%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP183^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:06 AM UTC 2026
% Result : Theorem 29.44s 8.27s
% Output : Refutation 30.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 260
% Syntax : Number of formulae : 522 ( 280 unt; 0 typ; 0 def)
% Number of atoms : 1598 ( 497 equ; 8 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 6288 ( 257 ~; 20 |; 136 &;5079 @)
% ( 0 <=>; 796 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Number of types : 32 ( 31 usr)
% Number of type conns : 80 ( 80 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 65 usr; 13 con; 0-5 aty)
% Number of variables : 2188 ( 34 ^;2098 !; 56 ?;2188 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1569510577ion_pi_type,type,
set_Pr1569510577ion_pi: $tType ).
thf(produc1462499409ion_pi_type,type,
produc1462499409ion_pi: $tType ).
thf(set_Pr248416762ubject_type,type,
set_Pr248416762ubject: $tType ).
thf(set_Pr305743074reeRes_type,type,
set_Pr305743074reeRes: $tType ).
thf(set_Pr1294453099i_name_type,type,
set_Pr1294453099i_name: $tType ).
thf(produc691362330ubject_type,type,
produc691362330ubject: $tType ).
thf(produc1834551554reeRes_type,type,
produc1834551554reeRes: $tType ).
thf(set_Pr1694908217_pi_pi_type,type,
set_Pr1694908217_pi_pi: $tType ).
thf(produc405342261i_name_type,type,
produc405342261i_name: $tType ).
thf(produc629157763_pi_pi_type,type,
produc629157763_pi_pi: $tType ).
thf(produc1359399907ubject_type,type,
produc1359399907ubject: $tType ).
thf(produc355105483reeRes_type,type,
produc355105483reeRes: $tType ).
thf(produc214645451ubject_type,type,
produc214645451ubject: $tType ).
thf(produc1357834675reeRes_type,type,
produc1357834675reeRes: $tType ).
thf(produc1998742700t_name_type,type,
produc1998742700t_name: $tType ).
thf(produc2052722628s_name_type,type,
produc2052722628s_name: $tType ).
thf(produc865358760ubject_type,type,
produc865358760ubject: $tType ).
thf(produc2008547984reeRes_type,type,
produc2008547984reeRes: $tType ).
thf(produc140253050ect_pi_type,type,
produc140253050ect_pi: $tType ).
thf(produc992857746Res_pi_type,type,
produc992857746Res_pi: $tType ).
thf(set_Pr1834926343_pi_pi_type,type,
set_Pr1834926343_pi_pi: $tType ).
thf(product_prod_pi_pi_type,type,
product_prod_pi_pi: $tType ).
thf(noption_Late_subject_type,type,
noption_Late_subject: $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_decl,type,
input: name > name > pi > pi ).
thf(mismatch_decl,type,
mismatch: name > name > pi > pi ).
thf(output_decl,type,
output: name > name > pi > pi ).
thf(par_decl,type,
par: pi > pi > pi ).
thf(piNil_decl,type,
piNil: pi ).
thf(res_decl,type,
res: name > pi > pi ).
thf(sum_decl,type,
sum: pi > pi > pi ).
thf(tau_decl,type,
tau: pi > pi ).
thf(subs_decl,type,
subs: pi > name > name > pi ).
thf(late_OutputR_decl,type,
late_OutputR: name > name > late_freeRes ).
thf(late_TauR_decl,type,
late_TauR: late_freeRes ).
thf(late_BoundR_decl,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(late_FreeR_decl,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(late_BoundOutputS_decl,type,
late_BoundOutputS: name > late_subject ).
thf(late_InputS_decl,type,
late_InputS: name > late_subject ).
thf(late_transitions_decl,type,
late_transitions: pi > late_residual > $o ).
thf(abs_fun_name_name_decl,type,
abs_fun_name_name: name > name > name > noption_name ).
thf(abs_fun_name_pi_decl,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(abs_fu681348580reeRes_decl,type,
abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
thf(abs_fu1904601852ubject_decl,type,
abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject ).
thf(fresh_1093033124n_name_decl,type,
fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
thf(fresh_543891186ion_pi_decl,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
thf(fresh_785364841reeRes_decl,type,
fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
thf(fresh_728038529ubject_decl,type,
fresh_728038529ubject: name > ( name > noption_Late_subject ) > $o ).
thf(fresh_name_name_decl,type,
fresh_name_name: name > name > $o ).
thf(fresh_name_pi_decl,type,
fresh_name_pi: name > pi > $o ).
thf(fresh_1641682979reeRes_decl,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(fresh_81631222sidual_decl,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(fresh_717452603ubject_decl,type,
fresh_717452603ubject: name > late_subject > $o ).
thf(fresh_1963366730reeRes_decl,type,
fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
thf(fresh_820177506ubject_decl,type,
fresh_820177506ubject: name > produc865358760ubject > $o ).
thf(fresh_1627595501_pi_pi_decl,type,
fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
thf(fresh_2007541374s_name_decl,type,
fresh_2007541374s_name: name > produc2052722628s_name > $o ).
thf(fresh_1847501388Res_pi_decl,type,
fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
thf(fresh_493808761reeRes_decl,type,
fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
thf(fresh_1498103185ubject_decl,type,
fresh_1498103185ubject: name > produc214645451ubject > $o ).
thf(fresh_1953561446t_name_decl,type,
fresh_1953561446t_name: name > produc1998742700t_name > $o ).
thf(fresh_994896692ect_pi_decl,type,
fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).
thf(fresh_1638563217reeRes_decl,type,
fresh_1638563217reeRes: name > produc355105483reeRes > $o ).
thf(fresh_495373993ubject_decl,type,
fresh_495373993ubject: name > produc1359399907ubject > $o ).
thf(ord_le630093991_pi_pi_decl,type,
ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(produc1531804426reeRes_decl,type,
produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
thf(produc607574050ubject_decl,type,
produc607574050ubject: name > late_subject > produc865358760ubject ).
thf(product_Pair_pi_pi_decl,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(produc1701355766s_name_decl,type,
produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
thf(produc1177552196Res_pi_decl,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(produc1244821099reeRes_decl,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(produc320590723ubject_decl,type,
produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
thf(produc1647375838t_name_decl,type,
produc1647375838t_name: late_subject > name > produc1998742700t_name ).
thf(produc324947500ect_pi_decl,type,
produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
thf(produc242091907reeRes_decl,type,
produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
thf(produc1465345179ubject_decl,type,
produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
thf(eqvt_pi_decl,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(id_pi_decl,type,
id_pi: set_Pr1834926343_pi_pi ).
thf(collec1051790738_pi_pi_decl,type,
collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
thf(strong2129052853vative_decl,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(strong743114133lation_decl,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(member558706512_pi_pi_decl,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(p_decl,type,
p: pi ).
thf(pq_decl,type,
pq: pi ).
thf(q_decl,type,
q: pi ).
thf(q2_decl,type,
q2: pi ).
thf(rel_decl,type,
rel: set_Pr1834926343_pi_pi ).
