) ).
thf(461,plain,
! [A: pi,B: pi,C: set_Pr1834926343_pi_pi] :
( ! [D: late_subject,E: name,F: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ F ) )
=> ( ( fresh_name_pi @ E @ B )
=> ? [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ C ) ) ) )
=> ( ! [D: late_freeRes,E: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ C ) ) )
=> ( strong743114133lation @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(65,axiom,
( strong743114133lation
= ( ^ [A: pi,B: set_Pr1834926343_pi_pi,C: pi] :
( ! [D: late_subject,E: name,F: pi] :
( ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
& ( fresh_name_pi @ E @ A ) )
=> ? [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ B ) ) )
& ! [D: late_freeRes,E: pi] :
( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_simulation__def) ).
thf(456,plain,
( strong743114133lation
= ( ^ [A: pi,B: set_Pr1834926343_pi_pi,C: pi] :
( ! [D: late_subject,E: name,F: pi] :
( ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
& ( fresh_name_pi @ E @ A ) )
=> ? [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ B ) ) )
& ! [D: late_freeRes,E: pi] :
( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(140,axiom,
! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_resInputBoundOutputTrans) ).
thf(842,plain,
! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(110,axiom,
! [A: name,B: name,C: pi] :
( ( A != B )
=> ( late_transitions @ ( input @ B @ A @ C ) @ ( late_BoundR @ ( late_InputS @ B ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_transitions_OInput) ).
thf(697,plain,
! [A: name,B: name,C: pi] :
( ( A != B )
=> ( late_transitions @ ( input @ B @ A @ C ) @ ( late_BoundR @ ( late_InputS @ B ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(155,axiom,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
=> ~ ( fresh_717452603ubject @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_inputIneqTrans) ).
thf(948,plain,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
=> ~ ( fresh_717452603ubject @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(114,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: produc1141751126_pi_pi] :
( ( eqvt_pi @ A )
=> ( ! [F: pi,G: name] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
=> ( ( G != C )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
=> ( ! [F: pi,G: late_subject,H: name] :
( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
=> ( ( fresh_717452603ubject @ C @ G )
=> ( ( C != H )
=> ( ( fresh_1376661020_pi_pi @ H @ E )
=> ? [I: pi] :
( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
& ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
=> ( ! [F: pi,G: late_freeRes] :
( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
=> ( ( fresh_1641682979reeRes @ C @ G )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
=> ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_resSimCases) ).
thf(725,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: produc1141751126_pi_pi] :
( ( eqvt_pi @ A )
=> ( ! [F: pi,G: name] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
=> ( ( G != C )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
=> ( ! [F: pi,G: late_subject,H: name] :
( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
=> ( ( fresh_717452603ubject @ C @ G )
=> ( ( C != H )
=> ( ( fresh_1376661020_pi_pi @ H @ E )
=> ? [I: pi] :
( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
& ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
=> ( ! [F: pi,G: late_freeRes] :
( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
=> ( ( fresh_1641682979reeRes @ C @ G )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
=> ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(53,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_Late__Semantics_OComm2) ).
thf(403,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(42,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_Late__Semantics1_OfreeRes_Oinject) ).
thf(356,plain,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(101,axiom,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_subst__identity) ).
thf(610,plain,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(76,axiom,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_name__exists__fresh) ).
thf(499,plain,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(82,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( output @ A @ B @ C ) @ D )
=> ~ ! [E: name,F: name,G: pi] :
( ( ( A = E )
& ( B = F )
& ( C = G ) )
=> ( D
!= ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_outputCases_H) ).
thf(519,plain,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( output @ A @ B @ C ) @ D )
=> ~ ! [E: name,F: name,G: pi] :
( ( ( A = E )
& ( B = F )
& ( C = G ) )
=> ( D
!= ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(115,axiom,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi,F: late_freeRes > pi > $o] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
=> ( ( ( D
= ( late_OutputR @ A @ B ) )
=> ( ( C = E )
=> ( F @ ( late_OutputR @ A @ B ) @ C ) ) )
=> ( F @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_outputCases) ).
thf(742,plain,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi,F: late_freeRes > pi > $o] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
=> ( ( ( D
= ( late_OutputR @ A @ B ) )
=> ( ( C = E )
=> ( F @ ( late_OutputR @ A @ B ) @ C ) ) )
=> ( F @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(15,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( input @ A @ B @ C )
= ( input @ D @ E @ F ) )
= ( ( A = D )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_pi_Oinject_I3_J) ).
thf(256,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( input @ A @ B @ C )
= ( input @ D @ E @ F ) )
= ( ( A = D )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(165,axiom,
! [A: pi,B: late_residual,C: name] :
( ( late_transitions @ A @ B )
=> ( ( fresh_name_pi @ C @ A )
=> ( fresh_81631222sidual @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_freshResidual) ).
thf(1028,plain,
! [A: pi,B: late_residual,C: name] :
( ( late_transitions @ A @ B )
=> ( ( fresh_name_pi @ C @ A )
=> ( fresh_81631222sidual @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(73,axiom,
! [A: produc53907987_pi_pi > $o,B: produc53907987_pi_pi] :
( ! [C: name > noption_pi,D: name,E: product_prod_pi_pi] : ( A @ ( produc1275980869_pi_pi @ C @ ( produc235456326_pi_pi @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_prod__induct3) ).
thf(488,plain,
! [A: produc53907987_pi_pi > $o,B: produc53907987_pi_pi] :
( ! [C: name > noption_pi,D: name,E: product_prod_pi_pi] : ( A @ ( produc1275980869_pi_pi @ C @ ( produc235456326_pi_pi @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(6,axiom,
! [A: late_subject,B: name,C: pi,D: late_subject,E: name,F: pi] :
( ( ( late_BoundR @ A @ B @ C )
= ( late_BoundR @ D @ E @ F ) )
= ( ( A = D )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_residual_Oinject_I1_J) ).
thf(225,plain,
! [A: late_subject,B: name,C: pi,D: late_subject,E: name,F: pi] :
( ( ( late_BoundR @ A @ B @ C )
= ( late_BoundR @ D @ E @ F ) )
= ( ( A = D )
& ( ( abs_fun_name_pi @ B @ C )
= ( abs_fun_name_pi @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(38,axiom,
! [A: name,B: pi,C: late_freeRes,D: pi] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
=> ~ ! [E: pi,F: late_freeRes,G: pi,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ E ) )
=> ( ( ( late_FreeR @ C @ D )
= ( late_FreeR @ F @ ( res @ H @ G ) ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ F @ G ) )
=> ~ ( fresh_1641682979reeRes @ H @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_resCasesF_H) ).
