TSTP Solution File: ITP192^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP192^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:42 EDT 2024
% Result : Theorem 23.59s 6.58s
% Output : Refutation 24.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 335
% Syntax : Number of formulae : 587 ( 306 unt; 85 typ; 0 def)
% Number of atoms : 1452 ( 494 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 7507 ( 294 ~; 8 |; 140 &;5995 @)
% ( 0 <=>;1070 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Number of types : 27 ( 26 usr)
% Number of type conns : 193 ( 193 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 59 usr; 15 con; 0-5 aty)
% Number of variables : 2846 ( 8 ^2782 !; 56 ?;2846 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc1462499409ion_pi_type,type,
produc1462499409ion_pi: $tType ).
thf(produc691362330ubject_type,type,
produc691362330ubject: $tType ).
thf(produc1834551554reeRes_type,type,
produc1834551554reeRes: $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(bang_type,type,
bang: pi > pi ).
thf(input_type,type,
input: name > name > pi > pi ).
thf(match_type,type,
match: name > name > pi > pi ).
thf(mismatch_type,type,
mismatch: name > name > pi > pi ).
thf(output_type,type,
output: name > name > pi > pi ).
thf(par_type,type,
par: pi > pi > pi ).
thf(piNil_type,type,
piNil: pi ).
thf(res_type,type,
res: name > pi > pi ).
thf(sum_type,type,
sum: pi > pi > pi ).
thf(tau_type,type,
tau: pi > pi ).
thf(subs_type,type,
subs: pi > name > name > pi ).
thf(late_OutputR_type,type,
late_OutputR: name > name > late_freeRes ).
thf(late_TauR_type,type,
late_TauR: late_freeRes ).
thf(late_BoundR_type,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(late_FreeR_type,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(late_BoundOutputS_type,type,
late_BoundOutputS: name > late_subject ).
thf(late_InputS_type,type,
late_InputS: name > late_subject ).
thf(late_transitions_type,type,
late_transitions: pi > late_residual > $o ).
thf(abs_fun_name_pi_type,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(fresh_543891186ion_pi_type,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
thf(fresh_name_name_type,type,
fresh_name_name: name > name > $o ).
thf(fresh_name_pi_type,type,
fresh_name_pi: name > pi > $o ).
thf(fresh_1641682979reeRes_type,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(fresh_81631222sidual_type,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(fresh_717452603ubject_type,type,
fresh_717452603ubject: name > late_subject > $o ).
thf(fresh_1963366730reeRes_type,type,
fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
thf(fresh_820177506ubject_type,type,
fresh_820177506ubject: name > produc865358760ubject > $o ).
thf(fresh_2007541374s_name_type,type,
fresh_2007541374s_name: name > produc2052722628s_name > $o ).
thf(fresh_1847501388Res_pi_type,type,
fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
thf(fresh_493808761reeRes_type,type,
fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
thf(fresh_1498103185ubject_type,type,
fresh_1498103185ubject: name > produc214645451ubject > $o ).
thf(fresh_1953561446t_name_type,type,
fresh_1953561446t_name: name > produc1998742700t_name > $o ).
thf(fresh_994896692ect_pi_type,type,
fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).
thf(fresh_1638563217reeRes_type,type,
fresh_1638563217reeRes: name > produc355105483reeRes > $o ).
thf(produc1531804426reeRes_type,type,
produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
thf(produc607574050ubject_type,type,
produc607574050ubject: name > late_subject > produc865358760ubject ).
thf(product_Pair_pi_pi_type,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(produc1701355766s_name_type,type,
produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
thf(produc1177552196Res_pi_type,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(produc1244821099reeRes_type,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(produc320590723ubject_type,type,
produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
thf(produc1647375838t_name_type,type,
produc1647375838t_name: late_subject > name > produc1998742700t_name ).