thf(alpha_decl,type,
alpha: late_freeRes ).
thf(x_decl,type,
x: name ).
thf(32,axiom,
! [A: name,B: late_freeRes,C: late_freeRes] :
( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_fresh__prod) ).
thf(365,plain,
! [A: name,B: late_freeRes,C: late_freeRes] :
( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',fact_167_fresh__fact1) ).
thf(333,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)],[21]) ).
thf(110,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le630093991_pi_pi @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_order__subst2) ).
thf(628,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ ( C @ B ) @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le630093991_pi_pi @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(194,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/sandbox/benchmark/theBenchmark.p',fact_40_residual_Ostrong__induct) ).
thf(1083,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)],[194]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',fact_7_sumCases) ).
thf(962,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)],[166]) ).
thf(146,axiom,
! [A: name,B: name,C: pi] :
( ( fresh_name_pi @ A @ ( res @ B @ C ) )
= ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_pi_Ofresh_I9_J) ).
thf(762,plain,
! [A: name,B: name,C: pi] :
( ( fresh_name_pi @ A @ ( res @ B @ C ) )
= ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(13,axiom,
! [A: name,B: late_subject,C: late_freeRes] :
( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_fresh__prod) ).
thf(308,plain,
! [A: name,B: late_subject,C: late_freeRes] :
( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',fact_33_freshFreeDerivative_I1_J) ).
thf(1073,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)],[191]) ).
thf(208,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zeroTrans) ).
thf(1205,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(231,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( res @ C @ B )
= ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_substRes2) ).
thf(1305,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)],[231]) ).
thf(227,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( input @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_pi_Odistinct_I57_J) ).
thf(1290,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)],[227]) ).
thf(7,axiom,
( ord_le630093991_pi_pi
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
! [C: product_prod_pi_pi] :
( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_subset__eq) ).
thf(276,plain,
( ord_le630093991_pi_pi
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
! [C: product_prod_pi_pi] :
( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: product_prod_pi_pi] :
? [B: pi,C: pi] :
( A
= ( product_Pair_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_surj__pair) ).
thf(269,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)],[5]) ).
thf(124,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_equalityD1) ).
thf(677,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',fact_226_prod_Oinject) ).
thf(384,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)],[38]) ).
thf(233,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/sandbox/benchmark/theBenchmark.p',fact_302_inputCases_H) ).
thf(1310,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)],[233]) ).
thf(88,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_pi_Odistinct_I55_J) ).
thf(550,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)],[88]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',fact_155_Late__Semantics_OClose2) ).
thf(1233,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)],[215]) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',fact_181_resSimCases) ).
thf(1327,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)],[236]) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',fact_82_residual_Oinducts) ).
thf(1260,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)],[223]) ).
thf(84,axiom,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_freeRes_Ofresh_I2_J) ).
thf(538,plain,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(213,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ B ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_sumIdempRight) ).
thf(1222,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',fact_37_freshFreeDerivative_I2_J) ).
thf(898,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)],[163]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',fact_169_substRes3) ).
thf(1127,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)],[203]) ).
thf(184,axiom,
! [A: pi,B: late_subject,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_BoundR @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_tauBoundTrans) ).
thf(1046,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)],[184]) ).
thf(243,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( sum @ A @ B )
= ( sum @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_pi_Oinject_I6_J) ).
thf(1359,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)],[243]) ).
thf(93,axiom,
( fresh_name_name
= ( != @ name ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_name__fresh) ).
thf(565,plain,
( fresh_name_name
= ( ^ [A: name,B: name] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(224,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_nilCases_H) ).
thf(1265,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(118,axiom,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_dual__order_Orefl) ).
thf(651,plain,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',fact_94_Par1F) ).
thf(1298,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)],[229]) ).
thf(137,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_pi_Odistinct_I81_J) ).
thf(719,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(34,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: late_subject,D: name] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong2129052853vative @ B @ B @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_derivativeReflexive) ).
thf(372,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: late_subject,D: name] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong2129052853vative @ B @ B @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(74,axiom,
! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
~ ( strong743114133lation @ piNil @ A @ ( input @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_nilSim_I2_J) ).
thf(504,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)],[74]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',fact_44_residual_Ostrong__inducts) ).
thf(751,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)],[143]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',fact_45_residual_Ostrong__inducts) ).
thf(1055,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)],[187]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',fact_153_transitions_OClose2) ).
thf(1409,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)],[253]) ).
thf(235,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_pi_Odistinct_I79_J) ).
thf(1323,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(107,axiom,
! [A: name,B: late_subject,C: name] :
( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_fresh__prod) ).
thf(619,plain,
! [A: name,B: late_subject,C: name] :
( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',fact_186_simCasesCont) ).
thf(838,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)],[152]) ).
thf(91,axiom,
! [A: product_prod_pi_pi,B: product_prod_pi_pi > $o] :
( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_mem__Collect__eq) ).
thf(559,plain,
! [A: product_prod_pi_pi,B: product_prod_pi_pi > $o] :
( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(113,axiom,
! [A: name,B: late_subject,C: pi] :
( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_fresh__prod) ).
thf(638,plain,
! [A: name,B: late_subject,C: pi] :
( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(50,axiom,
! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
~ ( strong743114133lation @ piNil @ A @ ( output @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_nilSim_I3_J) ).
thf(421,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)],[50]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',fact_51_residual_Ofresh_I2_J) ).
thf(1347,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)],[238]) ).
thf(176,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ ( sum @ B @ C ) @ D ) @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_sumAssocLeft) ).
thf(1013,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ ( sum @ B @ C ) @ D ) @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',fact_256_old_Oprod_Oinducts) ).
thf(289,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)],[10]) ).
thf(58,axiom,
! [A: pi,B: name,C: name] :
( ( subs @ ( tau @ A ) @ B @ C )
= ( tau @ ( subs @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_simps_I2_J) ).
thf(448,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)],[58]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',fact_108_freeRes_Ofresh_I1_J) ).
thf(316,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)],[16]) ).
thf(244,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/sandbox/benchmark/theBenchmark.p',fact_62_parCasesB) ).
thf(1362,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)],[244]) ).
thf(261,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/sandbox/benchmark/theBenchmark.p',fact_177_transitions_OComm1) ).
thf(1450,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)],[261]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',fact_47_pi_Ofresh_I8_J) ).
thf(514,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)],[77]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',fact_49_pi_Ofresh_I2_J) ).
thf(353,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)],[29]) ).
thf(68,axiom,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_subject_Oexhaust) ).
thf(480,plain,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(26,axiom,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ B @ A )
& ( ord_le630093991_pi_pi @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_dual__order_Oeq__iff) ).
thf(348,plain,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ B @ A )
& ( ord_le630093991_pi_pi @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(96,axiom,
! [A: set_Pr1834926343_pi_pi] :
( ( collec1051790738_pi_pi
@ ^ [B: product_prod_pi_pi] : ( member558706512_pi_pi @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Collect__mem__eq) ).