thf(339,plain,
! [A: name,B: pi,C: late_freeRes,D: pi] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_FreeR @ C @ D ) )
=> ~ ! [E: pi,F: late_freeRes,G: pi,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ E ) )
=> ( ( ( late_FreeR @ C @ D )
= ( late_FreeR @ F @ ( res @ H @ G ) ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ F @ G ) )
=> ~ ( fresh_1641682979reeRes @ H @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(117,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_Late__Semantics_Osubject_Odistinct_I1_J) ).
thf(753,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(103,axiom,
! [A: produc53907987_pi_pi > $o,B: produc53907987_pi_pi] :
( ! [C: name > noption_pi,D: produc1141751126_pi_pi] : ( A @ ( produc1275980869_pi_pi @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_old_Oprod_Oinducts) ).
thf(669,plain,
! [A: produc53907987_pi_pi > $o,B: produc53907987_pi_pi] :
( ! [C: name > noption_pi,D: produc1141751126_pi_pi] : ( A @ ( produc1275980869_pi_pi @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(161,axiom,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( fresh_name_pi @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_freshFreeDerivative_I2_J) ).
thf(1016,plain,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( fresh_name_pi @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(106,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( par @ A @ B )
= ( par @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_pi_Oinject_I7_J) ).
thf(679,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( par @ A @ B )
= ( par @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(202,axiom,
fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Bound_Ohyps_I5_J) ).
thf(1155,plain,
fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(108,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ( eqvt_pi @ A )
=> ( ! [E: late_subject,F: name,G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_name_pi @ F @ C )
=> ( ( fresh_name_pi @ F @ B )
=> ( ( fresh_717452603ubject @ F @ E )
=> ( ( fresh_name_pi @ F @ D )
=> ? [H: pi] :
( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
& ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
=> ( ! [E: late_freeRes,F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
=> ? [G: pi] :
( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
=> ( strong743114133lation @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_simCasesCont) ).
thf(686,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ( eqvt_pi @ A )
=> ( ! [E: late_subject,F: name,G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_name_pi @ F @ C )
=> ( ( fresh_name_pi @ F @ B )
=> ( ( fresh_717452603ubject @ F @ E )
=> ( ( fresh_name_pi @ F @ D )
=> ? [H: pi] :
( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
& ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
=> ( ! [E: late_freeRes,F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
=> ? [G: pi] :
( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
=> ( strong743114133lation @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(180,axiom,
! [A: produc1141751126_pi_pi] :
~ ! [B: name,C: pi,D: pi] :
( A
!= ( produc235456326_pi_pi @ B @ ( product_Pair_pi_pi @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_prod__cases3) ).
thf(1075,plain,
! [A: produc1141751126_pi_pi] :
~ ! [B: name,C: pi,D: pi] :
( A
!= ( produc235456326_pi_pi @ B @ ( product_Pair_pi_pi @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(185,axiom,
! [A: name,B: name,C: produc1141751126_pi_pi] :
( ( fresh_2065563522_pi_pi @ A @ ( abs_fu385186459_pi_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_1376661020_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_abs__fresh_I1_J) ).
thf(1099,plain,
! [A: name,B: name,C: produc1141751126_pi_pi] :
( ( fresh_2065563522_pi_pi @ A @ ( abs_fu385186459_pi_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_1376661020_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(111,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_zeroTrans) ).
thf(701,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(201,axiom,
! [A: produc1141751126_pi_pi > late_residual > $o,B: produc1141751126_pi_pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: produc1141751126_pi_pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_residual_Ostrong__induct) ).
thf(1150,plain,
! [A: produc1141751126_pi_pi > late_residual > $o,B: produc1141751126_pi_pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: produc1141751126_pi_pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(194,axiom,
! [A: name,B: name,C: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_1627595501_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_fresh__prod) ).
thf(1131,plain,
! [A: name,B: name,C: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_1627595501_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(113,axiom,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_pi_Odistinct_I3_J) ).
thf(721,plain,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(94,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_pi_Odistinct_I35_J) ).
thf(569,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(99,axiom,
! [A: name,B: name,C: pi] : ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_Output) ).
thf(605,plain,
! [A: name,B: name,C: pi] : ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(50,axiom,
! [A: pi,B: pi,C: name,D: name] :
( ( subs @ ( sum @ A @ B ) @ C @ D )
= ( sum @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_simps_I7_J) ).
thf(393,plain,
! [A: pi,B: pi,C: name,D: name] :
( ( subs @ ( sum @ A @ B ) @ C @ D )
= ( sum @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(189,axiom,
! [A: name,B: name,C: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
=> ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_fresh__prodD_I1_J) ).
thf(1114,plain,
! [A: name,B: name,C: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
=> ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(175,axiom,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_resZeroTrans) ).
thf(1060,plain,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(172,axiom,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: pi,E: pi] : ( A @ ( produc235456326_pi_pi @ C @ ( product_Pair_pi_pi @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_prod__induct3) ).
thf(1050,plain,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: pi,E: pi] : ( A @ ( produc235456326_pi_pi @ C @ ( product_Pair_pi_pi @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(27,axiom,
! [A: name,B: name,C: name] :
( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_freeRes_Ofresh_I1_J) ).
thf(298,plain,
! [A: name,B: name,C: name] :
( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(56,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( C != B )
=> ( ( C != F )
=> ( ( fresh_name_pi @ C @ G )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_transitions_OComm1) ).
thf(412,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( C != B )
=> ( ( C != F )
=> ( ( fresh_name_pi @ C @ G )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(58,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: late_freeRes] :
( ( eqvt_pi @ A )
=> ( ! [E: late_subject,F: name,G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_name_pi @ F @ C )
=> ( ( fresh_name_pi @ F @ B )
=> ( ( fresh_717452603ubject @ F @ E )
=> ( ( fresh_1641682979reeRes @ F @ D )
=> ? [H: pi] :
( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
& ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
=> ( ! [E: late_freeRes,F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
=> ? [G: pi] :
( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
=> ( strong743114133lation @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_simCasesCont) ).
thf(425,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: late_freeRes] :
( ( eqvt_pi @ A )
=> ( ! [E: late_subject,F: name,G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_name_pi @ F @ C )
=> ( ( fresh_name_pi @ F @ B )
=> ( ( fresh_717452603ubject @ F @ E )
=> ( ( fresh_1641682979reeRes @ F @ D )
=> ? [H: pi] :
( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
& ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
=> ( ! [E: late_freeRes,F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
=> ? [G: pi] :
( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
=> ( strong743114133lation @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(144,axiom,
! [A: name,B: name,C: pi] :
( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_fresh__prod) ).
