%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP189^1 : 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 : n003.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 08:07:07 AM UTC 2026
% Result : Theorem 21.19s 5.77s
% Output : Refutation 22.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 254
% Syntax : Number of formulae : 510 ( 264 unt; 0 typ; 0 def)
% Number of atoms : 1552 ( 457 equ; 8 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 6424 ( 239 ~; 8 |; 128 &;5247 @)
% ( 0 <=>; 802 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Number of types : 32 ( 31 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 13 con; 0-5 aty)
% Number of variables : 2164 ( 34 ^;2074 !; 56 ?;2164 :)
% 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(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(subst_name_decl,type,
subst_name: name > name > name > name ).
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_pi_decl,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(fresh_543891186ion_pi_decl,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $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(p2_decl,type,
p2: pi ).
thf(pxQ_decl,type,
pxQ: pi ).
thf(q_decl,type,
q: pi ).
thf(rel_decl,type,
rel: set_Pr1834926343_pi_pi ).
thf(alpha_decl,type,
alpha: late_freeRes ).
thf(x_decl,type,
x: name ).
thf(112,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_126_fresh__prodD_I2_J) ).
thf(629,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)],[112]) ).
thf(185,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_47_outputBoundTrans) ).
thf(1024,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)],[185]) ).
thf(248,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_242_resOutputOutputTrans) ).
thf(1369,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)],[248]) ).
thf(187,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_73_residual_Ostrong__inducts) ).
thf(1031,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)],[187]) ).
thf(152,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_26_pi_Odistinct_I55_J) ).
thf(777,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)],[152]) ).
thf(234,axiom,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_pi_Odistinct_I45_J) ).
thf(1295,plain,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(208,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_101_simCasesCont) ).
thf(1110,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)],[208]) ).
thf(221,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_6_Par1F) ).
thf(1200,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)],[221]) ).
thf(225,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_64_parCasesB_H) ).
thf(1211,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)],[225]) ).
thf(9,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_205_old_Oprod_Oinducts) ).
thf(276,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)],[9]) ).
thf(19,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_Late__Semantics1_Osubject_Oinject_I2_J) ).
thf(308,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(226,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_97_simE_I2_J) ).
thf(1269,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)],[226]) ).
thf(216,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_310_tauOutputTrans) ).
thf(1158,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)],[216]) ).
thf(97,axiom,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_dual__order_Orefl) ).
thf(582,plain,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(148,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_pi_Odistinct_I81_J) ).
thf(762,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(144,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_240_inputBoundOutputTrans) ).
thf(741,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)],[144]) ).
thf(196,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ! [C: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ C @ piNil ) @ C ) @ A )
=> ( strong743114133lation @ ( par @ B @ piNil ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_parZeroLeft) ).
thf(1073,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ! [C: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ C @ piNil ) @ C ) @ A )
=> ( strong743114133lation @ ( par @ B @ piNil ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(120,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_43_nilSim_I2_J) ).
thf(655,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)],[120]) ).
thf(78,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_89_fresh__prod) ).
thf(511,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)],[78]) ).
thf(107,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_119_Collect__mono__iff) ).
thf(614,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)],[107]) ).
thf(7,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_256_subject_Oinducts) ).
thf(269,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)],[7]) ).
thf(43,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_270_forget) ).
thf(385,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)],[43]) ).
thf(74,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_162_IdD) ).
thf(500,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)],[74]) ).
thf(218,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_160_resSimCases) ).
thf(1164,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)],[218]) ).
thf(67,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_284_pi_Ofresh_I4_J) ).
thf(472,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)],[67]) ).
thf(86,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_103_subset__antisym) ).
thf(538,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)],[86]) ).
thf(160,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_278_transitions_OClose1) ).
thf(930,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)],[160]) ).
thf(50,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_187_order__class_Oorder_Oantisym) ).
thf(417,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)],[50]) ).
thf(245,axiom,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_pi_Odistinct_I13_J) ).
thf(1359,plain,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
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_50_Collect__cong) ).
thf(257,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(23,axiom,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_name__exists__fresh) ).
thf(320,plain,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(247,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_12_residual_Oinject_I2_J) ).
thf(1366,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)],[247]) ).
thf(44,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_217_Pair__inject) ).
thf(389,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)],[44]) ).
thf(158,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_102_simCasesCont) ).
thf(917,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)],[158]) ).
thf(229,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_31_freshFreeDerivative_I1_J) ).
thf(1279,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)],[229]) ).
thf(155,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_61_pi_Odistinct_I31_J) ).
thf(802,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)],[155]) ).
thf(31,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( sum @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_pi_Odistinct_I41_J) ).
thf(344,plain,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( sum @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(161,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_zeroTrans) ).
thf(934,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(35,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_Late__Semantics_Osubject_Oinject_I2_J) ).
thf(357,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(250,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_312_tauCases_H) ).
thf(1379,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)],[250]) ).
thf(11,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_244_sumZeroRight) ).
thf(284,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)],[11]) ).
thf(13,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_117_subset__trans) ).
thf(289,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)],[13]) ).
thf(68,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_182_dual__order_Oantisym) ).
thf(475,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)],[68]) ).