thf(574,plain,
! [A: set_Pr1834926343_pi_pi] :
( ( collec1051790738_pi_pi
@ ^ [B: product_prod_pi_pi] : ( member558706512_pi_pi @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(128,axiom,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: set_Pr1834926343_pi_pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( ord_le630093991_pi_pi @ B @ D )
=> ( strong743114133lation @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_monotonic) ).
thf(692,plain,
! [A: pi,B: set_Pr1834926343_pi_pi,C: pi,D: set_Pr1834926343_pi_pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( ord_le630093991_pi_pi @ B @ D )
=> ( strong743114133lation @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',fact_113_Open) ).
thf(866,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)],[159]) ).
thf(121,axiom,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_785364841reeRes @ A @ ( abs_fu681348580reeRes @ B @ C ) )
= ( ( A = B )
| ( fresh_1641682979reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_abs__fresh_I1_J) ).
thf(660,plain,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_785364841reeRes @ A @ ( abs_fu681348580reeRes @ B @ C ) )
= ( ( A = B )
| ( fresh_1641682979reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(237,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/sandbox/benchmark/theBenchmark.p',fact_8_sumCases_H) ).
thf(1345,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)],[237]) ).
thf(257,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/sandbox/benchmark/theBenchmark.p',fact_294_pi_Oinject_I8_J) ).
thf(1433,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)],[257]) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',fact_61_Late__Semantics_OPar2B) ).
thf(1242,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)],[217]) ).
thf(75,axiom,
! [A: name,B: name,C: late_subject] :
( ( fresh_728038529ubject @ A @ ( abs_fu1904601852ubject @ B @ C ) )
= ( ( A = B )
| ( fresh_717452603ubject @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_name__fresh__abs) ).
thf(507,plain,
! [A: name,B: name,C: late_subject] :
( ( fresh_728038529ubject @ A @ ( abs_fu1904601852ubject @ B @ C ) )
= ( ( A = B )
| ( fresh_717452603ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(81,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_order__trans) ).
thf(527,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(259,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_pi_Odistinct_I85_J) ).
thf(1438,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(37,axiom,
! [A: late_subject] :
~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_name__exists__fresh) ).
thf(381,plain,
! [A: late_subject] :
~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',fact_39_residual_Ostrong__induct) ).
thf(1067,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)],[190]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',fact_150_transitions_OInput) ).
thf(894,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)],[162]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',fact_58_freshBoundDerivative_I2_J) ).
thf(1123,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)],[202]) ).
thf(51,axiom,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_name__exists__fresh) ).
thf(424,plain,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(45,axiom,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
& ( ord_le630093991_pi_pi @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_eq__iff) ).
thf(407,plain,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
& ( ord_le630093991_pi_pi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(64,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_pi_Odistinct_I29_J) ).
thf(467,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)],[64]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',fact_72_outputBoundTrans) ).
thf(1032,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)],[182]) ).
thf(109,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_subject_Ofresh_I2_J) ).
thf(625,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(54,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_antisym) ).
thf(435,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(62,axiom,
! [A: name,B: late_freeRes,C: name] :
( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_fresh__prod) ).
thf(461,plain,
! [A: name,B: late_freeRes,C: name] :
( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(144,axiom,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_freshRes) ).
thf(757,plain,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(250,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/sandbox/benchmark/theBenchmark.p',fact_13_ResF) ).
thf(1392,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)],[250]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',fact_293_residual_Oinject_I1_J) ).
thf(710,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)],[134]) ).
thf(153,axiom,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_resZeroTrans) ).
thf(847,plain,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(69,axiom,
! [A: name,B: name,C: pi] :
( ( A != B )
=> ( fresh_name_pi @ A @ ( subs @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_fresh__fact2) ).
thf(484,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)],[69]) ).
thf(239,axiom,
! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_Late__Semantics_OInput) ).
thf(1350,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)],[239]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',fact_32_outputFreshTrans) ).
thf(1143,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)],[206]) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',fact_176_Late__Semantics_OComm2) ).
thf(1375,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)],[245]) ).
thf(189,axiom,
! [A: pi,B: late_residual,C: name] :
( ( late_transitions @ A @ B )
=> ( ( fresh_name_pi @ C @ A )
=> ( fresh_81631222sidual @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_freshResidual) ).
thf(1064,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)],[189]) ).
thf(199,axiom,
! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_residual_Ostrong__induct) ).
thf(1111,plain,
! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(30,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( ord_le630093991_pi_pi @ E @ F )
=> ( strong2129052853vative @ A @ B @ C @ D @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_derivativeMonotonic) ).
thf(356,plain,
! [A: pi,B: pi,C: late_subject,D: name,E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( ord_le630093991_pi_pi @ E @ F )
=> ( strong2129052853vative @ A @ B @ C @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(100,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_subject_Ofresh_I1_J) ).
thf(593,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(160,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: late_subject] :
( ( 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_717452603ubject @ 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/sandbox/benchmark/theBenchmark.p',fact_179_resSimCases) ).
thf(869,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: name,D: pi,E: late_subject] :
( ( 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_717452603ubject @ 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)],[160]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',fact_238_prod__cases) ).
thf(499,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)],[73]) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',fact_180_resSimCases) ).
thf(989,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)],[173]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',fact_93_resOutputTauTrans) ).
thf(857,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)],[157]) ).
thf(130,axiom,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_name__exists__fresh) ).
thf(697,plain,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(195,axiom,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_pi_Odistinct_I15_J) ).
thf(1089,plain,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(65,axiom,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_name__exists__fresh) ).
thf(471,plain,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(181,axiom,
! [A: pi,B: pi] :
( piNil
!= ( sum @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_pi_Odistinct_I11_J) ).
thf(1028,plain,
! [A: pi,B: pi] :
( piNil
!= ( sum @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_53_pi_Oinject_I1_J) ).
thf(488,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)],[70]) ).
thf(23,axiom,
! [A: name,B: pi,C: name] :
( ( fresh_name_pi @ A @ B )
=> ( ( subs @ B @ A @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_forget) ).
thf(339,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)],[23]) ).
thf(89,axiom,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
& ( ord_le630093991_pi_pi @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_order__class_Oorder_Oeq__iff) ).
thf(554,plain,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
& ( ord_le630093991_pi_pi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',fact_63_parCasesB_H) ).
thf(901,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)],[164]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',fact_297_resTauBoundTrans) ).
thf(1016,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)],[177]) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',fact_185_simCasesCont) ).
thf(970,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)],[169]) ).
thf(87,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_subset__antisym) ).
thf(547,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(133,axiom,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_pi_Odistinct_I3_J) ).
thf(706,plain,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(108,axiom,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_fresh__prod) ).
thf(622,plain,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_1641682979reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(247,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_resTrans_I1_J) ).
thf(1382,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)],[247]) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',fact_187_simCasesCont) ).
thf(1131,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)],[204]) ).
thf(61,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Late__Semantics1_Osubject_Odistinct_I1_J) ).
thf(457,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(171,axiom,
! [A: set_Pr1834926343_pi_pi,B: name,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( ( eqvt_pi @ A )
=> ( strong743114133lation @ ( sum @ ( res @ B @ C ) @ ( res @ B @ D ) ) @ A @ ( res @ B @ ( sum @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_sumResLeft) ).