thf(856,plain,
! [A: name,B: name,C: pi] :
( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(21,axiom,
! [A: name,B: name,C: name,D: pi,E: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_FreeR @ late_TauR @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_resOutputTauTrans) ).
thf(279,plain,
! [A: name,B: name,C: name,D: pi,E: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_FreeR @ late_TauR @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(95,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_Late__Semantics1_Osubject_Odistinct_I1_J) ).
thf(573,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(98,axiom,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_pi_Odistinct_I13_J) ).
thf(601,plain,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(133,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_old_Oprod_Oinject) ).
thf(819,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(23,axiom,
! [A: pi,B: name,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_tauOutputTrans) ).
thf(286,plain,
! [A: pi,B: name,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(96,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: pi] :
( ( eqvt_pi @ A )
=> ( ! [F: pi,G: name] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
=> ( ( G != C )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
=> ( ! [F: pi,G: late_subject,H: name] :
( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
=> ( ( fresh_717452603ubject @ C @ G )
=> ( ( C != H )
=> ( ( fresh_name_pi @ H @ E )
=> ? [I: pi] :
( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
& ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
=> ( ! [F: pi,G: late_freeRes] :
( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
=> ( ( fresh_1641682979reeRes @ C @ G )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
=> ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_resSimCases) ).
thf(577,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: pi] :
( ( eqvt_pi @ A )
=> ( ! [F: pi,G: name] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
=> ( ( G != C )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
=> ( ! [F: pi,G: late_subject,H: name] :
( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
=> ( ( fresh_717452603ubject @ C @ G )
=> ( ( C != H )
=> ( ( fresh_name_pi @ H @ E )
=> ? [I: pi] :
( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
& ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
=> ( ! [F: pi,G: late_freeRes] :
( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
=> ( ( fresh_1641682979reeRes @ C @ G )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
=> ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(192,axiom,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] : ( A @ ( produc235456326_pi_pi @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_old_Oprod_Oinducts) ).
thf(1124,plain,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] : ( A @ ( produc235456326_pi_pi @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(16,axiom,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
=> ~ ( ( fresh_1641682979reeRes @ A @ D )
| ( fresh_1641682979reeRes @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_outputFreshTrans) ).
thf(259,plain,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
=> ~ ( ( fresh_1641682979reeRes @ A @ D )
| ( fresh_1641682979reeRes @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(158,axiom,
! [A: product_prod_pi_pi] :
? [B: pi,C: pi] :
( A
= ( product_Pair_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_surj__pair) ).
thf(1007,plain,
! [A: product_prod_pi_pi] :
? [B: pi,C: pi] :
( A
= ( product_Pair_pi_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(109,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( output @ A @ B @ C )
= ( output @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_pi_Oinject_I1_J) ).
thf(694,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( output @ A @ B @ C )
= ( output @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(197,axiom,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_sumCases) ).
thf(1139,plain,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(187,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_transitions_OPar1B) ).
thf(1107,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(184,axiom,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Pair__inject) ).
thf(1092,plain,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(112,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: name] :
( ( eqvt_pi @ A )
=> ( ! [F: pi,G: name] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
=> ( ( G != C )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
=> ( ! [F: pi,G: late_subject,H: name] :
( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
=> ( ( fresh_717452603ubject @ C @ G )
=> ( ( C != H )
=> ( ( fresh_name_name @ H @ E )
=> ? [I: pi] :
( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
& ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
=> ( ! [F: pi,G: late_freeRes] :
( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
=> ( ( fresh_1641682979reeRes @ C @ G )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
=> ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_resSimCases) ).
thf(704,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: name] :
( ( eqvt_pi @ A )
=> ( ! [F: pi,G: name] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ C ) @ F ) )
=> ( ( G != C )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_BoundR @ ( late_BoundOutputS @ G ) @ C @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ F ) @ A ) ) ) )
=> ( ! [F: pi,G: late_subject,H: name] :
( ( late_transitions @ B @ ( late_BoundR @ G @ H @ F ) )
=> ( ( fresh_717452603ubject @ C @ G )
=> ( ( C != H )
=> ( ( fresh_name_name @ H @ E )
=> ? [I: pi] :
( ( late_transitions @ D @ ( late_BoundR @ G @ H @ I ) )
& ( strong2129052853vative @ I @ ( res @ C @ F ) @ G @ H @ A ) ) ) ) ) )
=> ( ! [F: pi,G: late_freeRes] :
( ( late_transitions @ B @ ( late_FreeR @ G @ F ) )
=> ( ( fresh_1641682979reeRes @ C @ G )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
=> ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(104,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_pi_Odistinct_I53_J) ).
thf(672,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( sum @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(63,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: name] :
( ( eqvt_pi @ A )
=> ( ! [E: late_subject,F: name,G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_name_pi @ F @ C )
=> ( ( fresh_name_pi @ F @ B )
=> ( ( fresh_717452603ubject @ F @ E )
=> ( ( fresh_name_name @ F @ D )
=> ? [H: pi] :
( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
& ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
=> ( ! [E: late_freeRes,F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
=> ? [G: pi] :
( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
=> ( strong743114133lation @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_simCasesCont) ).
thf(445,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: name] :
( ( eqvt_pi @ A )
=> ( ! [E: late_subject,F: name,G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_name_pi @ F @ C )
=> ( ( fresh_name_pi @ F @ B )
=> ( ( fresh_717452603ubject @ F @ E )
=> ( ( fresh_name_name @ F @ D )
=> ? [H: pi] :
( ( late_transitions @ C @ ( late_BoundR @ E @ F @ H ) )
& ( strong2129052853vative @ H @ G @ E @ F @ A ) ) ) ) ) ) )
=> ( ! [E: late_freeRes,F: pi] :
( ( late_transitions @ B @ ( late_FreeR @ E @ F ) )
=> ? [G: pi] :
( ( late_transitions @ C @ ( late_FreeR @ E @ G ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ G @ F ) @ A ) ) )
=> ( strong743114133lation @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(152,axiom,
! [A: pi > late_residual > $o,B: pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_residual_Ostrong__inducts) ).
thf(936,plain,
! [A: pi > late_residual > $o,B: pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(54,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( B != C )
=> ( late_transitions @ ( res @ C @ A ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_Open) ).
thf(406,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( B != C )
=> ( late_transitions @ ( res @ C @ A ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(190,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_resTrans_I2_J) ).
thf(1117,plain,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(199,axiom,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] : ( A @ ( produc235456326_pi_pi @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_prod__cases) ).