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_72_freshResidual) ).
thf(1040,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(71,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_192_order_Otrans) ).
thf(485,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)],[71]) ).
thf(79,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_308_abs__fresh_I1_J) ).
thf(514,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)],[79]) ).
thf(162,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ C @ 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(937,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)],[162]) ).
thf(32,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_98_Strong__Late__Sim_Oreflexive) ).
thf(348,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)],[32]) ).
thf(156,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_241_resCases_H) ).
thf(806,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)],[156]) ).
thf(149,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_170_sumCases) ).
thf(766,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)],[149]) ).
thf(130,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_132_fresh__prodD_I1_J) ).
thf(687,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)],[130]) ).
thf(114,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_107_derivativeReflexive) ).
thf(634,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)],[114]) ).
thf(61,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_46_pi_Oinject_I1_J) ).
thf(453,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)],[61]) ).
thf(209,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_140_simulation__def) ).
thf(1119,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)],[209]) ).
thf(177,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_277_transitions_OClose2) ).
thf(998,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)],[177]) ).
thf(48,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_168_freeRes_Ofresh_I1_J) ).
thf(411,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)],[48]) ).
thf(205,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_259_Late__Semantics_OInput) ).
thf(1104,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)],[205]) ).
thf(14,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_198_order__subst2) ).
thf(292,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)],[14]) ).
thf(223,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_62_pi_Odistinct_I29_J) ).
thf(1206,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)],[223]) ).
thf(56,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_90_fresh__prod) ).
thf(439,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)],[56]) ).
thf(83,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_183_dual__order_Oeq__iff) ).
thf(529,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)],[83]) ).
thf(122,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_176_pi_Odistinct_I53_J) ).
thf(661,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)],[122]) ).
thf(42,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_pi_Odistinct_I35_J) ).
thf(381,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(85,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_104_subsetI) ).
thf(534,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)],[85]) ).
thf(195,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_75_residual_Ostrong__inducts) ).
thf(1067,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)],[195]) ).
thf(227,axiom,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_pi_Odistinct_I15_J) ).
thf(1274,plain,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(28,axiom,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_freeRes_Ofresh_I2_J) ).
thf(334,plain,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(242,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_17_pi_Ofresh_I8_J) ).
thf(1343,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)],[242]) ).
thf(4,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_93_fresh__prod) ).
thf(260,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)],[4]) ).
thf(15,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_subject_Ofresh_I2_J) ).
thf(297,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(54,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_197_ord__eq__le__subst) ).
thf(429,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)],[54]) ).
thf(140,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_276_transitions_OComm2) ).
thf(729,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)],[140]) ).
thf(47,axiom,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_pi_Odistinct_I3_J) ).
thf(407,plain,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(132,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_186_order__trans) ).
thf(693,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)],[132]) ).
thf(111,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Late__Semantics_OfreeRes_Odistinct_I1_J) ).
thf(625,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(26,axiom,
ord_le630093991_pi_pi @ id_pi @ rel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Id) ).
thf(329,plain,
ord_le630093991_pi_pi @ id_pi @ rel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(123,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_pi_Odistinct_I19_J) ).
thf(665,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(81,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_138_subrelI) ).
thf(522,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)],[81]) ).
thf(224,axiom,
fresh_1641682979reeRes @ x @ alpha,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062x_A_092_060sharp_062_A_092_060alpha_062_092_060close_062) ).
thf(1210,plain,
fresh_1641682979reeRes @ x @ alpha,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
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_184_dual__order_Otrans) ).
thf(551,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(253,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_158_resSimCases) ).
thf(1392,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)],[253]) ).
thf(62,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_237_sumIdempLeft) ).
thf(456,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)],[62]) ).
thf(170,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_79_residual_Ostrong__induct) ).
thf(974,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)],[170]) ).
thf(181,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_14_resInputFreeTrans) ).
thf(1012,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)],[181]) ).
thf(206,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_171_sumCases_H) ).
thf(1106,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)],[206]) ).
thf(198,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_172_Sum1) ).
thf(1079,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)],[198]) ).
thf(186,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_272_Agent_OsubstRes3) ).
thf(1027,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)],[186]) ).
thf(244,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_100_simCasesCont) ).
thf(1350,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)],[244]) ).
thf(201,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi] :
( ! [D: pi,E: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ D @ E ) @ ( par @ E @ D ) ) @ A )
=> ( ! [D: pi,E: pi,F: name] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ D @ E ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ F @ D ) @ ( res @ F @ E ) ) @ A ) )
=> ( strong743114133lation @ ( par @ B @ C ) @ A @ ( par @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_parSym) ).
thf(1089,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi] :
( ! [D: pi,E: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ D @ E ) @ ( par @ E @ D ) ) @ A )
=> ( ! [D: pi,E: pi,F: name] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ D @ E ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ F @ D ) @ ( res @ F @ E ) ) @ A ) )
=> ( strong743114133lation @ ( par @ B @ C ) @ A @ ( par @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(164,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_80_residual_Ostrong__induct) ).
thf(948,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)],[164]) ).
thf(210,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_245_resInputBoundOutputTrans) ).
thf(1121,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)],[210]) ).
thf(194,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_nilCases_H) ).
thf(1064,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(100,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_243_sumZeroLeft) ).
thf(593,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)],[100]) ).
thf(51,axiom,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_simps_I1_J) ).
thf(420,plain,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(174,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh_name_pi @ A @ B )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ A @ ( par @ B @ C ) ) @ ( par @ B @ ( res @ A @ C ) ) ) @ rel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Res) ).
thf(989,plain,
! [A: name,B: pi,C: pi] :
( ( fresh_name_pi @ A @ B )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ A @ ( par @ B @ C ) ) @ ( par @ B @ ( res @ A @ C ) ) ) @ rel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(171,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_287_pi_Oinject_I8_J) ).
thf(980,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)],[171]) ).