thf(984,plain,
! [A: set_Pr1834926343_pi_pi,B: name,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( ( eqvt_pi @ A )
=> ( strong743114133lation @ ( sum @ ( res @ B @ C ) @ ( res @ B @ D ) ) @ A @ ( res @ B @ ( sum @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(103,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_Late__Semantics_OfreeRes_Odistinct_I1_J) ).
thf(605,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(24,axiom,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_simps_I1_J) ).
thf(343,plain,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_subset__trans) ).
thf(266,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(111,axiom,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_order__refl) ).
thf(633,plain,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(14,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_Late__Semantics_Osubject_Oinject_I2_J) ).
thf(311,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',fact_101_resInputBoundOutputTrans) ).
thf(765,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)],[147]) ).
thf(82,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( B = C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_ord__le__eq__trans) ).
thf(530,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( B = C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',fact_268_fresh__prodD_I1_J) ).
thf(398,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)],[42]) ).
thf(183,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ~ ! [E: pi,F: name,G: name] :
( ( ( A = F )
& ( B = G )
& ( C = E ) )
=> ( ( late_transitions @ E @ D )
=> ( F = G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_mismatchCases_H) ).
thf(1035,plain,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ~ ! [E: pi,F: name,G: name] :
( ( ( A = F )
& ( B = G )
& ( C = E ) )
=> ( ( late_transitions @ E @ D )
=> ( F = G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(47,axiom,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( tau @ B ) )
= ( fresh_name_pi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_pi_Ofresh_I3_J) ).
thf(412,plain,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( tau @ B ) )
= ( fresh_name_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(212,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ piNil ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_sumZeroLeft) ).
thf(1219,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ piNil ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(141,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ B @ A @ ( sum @ B @ piNil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_sumZeroRight) ).
thf(745,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ B @ A @ ( sum @ B @ piNil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(230,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/sandbox/benchmark/theBenchmark.p',fact_81_residual_Odistinct_I1_J) ).
thf(1301,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)],[230]) ).
thf(35,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_order_Otrans) ).
thf(375,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(102,axiom,
! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( ( B != C )
=> ( strong743114133lation @ D @ A @ ( mismatch @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_mismatchIdRight) ).
thf(601,plain,
! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( ( B != C )
=> ( strong743114133lation @ D @ A @ ( mismatch @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(99,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( A
= ( B @ C ) )
=> ( ( ord_le630093991_pi_pi @ C @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_ord__eq__le__subst) ).
thf(584,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( A
= ( B @ C ) )
=> ( ( ord_le630093991_pi_pi @ C @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_162_simps_I8_J) ).
thf(562,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)],[92]) ).
thf(174,axiom,
! [A: name,B: pi,C: late_residual] :
~ ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_mismatchTrans) ).
thf(1007,plain,
! [A: name,B: pi,C: late_residual] :
~ ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(249,axiom,
! [A: pi,B: name,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_tauOutputTrans) ).
thf(1389,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)],[249]) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',fact_144_resCasesB_H) ).
thf(772,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)],[150]) ).
thf(9,axiom,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_subst__identity) ).
thf(286,plain,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',fact_41_residual_Ostrong__induct) ).
thf(1403,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)],[252]) ).
thf(222,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/sandbox/benchmark/theBenchmark.p',fact_161_simps_I9_J) ).
thf(1256,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)],[222]) ).
thf(151,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: late_subject] :
( ( 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_717452603ubject @ 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/sandbox/benchmark/theBenchmark.p',fact_184_simCasesCont) ).
thf(826,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: late_subject] :
( ( 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_717452603ubject @ 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)],[151]) ).
thf(97,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( input @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_pi_Ofresh_I4_J) ).
thf(577,plain,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( input @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(57,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_antisym__conv) ).
thf(445,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(135,axiom,
! [A: name,B: name,C: pi] :
( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_name__fresh__abs) ).
thf(713,plain,
! [A: name,B: name,C: pi] :
( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(198,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( output @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_pi_Odistinct_I31_J) ).
thf(1107,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)],[198]) ).
thf(27,axiom,
ord_le630093991_pi_pi @ id_pi @ rel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Id) ).
thf(350,plain,
ord_le630093991_pi_pi @ id_pi @ rel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',fact_163_substTrans) ).
thf(540,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)],[85]) ).
thf(114,axiom,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_785364841reeRes @ A @ ( abs_fu681348580reeRes @ B @ C ) )
= ( ( A = B )
| ( fresh_1641682979reeRes @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_name__fresh__abs) ).
thf(641,plain,
! [A: name,B: name,C: late_freeRes] :
( ( fresh_785364841reeRes @ A @ ( abs_fu681348580reeRes @ B @ C ) )
= ( ( A = B )
| ( fresh_1641682979reeRes @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',fact_183_simE_I1_J) ).
thf(1428,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)],[256]) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',fact_191_simE_I2_J) ).
thf(979,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)],[170]) ).
thf(125,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ! [C: product_prod_pi_pi] :
( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_subsetI) ).
thf(681,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ! [C: product_prod_pi_pi] :
( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(200,axiom,
! [A: name,B: name,C: pi,D: pi] :
~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ late_TauR @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_outputTauTrans) ).
thf(1117,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)],[200]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',fact_299_tauCases) ).
thf(737,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)],[140]) ).
thf(117,axiom,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_subset__refl) ).
thf(649,plain,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',fact_212_fresh__prod) ).
thf(451,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)],[59]) ).
thf(94,axiom,
! [A: product_prod_pi_pi] :
~ ! [B: pi,C: pi] :
( A
!= ( product_Pair_pi_pi @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_old_Oprod_Oexhaust) ).
thf(567,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)],[94]) ).
thf(106,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Late__Semantics_OfreeRes_Oinject) ).
thf(616,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)],[106]) ).
thf(12,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ ( B @ C ) )
=> ( ( ord_le630093991_pi_pi @ C @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_order__subst1) ).
thf(303,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ ( B @ C ) )
=> ( ( ord_le630093991_pi_pi @ C @ D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le630093991_pi_pi @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(67,axiom,
! [A: name,B: name,C: name] :
( ( fresh_1093033124n_name @ A @ ( abs_fun_name_name @ B @ C ) )
= ( ( A = B )
| ( fresh_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_abs__fresh_I1_J) ).
thf(477,plain,
! [A: name,B: name,C: name] :
( ( fresh_1093033124n_name @ A @ ( abs_fun_name_name @ B @ C ) )
= ( ( A = B )
| ( fresh_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(39,axiom,
! [A: name,B: late_freeRes,C: late_subject] :
( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_fresh__prod) ).
thf(387,plain,
! [A: name,B: late_freeRes,C: late_subject] :
( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ B @ C ) )
= ( ( fresh_1641682979reeRes @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',fact_156_Late__Semantics_OClose1) ).
thf(1080,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)],[193]) ).
thf(83,axiom,
! [A: pi,B: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_IdD) ).
thf(535,plain,
! [A: pi,B: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(104,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).