thf(produc324947500ect_pi_type,type,
produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
thf(produc242091907reeRes_type,type,
produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
thf(eqvt_pi_type,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(strong2129052853vative_type,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(strong743114133lation_type,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(member558706512_pi_pi_type,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(p_type,type,
p: pi ).
thf(pq_type,type,
pq: pi ).
thf(p2_type,type,
p2: pi ).
thf(q_type,type,
q: pi ).
thf(q2_type,type,
q2: pi ).
thf(alpha_type,type,
alpha: late_freeRes ).
thf(aa_type,type,
aa: name ).
thf(x_type,type,
x: name ).
thf(xPQ_type,type,
xPQ: pi ).
thf(y_type,type,
y: name ).
thf(z_type,type,
z: name ).
thf(248,axiom,
z != aa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_cClose1_Ohyps_I10_J) ).
thf(1501,plain,
z != aa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(219,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_154_Late__Semantics_OComm2) ).
thf(1411,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)],[219]) ).
thf(26,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_171_simulation__def) ).
thf(365,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)],[26]) ).
thf(232,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_22_resCasesF) ).
thf(1454,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)],[232]) ).
thf(107,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_204_tauCases) ).
thf(846,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)],[107]) ).
thf(69,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_pi_Odistinct_I43_J) ).
thf(628,plain,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
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_269_nilSim_I3_J) ).
thf(893,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(188,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_50_residual_Ostrong__inducts) ).
thf(1315,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)],[188]) ).
thf(130,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( input @ A @ B @ C )
!= ( match @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_pi_Odistinct_I49_J) ).
thf(962,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( input @ A @ B @ C )
!= ( match @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(146,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_194_tauBoundTrans) ).
thf(1024,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)],[146]) ).
thf(236,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_132_transitions_OResB) ).
thf(1469,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)],[236]) ).
thf(223,axiom,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_subject_Oexhaust) ).
thf(1422,plain,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(89,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_268_nilSim_I2_J) ).
thf(741,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)],[89]) ).
thf(166,axiom,
fresh_name_pi @ z @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_cClose1_Ohyps_I8_J) ).
thf(1142,plain,
fresh_name_pi @ z @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(227,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_205_outputFreshTrans) ).
thf(1437,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)],[227]) ).
thf(244,axiom,
fresh_name_pi @ x @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I1_J) ).
thf(1497,plain,
fresh_name_pi @ x @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(224,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_55_residual_Ostrong__induct) ).
thf(1426,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)],[224]) ).
thf(32,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_177_parAssocLeft) ).
thf(384,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)],[32]) ).
thf(56,axiom,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_freeRes_Oexhaust) ).
thf(533,plain,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(174,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_101_freshBoundDerivative_I1_J) ).
thf(1164,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)],[174]) ).
thf(250,axiom,
fresh_1641682979reeRes @ x @ alpha,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_cRes_Ohyps_I2_J) ).
thf(1507,plain,
fresh_1641682979reeRes @ x @ alpha,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(152,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( match @ 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_272_pi_Ofresh_I5_J) ).
thf(1095,plain,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( match @ 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)],[152]) ).
thf(120,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_167_resSimCases) ).
thf(898,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)],[120]) ).
thf(212,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_61_fresh__prod) ).
thf(1391,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)],[212]) ).
thf(228,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_Late__Semantics_Osubject_Odistinct_I1_J) ).
thf(1441,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(11,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_80_old_Oprod_Oinject) ).
thf(288,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)],[11]) ).
thf(201,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_158_freeRes_Ofresh_I1_J) ).
thf(1359,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)],[201]) ).
thf(4,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_309_Sum2) ).
thf(257,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)],[4]) ).
thf(125,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ~ ! [E: pi] :
( ( ( B = A )
& ( C = E ) )
=> ~ ( late_transitions @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_matchCases_H) ).
thf(934,plain,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ~ ! [E: pi] :
( ( ( B = A )
& ( C = E ) )
=> ~ ( late_transitions @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(234,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_pi_Odistinct_I85_J) ).