thf(46,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_116_Collect__mono) ).
thf(403,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)],[46]) ).
thf(1,conjecture,
late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ ( par @ p2 @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ ( par @ p2 @ q ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(256,plain,
~ ( late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ ( par @ p2 @ q ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(199,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_pi_Odistinct_I85_J) ).
thf(1082,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(72,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_196_ord__le__eq__subst) ).
thf(488,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)],[72]) ).
thf(30,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_199_order__subst1) ).
thf(339,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)],[30]) ).
thf(233,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_173_Sum2) ).
thf(1292,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)],[233]) ).
thf(91,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_164_Late__Semantics_OfreeRes_Oinject) ).
thf(554,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)],[91]) ).
thf(219,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_232_outputCases_H) ).
thf(1182,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)],[219]) ).
thf(124,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_194_antisym) ).
thf(669,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)],[124]) ).
thf(82,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_94_fresh__prod) ).
thf(526,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)],[82]) ).
thf(115,axiom,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_name__exists__fresh) ).
thf(637,plain,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(136,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_77_residual_Ostrong__induct) ).
thf(706,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)],[136]) ).
thf(127,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_195_eq__iff) ).
thf(679,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)],[127]) ).
thf(169,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_pi_Odistinct_I43_J) ).
thf(970,plain,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(215,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_71_resOutputTauTrans) ).
thf(1155,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)],[215]) ).
thf(89,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_67_pi_Odistinct_I21_J) ).
thf(547,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)],[89]) ).
thf(110,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_155_old_Oprod_Oinject) ).
thf(622,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)],[110]) ).
thf(238,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_10_resCasesF_H) ).
thf(1324,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)],[238]) ).
thf(143,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_42_Late__Semantics_OPar1B) ).
thf(738,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)],[143]) ).
thf(220,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_139_simCases) ).
thf(1192,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)],[220]) ).
thf(192,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_63_transitions_OResB) ).
thf(1050,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)],[192]) ).
thf(178,axiom,
late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ ( par @ p2 @ q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062) ).
thf(1002,plain,
late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ ( par @ p2 @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(39,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_106_derivativeMonotonic) ).
thf(371,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)],[39]) ).
thf(75,axiom,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_pi_Oinject_I2_J) ).
thf(503,plain,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(104,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_96_fresh__prod) ).
thf(605,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)],[104]) ).
thf(200,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_181_Open) ).
thf(1086,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)],[200]) ).
thf(6,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_48_mem__Collect__eq) ).
thf(266,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)],[6]) ).
thf(36,axiom,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_freeRes_Oexhaust) ).
thf(360,plain,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(77,axiom,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_subst__identity) ).
thf(508,plain,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(20,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_268_fresh__fact2) ).
thf(311,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)],[20]) ).
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 )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_antisym__conv) ).
thf(541,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)],[87]) ).
thf(193,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_314_inputCases_H) ).
thf(1054,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)],[193]) ).
thf(231,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_264_simps_I8_J) ).
thf(1286,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)],[231]) ).
thf(154,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_9_resCasesF) ).
thf(794,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)],[154]) ).
thf(228,axiom,
fresh_name_pi @ x @ p2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062x_A_092_060sharp_062_AP_H_092_060close_062) ).
thf(1278,plain,
fresh_name_pi @ x @ p2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(146,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_231_outputCases) ).
thf(750,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)],[146]) ).
thf(212,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_32_freshFreeDerivative_I2_J) ).
thf(1146,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)],[212]) ).
thf(141,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_11_ResF) ).
thf(733,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)],[141]) ).
thf(103,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_265_substTrans) ).
thf(601,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)],[103]) ).
thf(98,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_189_ord__eq__le__trans) ).
thf(584,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)],[98]) ).
thf(52,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_109_subsetD) ).
thf(423,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)],[52]) ).
thf(252,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_274_Late__Semantics_OComm1) ).
thf(1389,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)],[252]) ).
thf(167,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_99_simCasesCont) ).
thf(958,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)],[167]) ).
thf(211,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_159_resSimCases) ).
thf(1124,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)],[211]) ).
thf(10,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_91_fresh__prod) ).
thf(281,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)],[10]) ).
thf(58,axiom,
! [A: name] : ( fresh_name_pi @ A @ piNil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_pi_Ofresh_I1_J) ).
thf(445,plain,
! [A: name] : ( fresh_name_pi @ A @ piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(95,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Late__Semantics1_Osubject_Odistinct_I1_J) ).
thf(572,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(239,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_263_simps_I9_J) ).
thf(1332,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)],[239]) ).
thf(65,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_Late__Semantics_Osubject_Odistinct_I1_J) ).
thf(466,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(125,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_236_sumAssocRight) ).
thf(672,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)],[125]) ).
thf(128,axiom,
! [A: late_subject] :
~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_name__exists__fresh) ).
thf(681,plain,
! [A: late_subject] :
~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(230,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_25_pi_Odistinct_I57_J) ).
thf(1282,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)],[230]) ).
thf(8,axiom,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_subset__refl) ).
thf(274,plain,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,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_111_subset__eq) ).
thf(318,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)],[22]) ).
thf(17,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_190_order__class_Oorder_Oeq__iff) ).
thf(303,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)],[17]) ).
thf(102,axiom,
! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_IdI) ).