thf(1144,plain,
! [A: produc1141751126_pi_pi > $o,B: produc1141751126_pi_pi] :
( ! [C: name,D: product_prod_pi_pi] : ( A @ ( produc235456326_pi_pi @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(19,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_pi_Odistinct_I19_J) ).
thf(271,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(49,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) )
=> ~ ( ( A != D )
| ( B != E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_outputIneqTrans) ).
thf(387,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) )
=> ~ ( ( A != D )
| ( B != E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(90,axiom,
! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_residual_Ostrong__induct) ).
thf(552,plain,
! [A: late_freeRes > late_residual > $o,B: late_freeRes,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_freeRes] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(85,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_pi_Odistinct_I5_J) ).
thf(535,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(132,axiom,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_prod_Oinject) ).
thf(816,plain,
! [A: name,B: product_prod_pi_pi,C: name,D: product_prod_pi_pi] :
( ( ( produc235456326_pi_pi @ A @ B )
= ( produc235456326_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(163,axiom,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_BoundR @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_resTauBoundTrans) ).
thf(1022,plain,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_BoundR @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(52,axiom,
! [A: name,B: name,C: pi] :
( ( A != B )
=> ( fresh_name_pi @ A @ ( subs @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_fresh__fact2) ).
thf(399,plain,
! [A: name,B: name,C: pi] :
( ( A != B )
=> ( fresh_name_pi @ A @ ( subs @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(170,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Late__Semantics_OPar1B) ).
thf(1044,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(5,axiom,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_Tau) ).
thf(223,plain,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(78,axiom,
! [A: pi,B: set_Pr1834926343_pi_pi] : ( strong743114133lation @ A @ B @ piNil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_nilSimRight) ).
thf(505,plain,
! [A: pi,B: set_Pr1834926343_pi_pi] : ( strong743114133lation @ A @ B @ piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(177,axiom,
! [A: name,B: name,C: produc1141751126_pi_pi] :
( ( fresh_2065563522_pi_pi @ A @ ( abs_fu385186459_pi_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_1376661020_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_name__fresh__abs) ).
thf(1066,plain,
! [A: name,B: name,C: produc1141751126_pi_pi] :
( ( fresh_2065563522_pi_pi @ A @ ( abs_fu385186459_pi_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_1376661020_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(147,axiom,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_prod__cases) ).
thf(868,plain,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(18,axiom,
! [A: pi,B: pi] :
( piNil
!= ( sum @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_pi_Odistinct_I11_J) ).
thf(267,plain,
! [A: pi,B: pi] :
( piNil
!= ( sum @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(186,axiom,
! [A: pi > late_residual > $o,B: pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_residual_Ostrong__induct) ).
thf(1102,plain,
! [A: pi > late_residual > $o,B: pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(69,axiom,
! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_Late__Semantics_OInput) ).
thf(473,plain,
! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(167,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ E @ A )
=> ( ( E != C )
=> ( fresh_name_pi @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_freshBoundDerivative_I2_J) ).
thf(1034,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ E @ A )
=> ( ( E != C )
=> ( fresh_name_pi @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(154,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_717452603ubject @ E @ B )
=> ( ( E != C )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Late__Semantics_OResB) ).
thf(944,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_717452603ubject @ E @ B )
=> ( ( E != C )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(195,axiom,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_name__exists__fresh) ).
thf(1134,plain,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(131,axiom,
! [A: name,B: pi,C: name,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ ( subs @ B @ C @ A ) @ A @ D )
= ( subs @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_substTrans) ).
thf(812,plain,
! [A: name,B: pi,C: name,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ ( subs @ B @ C @ A ) @ A @ D )
= ( subs @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(116,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ B @ A @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_forget) ).
thf(749,plain,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ B @ A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(66,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( output @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C )
& ( fresh_name_pi @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_pi_Ofresh_I2_J) ).
thf(458,plain,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( output @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C )
& ( fresh_name_pi @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(138,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_fresh__prod) ).
thf(836,plain,
! [A: name,B: pi,C: name] :
( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(91,axiom,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_freeRes,E: pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_simE_I2_J) ).
thf(557,plain,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_freeRes,E: pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( late_transitions @ C @ ( late_FreeR @ D @ E ) )
=> ? [F: pi] :
( ( late_transitions @ A @ ( late_FreeR @ D @ F ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ F @ E ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(157,axiom,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [F: pi,G: name,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ F ) )
=> ! [I: pi] :
( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ ( late_BoundOutputS @ G ) @ H @ I ) )
=> ( ( late_transitions @ F @ ( late_FreeR @ ( late_OutputR @ G @ H ) @ I ) )
=> ( G = H ) ) ) )
=> ~ ! [F: pi,G: late_subject,H: name,I: pi,J: name] :
( ( ( res @ A @ B )
= ( res @ J @ F ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( res @ J @ I ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_717452603ubject @ J @ G )
=> ( ( J != H )
=> ( ( fresh_name_pi @ H @ F )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_resCasesB_H) ).
thf(954,plain,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [F: pi,G: name,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ F ) )
=> ! [I: pi] :
( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ ( late_BoundOutputS @ G ) @ H @ I ) )
=> ( ( late_transitions @ F @ ( late_FreeR @ ( late_OutputR @ G @ H ) @ I ) )
=> ( G = H ) ) ) )
=> ~ ! [F: pi,G: late_subject,H: name,I: pi,J: name] :
( ( ( res @ A @ B )
= ( res @ J @ F ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( res @ J @ I ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_717452603ubject @ J @ G )
=> ( ( J != H )
=> ( ( fresh_name_pi @ H @ F )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(55,axiom,
! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
( ( ( late_FreeR @ A @ B )
= ( late_FreeR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_residual_Oinject_I2_J) ).
thf(409,plain,
! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
( ( ( late_FreeR @ A @ B )
= ( late_FreeR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(17,axiom,
! [A: produc53907987_pi_pi] :
~ ! [B: name > noption_pi,C: name,D: product_prod_pi_pi] :
( A
!= ( produc1275980869_pi_pi @ B @ ( produc235456326_pi_pi @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_prod__cases3) ).
thf(263,plain,
! [A: produc53907987_pi_pi] :
~ ! [B: name > noption_pi,C: name,D: product_prod_pi_pi] :
( A
!= ( produc1275980869_pi_pi @ B @ ( produc235456326_pi_pi @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(164,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( sum @ A @ B )
= ( sum @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_pi_Oinject_I6_J) ).
thf(1025,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( sum @ A @ B )
= ( sum @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(26,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_subject_Ofresh_I1_J) ).