thf(609,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',fact_292_pi_Oinject_I3_J) ).
thf(323,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)],[18]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',fact_46_Par2F) ).
thf(964,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)],[167]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',fact_48_pi_Ofresh_I7_J) ).
thf(769,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)],[149]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',fact_59_freshBoundDerivative_I1_J) ).
thf(1022,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)],[179]) ).
thf(20,axiom,
! [A: pi,B: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_pair__in__Id__conv) ).
thf(330,plain,
! [A: pi,B: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(188,axiom,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Sum2) ).
thf(1061,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)],[188]) ).
thf(131,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ B @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Strong__Late__Sim_Oreflexive) ).
thf(700,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ B @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(79,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ord_le630093991_pi_pi @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_equalityD2) ).
thf(520,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ord_le630093991_pi_pi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',fact_220_old_Oprod_Oinject) ).
thf(685,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)],[126]) ).
thf(165,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ C ) @ A @ ( sum @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_sumSym) ).
thf(959,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ C ) @ A @ ( sum @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(148,axiom,
late_transitions @ q @ ( late_FreeR @ alpha @ q2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_cRes_Ohyps_I1_J) ).
thf(768,plain,
late_transitions @ q @ ( late_FreeR @ alpha @ q2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(8,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ~ ( ( ord_le630093991_pi_pi @ A @ B )
=> ~ ( ord_le630093991_pi_pi @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_equalityE) ).
thf(278,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ~ ( ( ord_le630093991_pi_pi @ A @ B )
=> ~ ( ord_le630093991_pi_pi @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( input @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_pi_Odistinct_I21_J) ).
thf(394,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)],[41]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',fact_16_resInputFreeTrans) ).
thf(851,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)],[155]) ).
thf(55,axiom,
! [A: name,B: late_subject,C: name,D: pi] :
( ( fresh_81631222sidual @ A @ ( late_BoundR @ B @ C @ D ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_residual_Ofresh_I1_J) ).
thf(438,plain,
! [A: name,B: late_subject,C: name,D: pi] :
( ( fresh_81631222sidual @ A @ ( late_BoundR @ B @ C @ D ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(119,axiom,
! [A: name,B: late_subject,C: late_subject] :
( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_fresh__prod) ).
thf(653,plain,
! [A: name,B: late_subject,C: late_subject] :
( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ B @ C ) )
= ( ( fresh_717452603ubject @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(129,axiom,
! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_IdI) ).
thf(695,plain,
! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(218,axiom,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Sum1) ).
thf(1245,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)],[218]) ).
thf(209,axiom,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_pi_Odistinct_I45_J) ).
thf(1208,plain,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(122,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_eq__refl) ).
thf(663,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(255,axiom,
! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ( ( ( late_transitions @ C @ D )
=> ( ( A != B )
=> ( E @ A @ B ) ) )
=> ( E @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_mismatchCases) ).
thf(1420,plain,
! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ( ( ( late_transitions @ C @ D )
=> ( ( A != B )
=> ( E @ A @ B ) ) )
=> ( E @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(116,axiom,
eqvt_pi @ rel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Eqvt) ).
thf(648,plain,
eqvt_pi @ rel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',fact_164_simps_I7_J) ).
thf(1049,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)],[185]) ).
thf(254,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/sandbox/benchmark/theBenchmark.p',fact_146_outputIneqTrans) ).
thf(1413,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)],[254]) ).
thf(192,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_pi_Odistinct_I53_J) ).
thf(1076,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)],[192]) ).
thf(98,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( mismatch @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_pi_Odistinct_I39_J) ).
thf(580,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( mismatch @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',fact_15_residual_Oinject_I2_J) ).
thf(1025,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)],[180]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',fact_190_simCases) ).
thf(1225,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)],[214]) ).
thf(220,axiom,
fresh_1641682979reeRes @ x @ alpha,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_cRes_Ohyps_I2_J) ).
thf(1252,plain,
fresh_1641682979reeRes @ x @ alpha,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(46,axiom,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi > $o] :
( ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ A ) @ ( collec1051790738_pi_pi @ B ) )
= ( ! [C: product_prod_pi_pi] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Collect__mono__iff) ).
thf(409,plain,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi > $o] :
( ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ A ) @ ( collec1051790738_pi_pi @ B ) )
= ( ! [C: product_prod_pi_pi] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(3,axiom,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi > $o] :
( ! [C: product_prod_pi_pi] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec1051790738_pi_pi @ A )
= ( collec1051790738_pi_pi @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Collect__cong) ).
thf(263,plain,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi > $o] :
( ! [C: product_prod_pi_pi] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec1051790738_pi_pi @ A )
= ( collec1051790738_pi_pi @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(56,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_pi_Odistinct_I43_J) ).
thf(441,plain,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',fact_111_freeRes_Oinducts) ).
thf(359,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)],[31]) ).
thf(86,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: product_prod_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_in__mono) ).
thf(544,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: product_prod_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(132,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_nilSim_I1_J) ).
thf(703,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(120,axiom,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_freeRes_Oexhaust) ).
thf(656,plain,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(105,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( mismatch @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C )
& ( fresh_name_pi @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_pi_Ofresh_I6_J) ).
thf(613,plain,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( mismatch @ 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)],[105]) ).
thf(241,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( sum @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_pi_Odistinct_I41_J) ).
thf(1353,plain,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( sum @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',fact_60_Late__Semantics_OPar1B) ).
thf(1052,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)],[186]) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',fact_78_inputIneqTrans) ).
thf(1140,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)],[205]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',fact_262_fresh__prodD_I2_J) ).
thf(314,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)],[15]) ).
thf(95,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: product_prod_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_subsetD) ).
thf(571,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: product_prod_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(226,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/sandbox/benchmark/theBenchmark.p',fact_182_resSimCases) ).
thf(1272,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)],[226]) ).
thf(90,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ C @ A )
=> ( ord_le630093991_pi_pi @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_dual__order_Otrans) ).
thf(556,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ C @ A )
=> ( ord_le630093991_pi_pi @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(127,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_pi_Odistinct_I35_J) ).
thf(688,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(80,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Late__Semantics1_Osubject_Oinject_I2_J) ).
thf(524,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(72,axiom,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi > $o] :
( ! [C: product_prod_pi_pi] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ A ) @ ( collec1051790738_pi_pi @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Collect__mono) ).
thf(495,plain,
! [A: product_prod_pi_pi > $o,B: product_prod_pi_pi > $o] :
( ! [C: product_prod_pi_pi] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ A ) @ ( collec1051790738_pi_pi @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',fact_151_inputBoundOutputTrans) ).
thf(759,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)],[145]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',fact_30_inputFreeTrans) ).
thf(1010,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)],[175]) ).
thf(33,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_pi_Odistinct_I73_J) ).
thf(368,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( par @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',fact_66_transitions_OPar2B) ).
thf(1216,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)],[211]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',fact_100_resOutputInputTrans) ).
thf(891,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)],[161]) ).
thf(221,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_resTrans_I2_J) ).
thf(1253,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)],[221]) ).