thf(599,plain,
! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(157,axiom,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [F: pi,G: name,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ F ) )
=> ! [I: pi] :
( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ ( late_BoundOutputS @ G ) @ H @ I ) )
=> ( ( late_transitions @ F @ ( late_FreeR @ ( late_OutputR @ G @ H ) @ I ) )
=> ( G = H ) ) ) )
=> ~ ! [F: pi,G: late_subject,H: name,I: pi,J: name] :
( ( ( res @ A @ B )
= ( res @ J @ F ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( res @ J @ I ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_717452603ubject @ J @ G )
=> ( ( J != H )
=> ( ( fresh_name_pi @ H @ F )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_resCasesB_H) ).
thf(863,plain,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [F: pi,G: name,H: name] :
( ( ( res @ A @ B )
= ( res @ H @ F ) )
=> ! [I: pi] :
( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ ( late_BoundOutputS @ G ) @ H @ I ) )
=> ( ( late_transitions @ F @ ( late_FreeR @ ( late_OutputR @ G @ H ) @ I ) )
=> ( G = H ) ) ) )
=> ~ ! [F: pi,G: late_subject,H: name,I: pi,J: name] :
( ( ( res @ A @ B )
= ( res @ J @ F ) )
=> ( ( ( late_BoundR @ C @ D @ E )
= ( late_BoundR @ G @ H @ ( res @ J @ I ) ) )
=> ( ( late_transitions @ F @ ( late_BoundR @ G @ H @ I ) )
=> ( ( fresh_717452603ubject @ J @ G )
=> ( ( J != H )
=> ( ( fresh_name_pi @ H @ F )
=> ~ ( fresh_717452603ubject @ H @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(191,axiom,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_freshRes) ).
thf(1048,plain,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(142,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_234_Output) ).
thf(736,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)],[142]) ).
thf(118,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_51_nilSim_I3_J) ).
thf(649,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)],[118]) ).
thf(190,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_120_simE_I1_J) ).
thf(1043,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)],[190]) ).
thf(113,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_166_pi_Ofresh_I7_J) ).
thf(631,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)],[113]) ).
thf(147,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_275_transitions_OComm1) ).
thf(758,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)],[147]) ).
thf(38,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_pi_Odistinct_I5_J) ).
thf(367,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(24,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_235_sumIdempRight) ).
thf(323,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)],[24]) ).
thf(134,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_92_fresh__prod) ).
thf(700,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)],[134]) ).
thf(213,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_82_resTrans_I1_J) ).
thf(1149,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)],[213]) ).
thf(27,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_113_equalityD2) ).
thf(330,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)],[27]) ).
thf(64,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_142_IdE) ).
thf(462,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)],[64]) ).
thf(172,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_261_Late__Semantics_OClose2) ).
thf(983,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)],[172]) ).
thf(45,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_178_pi_Odistinct_I27_J) ).
thf(399,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)],[45]) ).
thf(150,axiom,
! [A: name,B: pi,C: name,D: pi] :
( ( fresh_name_pi @ A @ B )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ A @ ( res @ C @ ( par @ B @ D ) ) ) @ ( res @ C @ ( par @ B @ ( res @ A @ D ) ) ) ) @ rel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_ScopeExt) ).
thf(768,plain,
! [A: name,B: pi,C: name,D: pi] :
( ( fresh_name_pi @ A @ B )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ A @ ( res @ C @ ( par @ B @ D ) ) ) @ ( res @ C @ ( par @ B @ ( res @ A @ D ) ) ) ) @ rel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(182,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_60_outputTauTrans) ).
thf(1015,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)],[182]) ).
thf(105,axiom,
! [A: pi,B: pi] :
( piNil
!= ( sum @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_pi_Odistinct_I11_J) ).
thf(608,plain,
! [A: pi,B: pi] :
( piNil
!= ( sum @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(173,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_54_inputIneqTrans) ).
thf(986,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)],[173]) ).
thf(55,axiom,
eqvt_pi @ rel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_EqvtRel) ).
thf(438,plain,
eqvt_pi @ rel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(121,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_subject_Ofresh_I1_J) ).
thf(658,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(126,axiom,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_subject_Oexhaust) ).
thf(675,plain,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(53,axiom,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( tau @ B ) )
= ( fresh_name_pi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_pi_Ofresh_I3_J) ).
thf(426,plain,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( tau @ B ) )
= ( fresh_name_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(84,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_248_Late__Semantics1_OfreeRes_Oinject) ).
thf(531,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)],[84]) ).
thf(40,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).
thf(374,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(108,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_149_prod_Oinject) ).
thf(617,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)],[108]) ).
thf(241,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_251_resOutputInputTrans) ).
thf(1340,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)],[241]) ).
thf(183,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_57_residual_Oinducts) ).
thf(1018,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)],[183]) ).
thf(255,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_52_Late__Semantics_OResB) ).
thf(1413,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)],[255]) ).
thf(197,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_279_resTauOutputTrans) ).
thf(1076,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)],[197]) ).
thf(222,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ! [C: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ ( par @ C @ piNil ) ) @ A )
=> ( strong743114133lation @ B @ A @ ( par @ B @ piNil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_parZeroRight) ).
thf(1203,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
( ! [C: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ C @ ( par @ C @ piNil ) ) @ A )
=> ( strong743114133lation @ B @ A @ ( par @ B @ piNil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(99,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_269_fresh__fact1) ).
thf(589,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)],[99]) ).
thf(131,axiom,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_Late__Semantics1_Osubject_Oinject_I1_J) ).
thf(690,plain,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(116,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_193_eq__refl) ).
thf(640,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)],[116]) ).
thf(49,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_288_residual_Oinject_I1_J) ).