thf(295,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(22,axiom,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_pi_Odistinct_I45_J) ).
thf(282,plain,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(203,axiom,
fresh_name_pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Bound_Ohyps_I2_J) ).
thf(1156,plain,
fresh_name_pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(173,axiom,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_subject,E: name,F: pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
=> ( ( fresh_name_pi @ E @ A )
=> ? [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_simE_I1_J) ).
thf(1053,plain,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: late_subject,E: name,F: pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
=> ( ( fresh_name_pi @ E @ A )
=> ? [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(124,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_subject_Ofresh_I2_J) ).
thf(791,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(168,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_prod_Oinject) ).
thf(1038,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(77,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_BoundOutputS @ D ) @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_inputBoundOutputTrans) ).
thf(502,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_BoundOutputS @ D ) @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(183,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Pair__inject) ).
thf(1085,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( product_Pair_pi_pi @ A @ B )
= ( product_Pair_pi_pi @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(43,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_pi_Odistinct_I27_J) ).
thf(359,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( sum @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(156,axiom,
! [A: produc53907987_pi_pi > $o,B: produc53907987_pi_pi] :
( ! [C: name > noption_pi,D: name,E: pi,F: pi] : ( A @ ( produc1275980869_pi_pi @ C @ ( produc235456326_pi_pi @ D @ ( product_Pair_pi_pi @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_prod__induct4) ).
thf(951,plain,
! [A: produc53907987_pi_pi > $o,B: produc53907987_pi_pi] :
( ! [C: name > noption_pi,D: name,E: pi,F: pi] : ( A @ ( produc1275980869_pi_pi @ C @ ( produc235456326_pi_pi @ D @ ( product_Pair_pi_pi @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(130,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( F != B )
=> ( ( fresh_name_pi @ F @ D )
=> ( ( C != B )
=> ( ( fresh_name_pi @ C @ G )
=> ( ( F != C )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_transitions_OClose2) ).
thf(808,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ F @ A )
=> ( ( fresh_name_pi @ F @ E )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( F != B )
=> ( ( fresh_name_pi @ F @ D )
=> ( ( C != B )
=> ( ( fresh_name_pi @ C @ G )
=> ( ( F != C )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(37,axiom,
! [A: pi,B: late_freeRes,C: pi,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( late_transitions @ ( par @ D @ A ) @ ( late_FreeR @ B @ ( par @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Par2F) ).
thf(336,plain,
! [A: pi,B: late_freeRes,C: pi,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( late_transitions @ ( par @ D @ A ) @ ( late_FreeR @ B @ ( par @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(198,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ E @ A )
=> ( fresh_717452603ubject @ E @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_freshBoundDerivative_I1_J) ).
thf(1141,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ E @ A )
=> ( fresh_717452603ubject @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(102,axiom,
! [A: name,B: pi,C: late_residual] :
( ( late_transitions @ ( res @ A @ B ) @ C )
=> ( ! [D: pi,E: name,F: name] :
( ( ( res @ A @ B )
= ( res @ F @ D ) )
=> ! [G: pi] :
( ( C
= ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) )
=> ( ( late_transitions @ D @ ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) )
=> ( E = F ) ) ) )
=> ( ! [D: pi,E: late_subject,F: name,G: pi,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ D ) )
=> ( ( C
= ( late_BoundR @ E @ F @ ( res @ H @ G ) ) )
=> ( ( late_transitions @ D @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_717452603ubject @ H @ E )
=> ( ( H != F )
=> ( ( fresh_name_pi @ F @ D )
=> ~ ( fresh_717452603ubject @ F @ E ) ) ) ) ) ) )
=> ~ ! [D: pi,E: late_freeRes,F: pi,G: name] :
( ( ( res @ A @ B )
= ( res @ G @ D ) )
=> ( ( C
= ( late_FreeR @ E @ ( res @ G @ F ) ) )
=> ( ( late_transitions @ D @ ( late_FreeR @ E @ F ) )
=> ~ ( fresh_1641682979reeRes @ G @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_resCases_H) ).
thf(613,plain,
! [A: name,B: pi,C: late_residual] :
( ( late_transitions @ ( res @ A @ B ) @ C )
=> ( ! [D: pi,E: name,F: name] :
( ( ( res @ A @ B )
= ( res @ F @ D ) )
=> ! [G: pi] :
( ( C
= ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) )
=> ( ( late_transitions @ D @ ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) )
=> ( E = F ) ) ) )
=> ( ! [D: pi,E: late_subject,F: name,G: pi,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ D ) )
=> ( ( C
= ( late_BoundR @ E @ F @ ( res @ H @ G ) ) )
=> ( ( late_transitions @ D @ ( late_BoundR @ E @ F @ G ) )
=> ( ( fresh_717452603ubject @ H @ E )
=> ( ( H != F )
=> ( ( fresh_name_pi @ F @ D )
=> ~ ( fresh_717452603ubject @ F @ E ) ) ) ) ) ) )
=> ~ ! [D: pi,E: late_freeRes,F: pi,G: name] :
( ( ( res @ A @ B )
= ( res @ G @ D ) )
=> ( ( C
= ( late_FreeR @ E @ ( res @ G @ F ) ) )
=> ( ( late_transitions @ D @ ( late_FreeR @ E @ F ) )
=> ~ ( fresh_1641682979reeRes @ G @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(150,axiom,
! [A: name,B: pi,C: late_freeRes] :
( ( fresh_1504024600reeRes @ A @ ( produc1638681944reeRes @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_fresh__prod) ).
thf(876,plain,
! [A: name,B: pi,C: late_freeRes] :
( ( fresh_1504024600reeRes @ A @ ( produc1638681944reeRes @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(145,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: pi,F: pi > $o] :
( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( ( fresh_name_pi @ D @ B )
=> ( ! [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ C @ D @ G ) )
=> ( F @ ( par @ G @ B ) ) )
=> ( ! [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
=> ( F @ ( par @ A @ G ) ) )
=> ( F @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_parCasesB) ).
thf(859,plain,
! [A: pi,B: pi,C: late_subject,D: name,E: pi,F: pi > $o] :
( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ( fresh_name_pi @ D @ A )
=> ( ( fresh_name_pi @ D @ B )
=> ( ! [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ C @ D @ G ) )
=> ( F @ ( par @ G @ B ) ) )
=> ( ! [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
=> ( F @ ( par @ A @ G ) ) )
=> ( F @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(141,axiom,
! [A: produc1141751126_pi_pi > late_residual > $o,B: produc1141751126_pi_pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: produc1141751126_pi_pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_residual_Ostrong__inducts) ).