thf(248,axiom,
! [A: pi,B: late_residual,C: name,D: name] :
( ( late_transitions @ A @ B )
=> ( ( C != D )
=> ( late_transitions @ ( mismatch @ C @ D @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_Mismatch) ).
thf(1385,plain,
! [A: pi,B: late_residual,C: name,D: name] :
( ( late_transitions @ A @ B )
=> ( ( C != D )
=> ( late_transitions @ ( mismatch @ C @ D @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(78,axiom,
! [A: name,B: name,C: name] :
( ( fresh_1093033124n_name @ A @ ( abs_fun_name_name @ B @ C ) )
= ( ( A = B )
| ( fresh_name_name @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_name__fresh__abs) ).
thf(517,plain,
! [A: name,B: name,C: name] :
( ( fresh_1093033124n_name @ A @ ( abs_fun_name_name @ B @ C ) )
= ( ( A = B )
| ( fresh_name_name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(17,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Late__Semantics_Osubject_Odistinct_I1_J) ).
thf(319,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',fact_175_Late__Semantics_OComm1) ).
thf(748,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)],[142]) ).
thf(28,axiom,
! [A: pi,B: set_Pr1834926343_pi_pi] : ( strong743114133lation @ A @ B @ piNil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_nilSimRight) ).
thf(351,plain,
! [A: pi,B: set_Pr1834926343_pi_pi] : ( strong743114133lation @ A @ B @ piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(40,axiom,
! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( ( B != C )
=> ( strong743114133lation @ ( mismatch @ B @ C @ D ) @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_mismatchIdLeft) ).
thf(390,plain,
! [A: set_Pr1834926343_pi_pi,B: name,C: name,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( ( B != C )
=> ( strong743114133lation @ ( mismatch @ B @ C @ D ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(43,axiom,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_pi_Odistinct_I13_J) ).
thf(401,plain,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',fact_43_residual_Ostrong__inducts) ).
thf(731,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)],[139]) ).
thf(49,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_dual__order_Oantisym) ).
thf(418,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(36,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Late__Semantics1_OfreeRes_Oinject) ).
thf(378,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)],[36]) ).
thf(76,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_pi_Odistinct_I19_J) ).
thf(510,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(210,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_pi_Odistinct_I27_J) ).
thf(1212,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)],[210]) ).
thf(6,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ! [C: pi,D: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ B ) )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_subrelI) ).
thf(272,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ! [C: pi,D: pi] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ D ) @ B ) )
=> ( ord_le630093991_pi_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(260,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/sandbox/benchmark/theBenchmark.p',fact_12_resCasesF_H) ).
thf(1442,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)],[260]) ).
thf(136,axiom,
! [A: name,B: name,C: late_subject] :
( ( fresh_728038529ubject @ A @ ( abs_fu1904601852ubject @ B @ C ) )
= ( ( A = B )
| ( fresh_717452603ubject @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_abs__fresh_I1_J) ).
thf(716,plain,
! [A: name,B: name,C: late_subject] :
( ( fresh_728038529ubject @ A @ ( abs_fu1904601852ubject @ B @ C ) )
= ( ( A = B )
| ( fresh_717452603ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',fact_244_Pair__inject) ).
thf(667,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)],[123]) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',fact_77_Late__Semantics_OResB) ).
thf(1294,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)],[228]) ).
thf(25,axiom,
( ord_le630093991_pi_pi
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
! [C: product_prod_pi_pi] :
( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_subset__iff) ).
thf(346,plain,
( ord_le630093991_pi_pi
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
! [C: product_prod_pi_pi] :
( ( member558706512_pi_pi @ C @ A )
=> ( member558706512_pi_pi @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(232,axiom,
late_transitions @ ( res @ x @ q ) @ ( late_FreeR @ alpha @ pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_cSum2_Ohyps) ).
thf(1309,plain,
late_transitions @ ( res @ x @ q ) @ ( late_FreeR @ alpha @ pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(53,axiom,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Late__Semantics1_Osubject_Oinject_I1_J) ).
thf(432,plain,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(168,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ B @ A @ ( sum @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_sumIdempLeft) ).
thf(967,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ B @ A @ ( sum @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',fact_11_resCasesF) ).
thf(1395,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)],[251]) ).
thf(44,axiom,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
& ( ord_le630093991_pi_pi @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_set__eq__subset) ).
thf(405,plain,
( ( (=) @ set_Pr1834926343_pi_pi )
= ( ^ [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
& ( ord_le630093991_pi_pi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',fact_102_resOutputOutputTrans) ).
thf(854,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)],[156]) ).
thf(207,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/sandbox/benchmark/theBenchmark.p',fact_152_resCases_H) ).
thf(1148,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)],[207]) ).
thf(219,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/sandbox/benchmark/theBenchmark.p',fact_154_transitions_OClose1) ).
thf(1248,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)],[219]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',fact_147_outputCases_H) ).
thf(1097,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)],[197]) ).
thf(1,conjecture,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(262,plain,
~ ( late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(258,axiom,
! [A: name,B: name,C: pi] : ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Output) ).
thf(1436,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)],[258]) ).
thf(19,axiom,
! [A: product_prod_pi_pi] :
( ( member558706512_pi_pi @ A @ id_pi )
=> ~ ! [B: pi] :
( A
!= ( product_Pair_pi_pi @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_IdE) ).
thf(326,plain,
! [A: product_prod_pi_pi] :
( ( member558706512_pi_pi @ A @ id_pi )
=> ~ ! [B: pi] :
( A
!= ( product_Pair_pi_pi @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le630093991_pi_pi @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_ord__le__eq__subst) ).
thf(294,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,D: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Pr1834926343_pi_pi,F: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ E @ F )
=> ( ord_le630093991_pi_pi @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le630093991_pi_pi @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(66,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_order__class_Oorder_Oantisym) ).
thf(474,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
( ( ord_le630093991_pi_pi @ A @ B )
=> ( ( ord_le630093991_pi_pi @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(112,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( par @ A @ B )
= ( par @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_pi_Oinject_I7_J) ).
thf(635,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)],[112]) ).
thf(48,axiom,
! [A: name,B: name,C: late_subject] :
( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_fresh__prod) ).
thf(415,plain,
! [A: name,B: name,C: late_subject] :
( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ B @ C ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_717452603ubject @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',fact_178_transitions_OComm2) ).
thf(1093,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)],[196]) ).
thf(225,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_pi_Odistinct_I75_J) ).
thf(1268,plain,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( res @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',fact_109_subject_Oinducts) ).
thf(427,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)],[52]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',fact_300_tauCases_H) ).
thf(860,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)],[158]) ).
thf(178,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ ( sum @ C @ D ) ) @ A @ ( sum @ ( sum @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_sumAssocRight) ).
thf(1019,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( strong743114133lation @ ( sum @ B @ ( sum @ C @ D ) ) @ A @ ( sum @ ( sum @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(115,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_pi_Odistinct_I5_J) ).
thf(644,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',fact_189_simulation__def) ).
thf(1357,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)],[242]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',fact_148_outputCases) ).