thf(414,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)],[49]) ).
thf(165,axiom,
fresh_name_pi @ x @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms_I1_J) ).
thf(954,plain,
fresh_name_pi @ x @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(5,axiom,
! [A: name,B: pi,C: pi] :
( ( ( abs_fun_name_pi @ A @ B )
= ( abs_fun_name_pi @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_abs__fun__eq1) ).
thf(263,plain,
! [A: name,B: pi,C: pi] :
( ( ( abs_fun_name_pi @ A @ B )
= ( abs_fun_name_pi @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(137,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_37_outputFreshTrans) ).
thf(712,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)],[137]) ).
thf(92,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_282_simps_I2_J) ).
thf(557,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)],[92]) ).
thf(179,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_76_residual_Ostrong__inducts) ).
thf(1003,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)],[179]) ).
thf(138,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_13_pi_Oinject_I7_J) ).
thf(717,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)],[138]) ).
thf(240,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_258_transitions_OInput) ).
thf(1336,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)],[240]) ).
thf(88,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_84_pair__in__Id__conv) ).
thf(544,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)],[88]) ).
thf(66,axiom,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_order__refl) ).
thf(470,plain,
! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(96,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_180_freeRes_Oinducts) ).
thf(576,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)],[96]) ).
thf(145,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_78_residual_Ostrong__induct) ).
thf(744,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)],[145]) ).
thf(29,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_49_Collect__mem__eq) ).
thf(336,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)],[29]) ).
thf(135,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_309_resTauBoundTrans) ).
thf(703,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)],[135]) ).
thf(184,axiom,
late_transitions @ p @ ( late_FreeR @ alpha @ p2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cPar1_Ohyps) ).
thf(1023,plain,
late_transitions @ p @ ( late_FreeR @ alpha @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(202,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(1094,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)],[202]) ).
thf(249,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_233_outputIneqTrans) ).
thf(1372,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)],[249]) ).
thf(106,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_114_subset__iff) ).
thf(612,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)],[106]) ).
thf(73,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_239_sumSym) ).
thf(497,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)],[73]) ).
thf(60,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_87_fresh__prod) ).
thf(450,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)],[60]) ).
thf(70,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_45_pi_Ofresh_I2_J) ).
thf(482,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)],[70]) ).
thf(237,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_273_Late__Semantics_OComm2) ).
thf(1321,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)],[237]) ).
thf(232,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_53_freshBoundDerivative_I1_J) ).
thf(1289,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)],[232]) ).
thf(151,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_74_residual_Ostrong__inducts) ).
thf(771,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)],[151]) ).
thf(207,axiom,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_Tau) ).
thf(1108,plain,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(251,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_56_residual_Odistinct_I1_J) ).
thf(1385,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)],[251]) ).
thf(80,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_223_prod__cases) ).
thf(517,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)],[80]) ).
thf(204,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_41_Late__Semantics_OPar2B) ).
thf(1101,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)],[204]) ).
thf(153,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_40_parCasesB) ).
thf(781,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)],[153]) ).
thf(176,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_7_Par2F) ).
thf(995,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)],[176]) ).
thf(119,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_266_simps_I7_J) ).
thf(652,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)],[119]) ).
thf(33,axiom,
! [A: name,B: name,C: pi,D: name,E: name] :
( ( subs @ ( output @ A @ B @ C ) @ D @ E )
= ( output @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_simps_I3_J) ).
thf(351,plain,
! [A: name,B: name,C: pi,D: name,E: name] :
( ( subs @ ( output @ A @ B @ C ) @ D @ E )
= ( output @ ( subst_name @ A @ D @ E ) @ ( subst_name @ B @ D @ E ) @ ( subs @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(41,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_95_fresh__prod) ).
thf(378,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)],[41]) ).
thf(159,axiom,
late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Free_Ohyps) ).
thf(929,plain,
late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(69,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_112_equalityD1) ).
thf(478,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)],[69]) ).
thf(129,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_238_sumAssocLeft) ).
thf(684,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)],[129]) ).
thf(217,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_285_tauBoundTrans) ).
thf(1161,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)],[217]) ).
thf(12,axiom,
! [A: pi,B: set_Pr1834926343_pi_pi] : ( strong743114133lation @ A @ B @ piNil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_nilSimRight) ).
thf(287,plain,
! [A: pi,B: set_Pr1834926343_pi_pi] : ( strong743114133lation @ A @ B @ piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,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_280_residual_Ofresh_I1_J) ).
thf(300,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)],[16]) ).
thf(109,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_set__eq__subset) ).
thf(620,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)],[109]) ).
thf(59,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_229_surj__pair) ).
thf(447,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)],[59]) ).
thf(21,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_300_pi_Oinject_I3_J) ).
thf(315,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)],[21]) ).
thf(168,axiom,
! [A: set_Pr1834926343_pi_pi,B: name,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( ( eqvt_pi @ A )
=> ( strong743114133lation @ ( res @ B @ ( sum @ C @ D ) ) @ A @ ( sum @ ( res @ B @ C ) @ ( res @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_sumResRight) ).
thf(967,plain,
! [A: set_Pr1834926343_pi_pi,B: name,C: pi,D: pi] :
( ( ord_le630093991_pi_pi @ id_pi @ A )
=> ( ( eqvt_pi @ A )
=> ( strong743114133lation @ ( res @ B @ ( sum @ C @ D ) ) @ A @ ( sum @ ( res @ B @ C ) @ ( res @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(203,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_81_freshBoundDerivative_I2_J) ).