thf(845,plain,
! [A: produc1141751126_pi_pi > late_residual > $o,B: produc1141751126_pi_pi,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: produc1141751126_pi_pi] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(44,axiom,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( tau @ B ) )
= ( fresh_name_pi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_pi_Ofresh_I3_J) ).
thf(363,plain,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( tau @ B ) )
= ( fresh_name_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(86,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( input @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_pi_Odistinct_I57_J) ).
thf(539,plain,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( input @ A @ B @ C )
!= ( res @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(204,axiom,
fresh_name_pi @ y @ ( res @ x @ ( sum @ p @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Bound_Ohyps_I3_J) ).
thf(1157,plain,
fresh_name_pi @ y @ ( res @ x @ ( sum @ p @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(75,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_pi_Odistinct_I43_J) ).
thf(495,plain,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(159,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ ( res @ C @ B ) @ C @ A )
= ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_substRes3) ).
thf(1010,plain,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ ( res @ C @ B ) @ C @ A )
= ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(13,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_Late__Semantics_OfreeRes_Odistinct_I1_J) ).
thf(250,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [A: name,B: pi,C: name,D: pi] :
( ( ( res @ A @ B )
= ( res @ C @ D ) )
= ( ( abs_fun_name_pi @ A @ B )
= ( abs_fun_name_pi @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_pi_Oinject_I8_J) ).
thf(231,plain,
! [A: name,B: pi,C: name,D: pi] :
( ( ( res @ A @ B )
= ( res @ C @ D ) )
= ( ( abs_fun_name_pi @ A @ B )
= ( abs_fun_name_pi @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ A @ C ) ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_resOutputOutputTrans) ).
thf(319,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ A @ C ) ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(29,axiom,
! [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_BoundR @ A @ B @ C )
!= ( late_FreeR @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_residual_Odistinct_I1_J) ).
thf(304,plain,
! [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_BoundR @ A @ B @ C )
!= ( late_FreeR @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(121,axiom,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_pi_Odistinct_I15_J) ).
thf(781,plain,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(12,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).
thf(246,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
y != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
y != x,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(207,plain,
y != x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,axiom,
! [A: name,B: pi,C: name,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( A != C )
=> ( fresh_name_pi @ A @ ( subs @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_fresh__fact1) ).
thf(383,plain,
! [A: name,B: pi,C: name,D: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( A != C )
=> ( fresh_name_pi @ A @ ( subs @ B @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(137,axiom,
! [A: produc1141751126_pi_pi] :
~ ! [B: name,C: product_prod_pi_pi] :
( A
!= ( produc235456326_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_old_Oprod_Oexhaust) ).
thf(832,plain,
! [A: produc1141751126_pi_pi] :
~ ! [B: name,C: product_prod_pi_pi] :
( A
!= ( produc235456326_pi_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(39,axiom,
! [A: pi,B: late_freeRes,C: pi,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( late_transitions @ ( par @ A @ D ) @ ( late_FreeR @ B @ ( par @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Par1F) ).
thf(346,plain,
! [A: pi,B: late_freeRes,C: pi,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( late_transitions @ ( par @ A @ D ) @ ( late_FreeR @ B @ ( par @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(89,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_Late__Semantics_OClose2) ).
thf(549,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(127,axiom,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_name__exists__fresh) ).
thf(800,plain,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(59,axiom,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_1641682979reeRes @ D @ B )
=> ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_ResF) ).
thf(433,plain,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh_1641682979reeRes @ D @ B )
=> ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(80,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_pi_Odistinct_I85_J) ).
thf(510,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(31,axiom,
! [A: produc53907987_pi_pi] :
~ ! [B: name > noption_pi,C: produc1141751126_pi_pi] :
( A
!= ( produc1275980869_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_old_Oprod_Oexhaust) ).
thf(315,plain,
! [A: produc53907987_pi_pi] :
~ ! [B: name > noption_pi,C: produc1141751126_pi_pi] :
( A
!= ( produc1275980869_pi_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(146,axiom,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_old_Oprod_Oinducts) ).
thf(865,plain,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi] :
( ! [C: pi,D: pi] : ( A @ ( product_Pair_pi_pi @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(3,axiom,
! [A: pi,B: late_freeRes,C: pi,D: late_freeRes > pi > $o] :
( ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ B @ C ) )
=> ( ( ( B = late_TauR )
=> ( ( A = C )
=> ( D @ late_TauR @ A ) ) )
=> ( D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_tauCases) ).
thf(210,plain,
! [A: pi,B: late_freeRes,C: pi,D: late_freeRes > pi > $o] :
( ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ B @ C ) )
=> ( ( ( B = late_TauR )
=> ( ( A = C )
=> ( D @ late_TauR @ A ) ) )
=> ( D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,axiom,
! [A: pi,B: name,C: name] :
( ( subs @ ( tau @ A ) @ B @ C )
= ( tau @ ( subs @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_simps_I2_J) ).
thf(326,plain,
! [A: pi,B: name,C: name] :
( ( subs @ ( tau @ A ) @ B @ C )
= ( tau @ ( subs @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(84,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_Late__Semantics1_Osubject_Oinject_I2_J) ).
thf(532,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(10,axiom,
! [A: name,B: pi,C: pi] :
( ( ( abs_fun_name_pi @ A @ B )
= ( abs_fun_name_pi @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_abs__fun__eq1) ).
thf(239,plain,
! [A: name,B: pi,C: pi] :
( ( ( abs_fun_name_pi @ A @ B )
= ( abs_fun_name_pi @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_freeRes_Oexhaust) ).
thf(242,plain,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(139,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
=> ( fresh_name_pi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_fresh__prodD_I1_J) ).
thf(839,plain,
! [A: name,B: pi,C: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
=> ( fresh_name_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(36,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( input @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_pi_Odistinct_I21_J) ).
thf(332,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( input @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(162,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_transitions_OPar2B) ).
thf(1019,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ E )
=> ( ( fresh_name_pi @ C @ A )
=> ( ( fresh_717452603ubject @ C @ B )
=> ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(83,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_pi_Odistinct_I55_J) ).
thf(528,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( par @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(134,axiom,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_outputBoundTrans) ).
thf(822,plain,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(142,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_fresh__prod) ).
thf(850,plain,
! [A: name,B: pi,C: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
= ( ( fresh_name_pi @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(148,axiom,
! [A: name,B: name,C: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
=> ( fresh_1627595501_pi_pi @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_fresh__prodD_I2_J) ).