thf(723,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)],[138]) ).
thf(154,axiom,
late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Free_Ohyps) ).
thf(850,plain,
late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',fact_65_transitions_OPar1B) ).
thf(1120,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)],[201]) ).
thf(216,axiom,
! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_residual_Ostrong__inducts) ).
thf(1236,plain,
! [A: late_subject > late_residual > $o,B: late_subject,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_717452603ubject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: late_subject] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(172,axiom,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_Tau) ).
thf(987,plain,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(240,axiom,
late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AQ_H_092_060close_062) ).
thf(1352,plain,
late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(63,axiom,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_pi_Oinject_I2_J) ).
thf(464,plain,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(101,axiom,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_ord__eq__le__trans) ).
thf(596,plain,
! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C: set_Pr1834926343_pi_pi] :
( ( A = B )
=> ( ( ord_le630093991_pi_pi @ B @ C )
=> ( ord_le630093991_pi_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',fact_73_transitions_OResB) ).
thf(1378,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)],[246]) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',fact_271_resTauOutputTrans) ).
thf(1320,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)],[234]) ).
thf(22,axiom,
! [A: name] : ( fresh_name_pi @ A @ piNil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_pi_Ofresh_I1_J) ).
thf(337,plain,
! [A: name] : ( fresh_name_pi @ A @ piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(71,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_pi_Odistinct_I1_J) ).
thf(491,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(60,axiom,
! [A: name,B: name,C: pi] :
( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_name_pi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_abs__fresh_I1_J) ).
thf(454,plain,
! [A: name,B: name,C: pi] :
( ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ B @ C ) )
= ( ( A = B )
| ( fresh_name_pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1539,plain,
$false,
inference(e,[status(thm)],[365,333,628,1083,962,762,308,1073,1205,1305,1290,276,269,677,384,1310,550,1233,1327,1260,538,1222,898,1127,1046,1359,565,1265,651,1298,719,372,504,751,1055,1409,1323,619,838,559,638,421,1347,1013,289,448,316,1362,1450,514,353,480,348,574,692,866,660,1345,1433,1242,507,527,1438,381,1067,894,1123,424,407,467,1032,625,435,461,757,1392,710,847,484,1350,1143,1375,1064,1111,356,593,869,499,989,857,697,1089,471,1028,488,339,554,901,1016,970,547,706,622,1382,1131,457,984,605,343,266,633,311,765,530,398,1035,412,1219,745,1301,375,601,584,562,1007,1389,772,286,1403,1256,826,577,445,713,1107,350,540,641,1428,979,681,1117,737,649,451,567,616,303,477,387,1080,535,609,323,964,769,1022,330,1061,700,520,685,959,768,278,394,851,438,653,695,1245,1208,663,1420,648,1049,1413,1076,580,1025,1225,1252,409,263,441,359,544,703,656,613,1353,1052,1140,314,571,1272,556,688,524,495,759,1010,368,1216,891,1253,1385,517,319,748,351,390,401,731,418,378,510,1212,272,1442,716,667,1294,346,1309,432,967,1395,405,854,1148,1248,1097,262,1436,326,294,474,635,415,1093,1268,427,860,1019,644,1357,723,850,1120,1236,987,1352,464,596,1378,1320,337,491,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP183^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.22 % Computer : n010.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 20:08:18 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.18/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.05/1.27 % [INFO] Parsing done (367ms).
% 2.05/1.28 % [INFO] Running in sequential loop mode.
% 3.30/1.66 % [INFO] eprover registered as external prover.
% 3.30/1.67 % [INFO] Scanning for conjecture ...
% 3.74/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 313 axioms. Running axiom selection ...
% 3.97/1.94 % [INFO] Axiom selection finished. Selected 259 axioms (removed 54 axioms).
% 4.95/2.22 % [INFO] Problem is higher-order (TPTP THF).
% 4.95/2.25 % [INFO] Type checking passed.
% 4.95/2.26 % [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 ...
% 29.44/8.26 % External prover 'e' found a proof!
% 29.44/8.26 % [INFO] Killing All external provers ...
% 29.44/8.26 % Time passed: 7898ms (effective reasoning time: 6976ms)
% 29.44/8.26 % 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)>
% 29.44/8.27 % Axioms used in derivation (259): fact_50_pi_Ofresh_I1_J, fact_145_Output, fact_270_IdD, fact_187_simCasesCont, fact_10_Sum2, fact_161_simps_I9_J, fact_84_pi_Odistinct_I55_J, fact_39_residual_Ostrong__induct, fact_157_Late__Semantics1_Osubject_Oinject_I2_J, fact_28_pi_Odistinct_I11_J, fact_131_dual__order_Oantisym, fact_170_substRes2, fact_52_pi_Oinject_I7_J, fact_45_residual_Ostrong__inducts, fact_101_resInputBoundOutputTrans, fact_83_pi_Odistinct_I79_J, fact_256_old_Oprod_Oinducts, fact_56_Collect__cong, fact_86_pi_Odistinct_I13_J, fact_121_order_Otrans, fact_0_cRes_Ohyps_I2_J, fact_25_nilCases_H, fact_3_cRes_Ohyps_I1_J, fact_309_mismatchCases_H, fact_150_transitions_OInput, fact_140_Collect__mono, fact_276_pi_Ofresh_I4_J, fact_104_Late__Semantics_Osubject_Oinject_I2_J, fact_312_pi_Odistinct_I73_J, fact_132_in__mono, fact_15_residual_Oinject_I2_J, fact_78_inputIneqTrans, fact_288_pi_Odistinct_I35_J, fact_113_Open, fact_95_Strong__Late__Sim_Oreflexive, fact_213_fresh__prod, fact_107_subject_Ofresh_I2_J, fact_164_simps_I7_J, fact_181_resSimCases, fact_128_dual__order_Orefl, fact_192_derivativeReflexive, fact_53_pi_Oinject_