thf(1462,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(127,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_159_freeRes_Oinducts) ).
thf(949,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)],[127]) ).
thf(190,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_39_residual_Oinducts) ).
thf(1323,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)],[190]) ).
thf(66,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_186_pi_Oinject_I1_J) ).
thf(619,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)],[66]) ).
thf(105,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( match @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_pi_Odistinct_I23_J) ).
thf(838,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( match @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(96,axiom,
! [A: late_subject > pi > $o,B: late_subject,C: pi] :
( ! [D: late_subject] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_subject] :
( ( fresh_717452603ubject @ D @ F )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_pi_Ostrong__inducts) ).
thf(802,plain,
! [A: late_subject > pi > $o,B: late_subject,C: pi] :
( ! [D: late_subject] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_subject] :
( ( fresh_717452603ubject @ D @ F )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(21,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( sum @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_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)],[21]) ).
thf(108,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_183_simps_I2_J) ).
thf(853,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)],[108]) ).
thf(113,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ~ ! [E: pi,F: name,G: name] :
( ( ( A = F )
& ( B = G )
& ( C = E ) )
=> ( ( late_transitions @ E @ D )
=> ( F = G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_mismatchCases_H) ).
thf(870,plain,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ~ ! [E: pi,F: name,G: name] :
( ( ( A = F )
& ( B = G )
& ( C = E ) )
=> ( ( late_transitions @ E @ D )
=> ( F = G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(10,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_125_old_Oprod_Oexhaust) ).
thf(284,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)],[10]) ).
thf(202,axiom,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_name__exists__fresh) ).
thf(1362,plain,
! [A: name] :
~ ! [B: name] :
~ ( fresh_name_name @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(221,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_36_residual_Oinject_I2_J) ).
thf(1415,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)],[221]) ).
thf(123,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( input @ A @ B @ C )
!= ( bang @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_pi_Odistinct_I59_J) ).
thf(924,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( input @ A @ B @ C )
!= ( bang @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(93,axiom,
! [A: late_subject] :
~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_name__exists__fresh) ).
thf(756,plain,
! [A: late_subject] :
~ ! [B: name] :
~ ( fresh_717452603ubject @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(222,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_151_transitions_OComm1) ).
thf(1418,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)],[222]) ).
thf(74,axiom,
! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
( ! [D: late_freeRes] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_freeRes] :
( ( fresh_1641682979reeRes @ D @ F )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_pi_Ostrong__induct) ).
thf(646,plain,
! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
( ! [D: late_freeRes] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_freeRes] :
( ( fresh_1641682979reeRes @ D @ F )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(164,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_135_transitions_OPar2B) ).
thf(1136,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)],[164]) ).
thf(22,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_119_Pair__inject) ).
thf(348,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)],[22]) ).
thf(97,axiom,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_pi_Odistinct_I3_J) ).
thf(806,plain,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(131,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( bang @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_pi_Odistinct_I33_J) ).
thf(966,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( bang @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(65,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_166_resSimCases) ).
thf(602,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)],[65]) ).
thf(112,axiom,
! [A: pi > pi > $o,B: pi,C: pi] :
( ! [D: pi] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: pi] :
( ( fresh_name_pi @ D @ F )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_pi_Ostrong__inducts) ).
thf(866,plain,
! [A: pi > pi > $o,B: pi,C: pi] :
( ! [D: pi] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: pi] :
( ( fresh_name_pi @ D @ F )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(213,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_71_Late__Semantics_OClose2) ).
thf(1394,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)],[213]) ).
thf(137,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( match @ A @ B @ C )
!= ( bang @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_pi_Odistinct_I69_J) ).
thf(988,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( match @ A @ B @ C )
!= ( bang @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(217,axiom,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_name__exists__fresh) ).