thf(1097,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)],[203]) ).
thf(236,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_157_resSimCases) ).
thf(1303,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)],[236]) ).
thf(94,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_110_equalityE) ).
thf(564,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)],[94]) ).
thf(18,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_143_monotonic) ).
thf(305,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)],[18]) ).
thf(25,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_304_name__fresh__abs) ).
thf(326,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)],[25]) ).
thf(246,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_38_residual_Ofresh_I2_J) ).
thf(1363,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)],[246]) ).
thf(76,axiom,
( fresh_name_name
= ( != @ name ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_name__fresh) ).
thf(506,plain,
( fresh_name_name
= ( ^ [A: name,B: name] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(254,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_34_inputFreeTrans) ).
thf(1410,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)],[254]) ).
thf(133,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_211_old_Oprod_Oexhaust) ).
thf(696,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)],[133]) ).
thf(139,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ! [E: pi,F: pi,G: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ E @ F ) @ G ) @ ( par @ E @ ( par @ F @ G ) ) ) @ A )
=> ( ! [E: pi,F: pi,G: name] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ E @ F ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ G @ E ) @ ( res @ G @ F ) ) @ A ) )
=> ( ! [E: pi,F: pi,G: pi,H: name] :
( ( fresh_name_pi @ H @ E )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ H @ ( par @ ( par @ E @ F ) @ G ) ) @ ( par @ E @ ( res @ H @ ( par @ F @ G ) ) ) ) @ A ) )
=> ( ! [E: pi,F: pi,G: pi,H: name] :
( ( fresh_name_pi @ H @ G )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ H @ ( par @ E @ F ) ) @ G ) @ ( res @ H @ ( par @ E @ ( par @ F @ G ) ) ) ) @ A ) )
=> ( strong743114133lation @ ( par @ ( par @ B @ C ) @ D ) @ A @ ( par @ B @ ( par @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_parAssocLeft) ).
thf(720,plain,
! [A: set_Pr1834926343_pi_pi,B: pi,C: pi,D: pi] :
( ! [E: pi,F: pi,G: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ E @ F ) @ G ) @ ( par @ E @ ( par @ F @ G ) ) ) @ A )
=> ( ! [E: pi,F: pi,G: name] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ E @ F ) @ A )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ G @ E ) @ ( res @ G @ F ) ) @ A ) )
=> ( ! [E: pi,F: pi,G: pi,H: name] :
( ( fresh_name_pi @ H @ E )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ H @ ( par @ ( par @ E @ F ) @ G ) ) @ ( par @ E @ ( res @ H @ ( par @ F @ G ) ) ) ) @ A ) )
=> ( ! [E: pi,F: pi,G: pi,H: name] :
( ( fresh_name_pi @ H @ G )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ H @ ( par @ E @ F ) ) @ G ) @ ( res @ H @ ( par @ E @ ( par @ F @ G ) ) ) ) @ A ) )
=> ( strong743114133lation @ ( par @ ( par @ B @ C ) @ D ) @ A @ ( par @ B @ ( par @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(166,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_260_Late__Semantics_OClose1) ).
thf(955,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)],[166]) ).
thf(243,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_pi_Odistinct_I79_J) ).
thf(1346,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(214,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_283_pi_Ofresh_I9_J) ).
thf(1152,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)],[214]) ).
thf(101,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_108_in__mono) ).
thf(596,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)],[101]) ).
thf(117,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_188_ord__le__eq__trans) ).
thf(644,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)],[117]) ).
thf(63,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_169_pi_Oinject_I6_J) ).
thf(459,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)],[63]) ).
thf(175,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_163_sumResLeft) ).
thf(992,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)],[175]) ).
thf(235,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_271_substRes2) ).
thf(1299,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)],[235]) ).
thf(57,axiom,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_name__exists__fresh) ).
thf(442,plain,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(163,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_313_tauCases) ).
thf(940,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)],[163]) ).
thf(34,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_88_fresh__prod) ).
thf(354,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)],[34]) ).
thf(180,axiom,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_resZeroTrans) ).
thf(1009,plain,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(37,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_nilSim_I1_J) ).
thf(364,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(188,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_33_resTrans_I2_J) ).
thf(1037,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)],[188]) ).
thf(93,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_pi_Odistinct_I1_J) ).
thf(560,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1459,plain,
$false,
inference(e,[status(thm)],[629,1024,1369,1031,777,1295,1110,1200,1211,276,308,1269,1158,582,762,741,1073,655,511,614,269,385,500,1164,472,538,930,417,1359,257,320,1366,389,917,1279,802,344,934,357,1379,284,289,475,1040,485,514,937,348,806,766,687,634,453,1119,998,411,1104,292,1206,439,529,661,381,534,1067,1274,334,1343,260,297,429,729,407,693,625,329,665,522,1210,551,1392,456,974,1012,1106,1079,1027,1350,1089,948,1121,1064,593,420,989,980,403,256,1082,488,339,1292,554,1182,669,526,637,706,679,970,1155,547,622,1324,738,1192,1050,1002,371,503,605,1086,266,360,508,311,541,1054,1286,794,1278,750,1146,733,601,584,423,1389,958,1124,281,445,572,1332,466,672,681,1282,274,318,303,599,863,1048,736,649,1043,631,758,367,323,700,1149,330,462,983,399,768,1015,608,986,438,658,675,426,531,374,617,1340,1018,1413,1076,1203,589,690,640,414,954,263,712,557,1003,717,1336,544,470,576,744,336,703,1023,1094,1372,612,497,450,482,1321,1289,771,1108,1385,517,1101,781,995,652,351,378,929,478,684,1161,287,300,620,447,315,967,1097,1303,564,305,326,1363,506,1410,696,720,955,1346,1152,596,644,459,992,1299,442,940,354,1009,364,1037,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP189^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n003.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 20:11:05 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.88/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.18/1.18 % [INFO] Parsing done (409ms).