thf(871,plain,
! [A: name,B: name,C: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ B @ C ) )
=> ( fresh_1627595501_pi_pi @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(191,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( res @ C @ B )
= ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_substRes2) ).
thf(1120,plain,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( res @ C @ B )
= ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(46,axiom,
! [A: name > noption_pi,B: produc1141751126_pi_pi,C: name > noption_pi,D: produc1141751126_pi_pi] :
( ( ( produc1275980869_pi_pi @ A @ B )
= ( produc1275980869_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_old_Oprod_Oinject) ).
thf(369,plain,
! [A: name > noption_pi,B: produc1141751126_pi_pi,C: name > noption_pi,D: produc1141751126_pi_pi] :
( ( ( produc1275980869_pi_pi @ A @ B )
= ( produc1275980869_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(100,axiom,
! [A: late_subject > $o,B: late_subject] :
( ! [C: name] : ( A @ ( late_InputS @ C ) )
=> ( ! [C: name] : ( A @ ( late_BoundOutputS @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_subject_Oinducts) ).
thf(607,plain,
! [A: late_subject > $o,B: late_subject] :
( ! [C: name] : ( A @ ( late_InputS @ C ) )
=> ( ! [C: name] : ( A @ ( late_BoundOutputS @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(14,axiom,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_freeRes_Ofresh_I2_J) ).
thf(254,plain,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(33,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_pi_Odistinct_I1_J) ).
thf(322,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(128,axiom,
! [A: name > noption_pi,B: produc1141751126_pi_pi,C: name > noption_pi,D: produc1141751126_pi_pi] :
( ( ( produc1275980869_pi_pi @ A @ B )
= ( produc1275980869_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_prod_Oinject) ).
thf(803,plain,
! [A: name > noption_pi,B: produc1141751126_pi_pi,C: name > noption_pi,D: produc1141751126_pi_pi] :
( ( ( produc1275980869_pi_pi @ A @ B )
= ( produc1275980869_pi_pi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(87,axiom,
! [A: produc53907987_pi_pi] :
? [B: name > noption_pi,C: produc1141751126_pi_pi] :
( A
= ( produc1275980869_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_surj__pair) ).
thf(543,plain,
! [A: produc53907987_pi_pi] :
? [B: name > noption_pi,C: produc1141751126_pi_pi] :
( A
= ( produc1275980869_pi_pi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(105,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_nilCases_H) ).
thf(676,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(74,axiom,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_subject_Oexhaust) ).
thf(491,plain,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(178,axiom,
! [A: name,B: late_freeRes,C: pi] :
( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_fresh__prod) ).
thf(1069,plain,
! [A: name,B: late_freeRes,C: pi] :
( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(160,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
=> ( fresh_name_pi @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_fresh__prodD_I2_J) ).
thf(1014,plain,
! [A: name,B: pi,C: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ B @ C ) )
=> ( fresh_name_pi @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1160,plain,
$false,
inference(e,[status(thm)],[794,760,1031,234,941,777,1110,352,1083,468,1158,217,308,873,1041,1137,797,1063,829,1127,301,565,436,785,372,853,1147,416,228,289,475,443,485,514,806,480,396,507,1072,453,292,439,546,366,1047,1057,825,349,598,561,275,788,879,329,1079,757,682,1159,461,456,842,697,948,725,403,356,610,499,519,742,256,1028,488,225,339,753,669,1016,679,1155,686,1075,1099,701,1150,1131,721,569,605,393,1114,1060,1050,298,412,425,856,279,573,601,819,286,577,1124,259,1007,694,1139,1107,1092,704,672,445,936,406,1117,1144,271,387,552,535,816,1022,399,1044,223,505,1066,868,267,1102,473,1034,944,1134,812,749,458,836,557,954,409,263,1025,295,282,1156,1053,791,1038,502,1085,359,951,808,336,1141,613,876,859,845,363,539,1157,495,1010,250,231,319,304,781,246,207,383,832,346,549,800,433,510,315,865,210,326,532,239,242,839,332,1019,528,822,850,871,1120,369,607,254,322,803,543,676,491,1069,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ITP181^1 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n025.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Mon May 6 14:30:09 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.89/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.99/1.21 % [INFO] Parsing done (337ms).
% 1.99/1.22 % [INFO] Running in sequential loop mode.
% 2.81/1.47 % [INFO] eprover registered as external prover.
% 2.81/1.47 % [INFO] cvc4 registered as external prover.
% 2.81/1.47 % [INFO] Scanning for conjecture ...
% 3.02/1.58 % [INFO] Found a conjecture and 352 axioms. Running axiom selection ...
% 3.47/1.71 % [INFO] Axiom selection finished. Selected 204 axioms (removed 148 axioms).
% 4.00/1.90 % [INFO] Problem is higher-order (TPTP THF).
% 4.29/1.93 % [INFO] Type checking passed.
% 4.29/1.93 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 19.11/5.63 % External prover 'e' found a proof!
% 19.11/5.63 % [INFO] Killing All external provers ...