thf(1405,plain,
! [A: pi] :
~ ! [B: name] :
~ ( fresh_name_pi @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(207,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_193_outputBoundTrans) ).
thf(1377,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)],[207]) ).
thf(9,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_pi_Odistinct_I81_J) ).
thf(280,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(55,axiom,
! [A: pi,B: pi,C: pi] :
( ( par @ A @ B )
!= ( bang @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_pi_Odistinct_I87_J) ).
thf(529,plain,
! [A: pi,B: pi,C: pi] :
( ( par @ A @ B )
!= ( bang @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(184,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_60_fresh__prod) ).
thf(1306,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)],[184]) ).
thf(98,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_207_residual_Ofresh_I1_J) ).
thf(810,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)],[98]) ).
thf(195,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_49_residual_Ostrong__inducts) ).
thf(1338,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)],[195]) ).
thf(31,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_107_surj__pair) ).
thf(381,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)],[31]) ).
thf(82,axiom,
! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
( ! [D: late_freeRes] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_freeRes] :
( ( fresh_1641682979reeRes @ D @ F )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_pi_Ostrong__inducts) ).
thf(714,plain,
! [A: late_freeRes > pi > $o,B: late_freeRes,C: pi] :
( ! [D: late_freeRes] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ( fresh_1641682979reeRes @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_freeRes] :
( ! [H: late_freeRes] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_freeRes] :
( ! [G: late_freeRes] : ( A @ G @ D )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_freeRes] :
( ( fresh_1641682979reeRes @ D @ F )
=> ( ! [G: late_freeRes] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_freeRes] :
( ! [F: late_freeRes] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(173,axiom,
fresh_name_pi @ y @ q2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_cClose1_Ohyps_I7_J) ).
thf(1163,plain,
fresh_name_pi @ y @ q2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(18,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_86_prod_Oinject) ).
thf(334,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)],[18]) ).
thf(196,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_62_fresh__prod) ).
thf(1343,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)],[196]) ).
thf(145,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_63_fresh__prod) ).
thf(1021,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)],[145]) ).
thf(86,axiom,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_pi_Odistinct_I45_J) ).
thf(729,plain,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(180,axiom,
fresh_name_pi @ y @ q,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_cClose1_Ohyps_I4_J) ).
thf(1238,plain,
fresh_name_pi @ y @ q,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(5,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_308_Sum1) ).
thf(260,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)],[5]) ).
thf(111,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_pi_Odistinct_I1_J) ).
thf(862,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(33,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_165_resSimCases) ).
thf(392,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)],[33]) ).
thf(241,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_236_resInputFreeTrans) ).
thf(1487,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)],[241]) ).
thf(1,conjecture,
x != aa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
x != aa,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(252,plain,
x != aa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(203,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_67_fresh__prod) ).
thf(1365,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)],[203]) ).
thf(68,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_156_Late__Semantics1_OfreeRes_Oinject) ).
thf(625,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)],[68]) ).
thf(53,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_157_Late__Semantics_OfreeRes_Oinject) ).
thf(522,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)],[53]) ).
thf(117,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_96_fresh__fact2) ).
thf(889,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)],[117]) ).
thf(172,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_70_transitions_OClose1) ).
thf(1159,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)],[172]) ).
thf(147,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_66_fresh__prod) ).
thf(1027,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)],[147]) ).
thf(162,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_54_residual_Ostrong__induct) ).
thf(1128,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)],[162]) ).
thf(106,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( match @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_pi_Odistinct_I67_J) ).
thf(842,plain,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( match @ A @ B @ C )
!= ( res @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(133,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( mismatch @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_pi_Odistinct_I39_J) ).
thf(974,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( mismatch @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(155,axiom,
alpha = late_TauR,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_cClose1_Ohyps_I14_J) ).
thf(1106,plain,
alpha = late_TauR,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(216,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_24_ResF) ).
thf(1402,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)],[216]) ).