I1_J, fact_88_pi_Odistinct_I31_J, fact_173_subject_Oexhaust, fact_282_abs__fresh_I1_J, fact_35_resTrans_I1_J, fact_98_monotonic, fact_295_tauBoundTrans, fact_178_transitions_OComm2, fact_307_mismatchCases, fact_133_subsetD, fact_160_Late__Semantics1_Osubject_Oinject_I1_J, fact_32_outputFreshTrans, fact_214_fresh__prod, fact_279_name__fresh__abs, fact_96_subset__antisym, fact_148_outputCases, fact_13_ResF, fact_299_tauCases, fact_280_name__fresh__abs, fact_85_sumResLeft, fact_38_residual_Ostrong__induct, fact_169_substRes3, fact_141_subset__trans, fact_211_fresh__prod, fact_65_transitions_OPar1B, fact_129_dual__order_Otrans, fact_11_resCasesF, fact_232_surj__pair, fact_8_sumCases_H, fact_80_freshRes, fact_108_freeRes_Ofresh_I1_J, fact_4_cSum2_Ohyps, fact_23_pi_Odistinct_I57_J, fact_207_fresh__prod, fact_165_simps_I1_J, fact_151_inputBoundOutputTrans, fact_298_tauOutputTrans, fact_166_forget, fact_100_resOutputInputTrans, fact_152_resCases_H, fact_122_antisym__conv, fact_172_Late__Semantics1_OfreeRes_Odistinct_I1_J, fact_291_pi_Odistinct_I45_J, fact_60_Late__Semantics_OPar1B, fact_93_resOutputTauTrans, fact_182_resSimCases, fact_55_Collect__mem__eq, fact_163_substTrans, fact_311_pi_Odistinct_I75_J, fact_171_freeRes_Oexhaust, fact_66_transitions_OPar2B, fact_156_Late__Semantics_OClose1, fact_300_tauCases_H, fact_58_freshBoundDerivative_I2_J, fact_310_Mismatch, fact_20_name__exists__fresh, fact_194_pair__in__Id__conv, fact_37_freshFreeDerivative_I2_J, fact_91_pi_Odistinct_I1_J, fact_54_mem__Collect__eq, fact_61_Late__Semantics_OPar2B, fact_153_transitions_OClose2, fact_74_nilSim_I3_J, fact_143_Collect__mono__iff, fact_190_simCases, fact_18_pi_Odistinct_I5_J, fact_274_simps_I2_J, fact_127_order__trans, fact_31_Id, fact_226_prod_Oinject, fact_76_sumZeroLeft, fact_41_residual_Ostrong__induct, fact_34_nilSim_I2_J, fact_139_subset__refl, fact_75_sumZeroRight, fact_135_subset__eq, fact_89_pi_Odistinct_I27_J, fact_111_freeRes_Oinducts, fact_48_pi_Ofresh_I7_J, fact_306_pi_Odistinct_I39_J, fact_40_residual_Ostrong__induct, fact_16_resInputFreeTrans, fact_82_residual_Oinducts, fact_33_freshFreeDerivative_I1_J, fact_292_pi_Oinject_I3_J, fact_301_Tau, fact_71_sumSym, fact_188_derivativeMonotonic, fact_183_simE_I1_J, fact_189_simulation__def, fact_196_IdI, fact_51_residual_Ofresh_I2_J, fact_68_sumAssocRight, fact_191_simE_I2_J, fact_72_outputBoundTrans, fact_142_set__eq__subset, fact_94_Par1F, fact_134_equalityE, fact_2__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AQ_H_092_060close_062, fact_73_transitions_OResB, fact_92_nilSimRight, fact_206_fresh__prod, fact_6_pi_Odistinct_I81_J, fact_304_mismatchIdLeft, fact_19_name__exists__fresh, fact_220_old_Oprod_Oinject, fact_244_Pair__inject, fact_297_resTauBoundTrans, fact_159_Late__Semantics1_OfreeRes_Oinject, fact_124_ord__eq__le__trans, fact_17_resZeroTrans, fact_36_freeRes_Ofresh_I2_J, fact_62_parCasesB, fact_114_order__subst1, fact_47_pi_Ofresh_I8_J, fact_175_Late__Semantics_OComm1, fact_117_ord__le__eq__subst, fact_5_Free_Ohyps, fact_97_subsetI, fact_162_simps_I8_J, fact_168_fresh__fact2, fact_290_pi_Odistinct_I43_J, fact_120_eq__refl, fact_285_pi_Oinject_I2_J, fact_147_outputCases_H, fact_119_antisym, fact_184_simCasesCont, fact_21_name__exists__fresh, fact_112_Late__Semantics_OfreeRes_Odistinct_I1_J, fact_302_inputCases_H, fact_180_resSimCases, fact_64_freshResidual, fact_262_fresh__prodD_I2_J, fact_283_abs__fresh_I1_J, fact_9_Sum1, fact_185_simCasesCont, fact_79_pi_Odistinct_I85_J, fact_63_parCasesB_H, fact_176_Late__Semantics_OComm2, fact_277_name__fresh__abs, fact_250_old_Oprod_Oexhaust, fact_87_outputTauTrans, fact_138_subset__iff, fact_30_inputFreeTrans, fact_308_mismatchTrans, fact_102_resOutputOutputTrans, fact_42_residual_Ostrong__inducts, fact_273_pi_Ofresh_I3_J, fact_287_pi_Odistinct_I19_J, fact_144_resCasesB_H, fact_137_equalityD2, fact_118_eq__iff, fact_268_fresh__prodD_I1_J, fact_90_pi_Odistinct_I21_J, fact_99_order__refl, fact_204_IdE, fact_210_fresh__prod, fact_126_order__class_Oorder_Oantisym, fact_284_abs__fresh_I1_J, fact_158_subst__identity, fact_303_mismatchIdRight, fact_44_residual_Ostrong__inducts, fact_281_abs__fresh_I1_J, fact_294_pi_Oinject_I8_J, fact_296_nilSim_I1_J, fact_305_pi_Ofresh_I6_J, fact_293_residual_Oinject_I1_J, fact_289_pi_Odistinct_I41_J, fact_202_subrelI, fact_77_Late__Semantics_OResB, fact_26_pi_Odistinct_I53_J, fact_7_sumCases, fact_212_fresh__prod, fact_1_Eqvt, fact_57_pi_Odistinct_I29_J, fact_12_resCasesF_H, fact_208_fresh__prod, fact_69_sumIdempLeft, fact_115_order__subst2, fact_130_dual__order_Oeq__iff, fact_46_Par2F, fact_43_residual_Ostrong__inducts, fact_278_name__fresh__abs, fact_125_ord__le__eq__trans, fact_49_pi_Ofresh_I2_J, fact_136_equalityD1, fact_272_residual_Ofresh_I1_J, fact_81_residual_Odistinct_I1_J, fact_22_name__exists__fresh, fact_103_Late__Semantics_OfreeRes_Oinject, fact_59_freshBoundDerivative_I1_J, fact_123_order__class_Oorder_Oeq__iff, fact_209_fresh__prod, fact_186_simCasesCont, fact_275_pi_Ofresh_I9_J, fact_286_pi_Odistinct_I3_J, fact_109_subject_Oinducts, fact_105_name__fresh, fact_149_Late__Semantics_OInput, fact_179_resSimCases, fact_238_prod__cases, fact_174_Late__Semantics1_Osubject_Odistinct_I1_J, fact_154_transitions_OClose1, fact_70_sumAssocLeft, fact_24_zeroTrans, fact_177_transitions_OComm1, fact_116_ord__eq__le__subst, fact_146_outputIneqTrans, fact_29_resTrans_I2_J, fact_106_subject_Ofresh_I1_J, fact_14_pi_Oinject_I6_J, fact_167_fresh__fact1, fact_110_Late__Semantics_Osubject_Odistinct_I1_J, fact_27_pi_Odistinct_I15_J, fact_271_resTauOutputTrans, fact_205_fresh__prod, fact_67_sumIdempRight, fact_155_Late__Semantics_OClose2
% 29.44/8.27 % No. of inferences in proof: 522
% 29.44/8.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7898 ms resp. 6976 ms w/o parsing
% 30.42/8.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.42/8.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------