% 2.41/1.20 % [INFO] Running in sequential loop mode.
% 3.48/1.59 % [INFO] eprover registered as external prover.
% 3.48/1.59 % [INFO] Scanning for conjecture ...
% 3.92/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 316 axioms. Running axiom selection ...
% 4.46/1.92 % [INFO] Axiom selection finished. Selected 253 axioms (removed 63 axioms).
% 5.52/2.24 % [INFO] Problem is higher-order (TPTP THF).
% 5.52/2.28 % [INFO] Type checking passed.
% 5.52/2.29 % [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 ...
% 21.19/5.76 % External prover 'e' found a proof!
% 21.19/5.76 % [INFO] Killing All external provers ...
% 21.19/5.76 % Time passed: 5420ms (effective reasoning time: 4561ms)
% 21.19/5.77 % 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)>
% 21.19/5.77 % Axioms used in derivation (253): fact_315_simps_I3_J, fact_180_freeRes_Oinducts, fact_312_tauCases_H, fact_25_pi_Odistinct_I57_J, fact_160_resSimCases, fact_42_Late__Semantics_OPar1B, fact_4_assms_I1_J, fact_60_outputTauTrans, fact_248_Late__Semantics1_OfreeRes_Oinject, fact_245_resInputBoundOutputTrans, fact_100_simCasesCont, fact_238_sumAssocLeft, fact_59_parZeroLeft, fact_197_ord__eq__le__subst, fact_107_derivativeReflexive, fact_46_pi_Oinject_I1_J, fact_28_nilCases_H, fact_176_pi_Odistinct_I53_J, fact_193_eq__refl, fact_138_subrelI, fact_102_simCasesCont, fact_246_sumResRight, fact_297_pi_Odistinct_I41_J, fact_177_pi_Odistinct_I11_J, fact_140_simulation__def, fact_283_pi_Ofresh_I9_J, fact_304_name__fresh__abs, fact_43_nilSim_I2_J, fact_295_pi_Odistinct_I3_J, fact_1__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062, fact_276_transitions_OComm2, fact_2_cPar1_Ohyps, fact_250_freeRes_Oexhaust, fact_159_resSimCases, fact_309_resTauBoundTrans, fact_53_freshBoundDerivative_I1_J, fact_0__092_060open_062x_A_092_060sharp_062_A_092_060alpha_062_092_060close_062, fact_143_monotonic, fact_194_antisym, fact_19_pi_Odistinct_I5_J, fact_45_pi_Ofresh_I2_J, fact_26_pi_Odistinct_I55_J, fact_41_Late__Semantics_OPar2B, fact_44_freeRes_Ofresh_I2_J, fact_278_transitions_OClose1, fact_112_equalityD1, fact_234_Output, fact_174_pi_Odistinct_I81_J, fact_61_pi_Odistinct_I31_J, fact_149_prod_Oinject, fact_24_freshRes, fact_116_Collect__mono, fact_249_Late__Semantics1_OfreeRes_Odistinct_I1_J, fact_67_pi_Odistinct_I21_J, fact_258_transitions_OInput, fact_96_fresh__prod, fact_272_Agent_OsubstRes3, fact_313_tauCases, fact_81_freshBoundDerivative_I2_J, fact_10_resCasesF_H, fact_217_Pair__inject, fact_6_Par1F, fact_311_Tau, fact_275_transitions_OComm1, fact_50_Collect__cong, fact_195_eq__iff, fact_178_pi_Odistinct_I27_J, fact_12_residual_Oinject_I2_J, fact_17_pi_Ofresh_I8_J, fact_188_ord__le__eq__trans, fact_273_Late__Semantics_OComm2, fact_71_resOutputTauTrans, fact_65_transitions_OPar1B, fact_244_sumZeroRight, fact_78_residual_Ostrong__induct, fact_263_simps_I9_J, fact_88_fresh__prod, fact_103_subset__antisym, fact_8_pi_Odistinct_I85_J, fact_261_Late__Semantics_OClose2, fact_139_simCases, fact_97_simE_I2_J, fact_13_pi_Oinject_I7_J, fact_293_abs__fun__eq1, fact_231_outputCases, fact_279_resTauOutputTrans, fact_66_transitions_OPar2B, fact_132_fresh__prodD_I1_J, fact_98_Strong__Late__Sim_Oreflexive, fact_86_IdI, fact_167_subject_Ofresh_I2_J, fact_20_name__exists__fresh, fact_182_dual__order_Oantisym, fact_39_Id, fact_18_pi_Ofresh_I1_J, fact_184_dual__order_Otrans, fact_33_resTrans_I2_J, fact_241_resCases_H, fact_237_sumIdempLeft, fact_240_inputBoundOutputTrans, fact_211_old_Oprod_Oexhaust, fact_77_residual_Ostrong__induct, fact_270_forget, fact_120_simE_I1_J, fact_232_outputCases_H, fact_251_resOutputInputTrans, fact_285_tauBoundTrans, fact_198_order__subst2, fact_82_resTrans_I1_J, fact_93_fresh__prod, fact_171_sumCases_H, fact_38_residual_Ofresh_I2_J, fact_288_residual_Oinject_I1_J, fact_265_substTrans, fact_187_order__class_Oorder_Oantisym, fact_73_residual_Ostrong__inducts, fact_181_Open, fact_62_pi_Odistinct_I29_J, fact_101_simCasesCont, fact_190_order__class_Oorder_Oeq__iff, fact_80_residual_Ostrong__induct, fact_74_residual_Ostrong__inducts, fact_110_equalityE, fact_264_simps_I8_J, fact_11_ResF, fact_268_fresh__fact2, fact_32_freshFreeDerivative_I2_J, fact_262_subst__identity, fact_94_fresh__prod, fact_179_Late__Semantics_OfreeRes_Odistinct_I1_J, fact_64_parCasesB_H, fact_170_sumCases, fact_254_subject_Oexhaust, fact_57_residual_Oinducts, fact_266_simps_I7_J, fact_5__092_060open_062x_A_092_060sharp_062_AP_H_092_060close_062, fact_92_fresh__prod, fact_169_pi_Oinject_I6_J, fact_289_pi_Oinject_I2_J, fact_126_fresh__prodD_I2_J, fact_260_Late__Semantics_OClose1, fact_233_outputIneqTrans, fact_89_fresh__prod, fact_90_fresh__prod, fact_239_sumSym, fact_15_EqvtRel, fact_164_Late__Semantics_OfreeRes_Oinject, fact_72_freshResidual, fact_54_inputIneqTrans, fact_242_resOutputOutputTrans, fact_30_pi_Odistinct_I13_J, fact_256_subject_Oinducts, fact_21_name__exists__fresh, fact_271_substRes2, fact_118_set__eq__subset, fact_76_residual_Ostrong__inducts, fact_162_IdD, fact_34_inputFreeTrans, fact_286_nilSim_I1_J, fact_23_name__exists__fresh, fact_205_old_Oprod_Oinducts, fact_314_inputCases_H, fact_142_IdE, fact_58_parZeroRight, fact_196_ord__le__eq__subst, fact_229_surj__pair, fact_277_transitions_OClose2, fact_247_Late__Semantics1_Osubject_Oinject_I2_J, fact_3_Free_Ohyps, fact_175_pi_Odistinct_I79_J, fact_69_nilSimRight, fact_281_pi_Ofresh_I3_J, fact_108_in__mono, fact_156_order__refl, fact_287_pi_Oinject_I8_J, fact_192_order_Otrans, fact_68_pi_Odistinct_I1_J, fact_48_mem__Collect__eq, fact_51_nilSim_I3_J, fact_114_subset__iff, fact_106_derivativeMonotonic, fact_56_residual_Odistinct_I1_J, fact_49_Collect__mem__eq, fact_117_subset__trans, fact_294_pi_Odistinct_I19_J, fact_47_outputBoundTrans, fact_29_pi_Odistinct_I15_J, fact_269_fresh__fact1, fact_172_Sum1, fact_84_pair__in__Id__conv, fact_7_Par2F, fact_235_sumIdempRight, fact_31_freshFreeDerivative_I1_J, fact_95_fresh__prod, fact_296_pi_Odistinct_I35_J, fact_55_parSym, fact_14_resInputFreeTrans, fact_166_pi_Ofresh_I7_J, fact_111_subset__eq, fact_236_sumAssocRight, fact_63_transitions_OResB, fact_186_order__trans, fact_168_freeRes_Ofresh_I1_J, fact_300_pi_Oinject_I3_J, fact_310_tauOutputTrans, fact_70_parAssocLeft, fact_284_pi_Ofresh_I4_J, fact_189_ord__eq__le__trans, fact_40_parCasesB, fact_27_zeroTrans, fact_274_Late__Semantics_OComm1, fact_259_Late__Semantics_OInput, fact_36_Res, fact_22_name__exists__fresh, fact_191_antisym__conv, fact_99_simCasesCont, fact_230_resCasesB_H, fact_75_residual_Ostrong__inducts, fact_199_order__subst1, fact_105_name__fresh, fact_253_subject_Ofresh_I1_J, fact_9_resCasesF, fact_87_fresh__prod, fact_252_Late__Semantics1_Osubject_Oinject_I1_J, fact_35_ScopeExt, fact_282_simps_I2_J, fact_16_resZeroTrans, fact_91_fresh__prod, fact_155_old_Oprod_Oinject, fact_280_residual_Ofresh_I1_J, fact_267_simps_I1_J, fact_223_prod__cases, fact_185_dual__order_Orefl, fact_165_Late__Semantics_Osubject_Oinject_I2_J, fact_298_pi_Odistinct_I43_J, fact_243_sumZeroLeft, fact_119_Collect__mono__iff, fact_163_sumResLeft, fact_37_outputFreshTrans, fact_157_resSimCases, fact_79_residual_Ostrong__induct, fact_183_dual__order_Oeq__iff, fact_115_subset__refl, fact_104_subsetI, fact_173_Sum2, fact_113_equalityD2, fact_308_abs__fresh_I1_J, fact_158_resSimCases, fact_255_Late__Semantics1_Osubject_Odistinct_I1_J, fact_52_Late__Semantics_OResB, fact_257_Late__Semantics_Osubject_Odistinct_I1_J, fact_299_pi_Odistinct_I45_J, fact_109_subsetD
% 21.19/5.77 % No. of inferences in proof: 510
% 21.19/5.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5420 ms resp. 4561 ms w/o parsing
% 22.44/6.02 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.44/6.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------