% 19.11/5.63 % Time passed: 5144ms (effective reasoning time: 4404ms)
% 19.11/5.63 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 19.11/5.64 % Axioms used in derivation (204): fact_105_surj__pair, fact_239_pi_Oinject_I8_J, fact_149_pi_Odistinct_I55_J, fact_316_pi_Odistinct_I1_J, fact_297_subst__identity, fact_232_subject_Ofresh_I2_J, fact_255_resSimCases, fact_114_name__exists__fresh, fact_259_simCases, fact_141_residual_Ostrong__induct, fact_163_pi_Odistinct_I41_J, fact_298_simps_I9_J, fact_312_freeRes_Oinducts, fact_339_transitions_OClose2, fact_154_inputFreeTrans, fact_285_nilSim_I1_J, fact_274_pi_Ofresh_I1_J, fact_147_pi_Odistinct_I35_J, fact_31_fresh__prodD_I1_J, fact_305_pi_Ofresh_I2_J, fact_173_parCasesB, fact_249_pi_Oinject_I3_J, fact_135_residual_Ostrong__inducts, fact_136_residual_Ostrong__inducts, fact_250_simE_I1_J, fact_308_pi_Odistinct_I31_J, fact_280_pi_Odistinct_I5_J, fact_324_resTrans_I1_J, fact_161_pi_Odistinct_I45_J, fact_111_name__exists__fresh, fact_304_freeRes_Ofresh_I2_J, fact_11_fresh__prod, fact_120_prod__cases3, fact_319_forget, fact_276_nilCases_H, fact_64_old_Oprod_Oinducts, fact_315_pi_Odistinct_I21_J, fact_162_pi_Odistinct_I53_J, fact_172_Late__Semantics_OPar2B, fact_20_fresh__prodD_I2_J, fact_233_freeRes_Ofresh_I1_J, fact_335_transitions_OComm1, fact_275_zeroTrans, fact_124_Sum1, fact_338_tauCases, fact_277_pi_Odistinct_I15_J, fact_104_surj__pair, fact_226_simCasesCont, fact_160_pi_Odistinct_I57_J, fact_140_residual_Ostrong__induct, fact_63_old_Oprod_Oinducts, fact_166_ResF, fact_132_parCasesB_H, fact_311_pi_Oinject_I1_J, fact_295_resOutputOutputTrans, fact_306_resOutputTauTrans, fact_334_transitions_OComm2, fact_229_resCases_H, fact_300_substTrans, fact_62_freshResidual, fact_291_subject_Oinducts, fact_153_Par1F, fact_262_tauOutputTrans, fact_318_fresh__fact1, fact_273_name__fresh, fact_148_pi_Odistinct_I43_J, fact_329_Output, fact_310_pi_Odistinct_I27_J, fact_185_subrelI, fact_252_Open, fact_170_tauBoundTrans, fact_328_Late__Semantics_OComm1, fact_17_transitions_OResB, fact_118_prod__induct3, fact_167_freshFreeDerivative_I2_J, fact_138_residual_Ostrong__inducts, fact_126_sumCases, fact_51_old_Oprod_Oinject, fact_145_residual_Ofresh_I2_J, fact_8_fresh__prod, fact_14_fresh__prod, fact_128_transitions_OPar2B, fact_231_Late__Semantics_Osubject_Oinject_I2_J, fact_15_fresh__prod, fact_158_residual_Odistinct_I1_J, fact_223_resTauOutputTrans, fact_292_Late__Semantics_OInput, fact_224_simCasesCont, fact_269_Late__Semantics1_Osubject_Oinject_I2_J, fact_283_resZeroTrans, fact_331_outputCases_H, fact_5_Bound_Ohyps_I1_J, fact_42_prod_Oinject, fact_256_resSimCases, fact_40_freshBoundDerivative_I2_J, fact_89_Pair__inject, fact_115_pi_Oinject_I6_J, fact_281_pi_Odistinct_I3_J, fact_157_pi_Odistinct_I79_J, fact_116_prod__induct4, fact_2_Bound_Ohyps_I4_J, fact_151_pi_Oinject_I7_J, fact_287_subject_Ofresh_I1_J, fact_52_old_Oprod_Oinject, fact_169_resTrans_I2_J, fact_123_Sum2, fact_93_prod__cases, fact_41_prod_Oinject, fact_119_prod__cases4, fact_142_residual_Ostrong__induct, fact_240_residual_Oinject_I1_J, fact_286_inputCases_H, fact_278_pi_Odistinct_I13_J, fact_125_sumCases_H, fact_309_pi_Odistinct_I29_J, fact_326_nilSim_I3_J, fact_288_Late__Semantics1_Osubject_Odistinct_I1_J, fact_57_old_Oprod_Oinject, fact_84_Pair__inject, fact_270_Late__Semantics1_OfreeRes_Oinject, fact_337_tauCases_H, fact_137_residual_Ostrong__inducts, fact_230_Late__Semantics_OfreeRes_Oinject, fact_139_residual_Ostrong__induct, fact_322_substRes3, fact_332_outputCases, fact_129_transitions_OPar1B, fact_294_resOutputInputTrans, fact_254_simE_I2_J, fact_165_resCasesF_H, fact_83_Pair__inject, fact_260_simulation__def, fact_171_Late__Semantics_OPar1B, fact_261_resCasesB_H, fact_341_Late__Semantics_OClose2, fact_155_resInputFreeTrans, fact_313_Late__Semantics_OfreeRes_Odistinct_I1_J, fact_1_Bound_Ohyps_I5_J, fact_282_nilSimRight, fact_156_pi_Odistinct_I85_J, fact_321_Late__Semantics1_OfreeRes_Odistinct_I1_J, fact_13_fresh__prod, fact_16_pi_Ofresh_I7_J, fact_152_Par2F, fact_302_simps_I2_J, fact_61_pi_Odistinct_I81_J, fact_69_old_Oprod_Oinducts, fact_225_simCasesCont, fact_317_fresh__fact2, fact_4_Bound_Ohyps_I2_J, fact_323_substRes2, fact_227_simCasesCont, fact_289_subject_Oexhaust, fact_222_resInputBoundOutputTrans, fact_146_residual_Oinject_I2_J, fact_73_old_Oprod_Oexhaust, fact_303_simps_I1_J, fact_293_transitions_OInput, fact_122_freshRes, fact_18_freshBoundDerivative_I1_J, fact_290_Late__Semantics_Osubject_Odistinct_I1_J, fact_47_prod_Oinject, fact_263_inputBoundOutputTrans, fact_12_fresh__prod, fact_74_old_Oprod_Oexhaust, fact_246_name__fresh__abs, fact_79_old_Oprod_Oexhaust, fact_320_freeRes_Oexhaust, fact_94_prod__cases, fact_134_resTauBoundTrans, fact_144_pi_Ofresh_I3_J, fact_314_pi_Odistinct_I19_J, fact_21_fresh__prodD_I2_J, fact_340_transitions_OClose1, fact_336_Tau, fact_133_inputIneqTrans, fact_30_fresh__prodD_I1_J, fact_164_resCasesF, fact_143_pi_Ofresh_I8_J, fact_19_Late__Semantics_OResB, fact_242_abs__fresh_I1_J, fact_159_residual_Oinducts, fact_168_freshFreeDerivative_I1_J, fact_117_prod__induct3, fact_279_pi_Odistinct_I11_J, fact_284_nilSim_I2_J, fact_325_outputBoundTrans, fact_237_abs__fun__eq1, fact_113_name__exists__fresh, fact_330_outputIneqTrans, fact_301_simps_I7_J, fact_333_outputFreshTrans, fact_299_simps_I8_J, fact_296_Late__Semantics_OClose1, fact_121_prod__cases3, fact_150_pi_Oinject_I2_J, fact_257_resSimCases, fact_107_surj__pair, fact_327_Late__Semantics_OComm2, fact_258_resSimCases, fact_99_prod__cases, fact_112_name__exists__fresh, fact_3_Bound_Ohyps_I3_J, fact_307_outputTauTrans
% 19.11/5.64 % No. of inferences in proof: 412
% 19.11/5.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5144 ms resp. 4404 ms w/o parsing
% 20.12/5.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.12/5.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------