thf(52,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_zeroTrans) ).
thf(519,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(167,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_51_residual_Ostrong__inducts) ).
thf(1143,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)],[167]) ).
thf(160,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_99_Agent_OsubstRes3) ).
thf(1121,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)],[160]) ).
thf(157,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_206_resInputBoundOutputTrans) ).
thf(1111,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)],[157]) ).
thf(85,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( match @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_pi_Odistinct_I7_J) ).
thf(725,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( match @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(36,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_307_sumCases_H) ).
thf(420,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)],[36]) ).
thf(214,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Late__Semantics1_Osubject_Oinject_I2_J) ).
thf(1397,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(150,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_168_simE_I1_J) ).
thf(1089,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)],[150]) ).
thf(179,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh_name_pi @ E @ A )
=> ( ( E != C )
=> ( fresh_name_pi @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_freshBoundDerivative_I2_J) ).
thf(1234,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)],[179]) ).
thf(135,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_90_substTrans) ).
thf(980,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)],[135]) ).
thf(245,axiom,
late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_cClose1_Ohyps_I1_J) ).
thf(1498,plain,
late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(192,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_97_freshResidual) ).
thf(1329,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)],[192]) ).
thf(57,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_pi_Odistinct_I19_J) ).
thf(537,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(75,axiom,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( tau @ B ) )
= ( fresh_name_pi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_pi_Ofresh_I3_J) ).
thf(686,plain,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( tau @ B ) )
= ( fresh_name_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(220,axiom,
late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_cRes_Ohyps_I1_J) ).
thf(1414,plain,
late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(132,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( match @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_pi_Odistinct_I37_J) ).
thf(970,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( match @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(67,axiom,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( bang @ B ) )
= ( fresh_name_pi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_pi_Ofresh_I10_J) ).
thf(622,plain,
! [A: name,B: pi] :
( ( fresh_name_pi @ A @ ( bang @ B ) )
= ( fresh_name_pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(158,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_64_fresh__prod) ).
thf(1114,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)],[158]) ).
thf(139,axiom,
! [A: pi,B: late_residual,C: name] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( match @ C @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_Match) ).
thf(997,plain,
! [A: pi,B: late_residual,C: name] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( match @ C @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(238,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_57_freshFreeDerivative_I2_J) ).
thf(1478,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)],[238]) ).
thf(183,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_233_inputCases_H) ).
thf(1297,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)],[183]) ).
thf(231,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_181_resOutputOutputTrans) ).
thf(1451,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)],[231]) ).
thf(178,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_43_Par2F) ).
thf(1231,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)],[178]) ).
thf(136,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( match @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_pi_Odistinct_I65_J) ).
thf(984,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( match @ A @ B @ C )
!= ( par @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(84,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_94_forget) ).
thf(721,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)],[84]) ).
thf(28,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_295_pi_Ofresh_I7_J) ).
thf(371,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)],[28]) ).
thf(226,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_21_freshFreeDerivative_I1_J) ).
thf(1434,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)],[226]) ).
thf(149,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_134_transitions_OPar1B) ).
thf(1086,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)],[149]) ).
thf(7,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_175_simCasesCont) ).
thf(266,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)],[7]) ).
thf(58,axiom,
! [A: pi > pi > $o,B: pi,C: pi] :
( ! [D: pi] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: pi] :
( ( fresh_name_pi @ D @ F )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_pi_Ostrong__induct) ).
thf(541,plain,
! [A: pi > pi > $o,B: pi,C: pi] :
( ! [D: pi] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ( fresh_name_pi @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: pi] :
( ! [H: pi] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: pi] :
( ! [G: pi] : ( A @ G @ D )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: pi] :
( ( fresh_name_pi @ D @ F )
=> ( ! [G: pi] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi] :
( ! [F: pi] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(235,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_65_fresh__prod) ).
thf(1466,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)],[235]) ).
thf(175,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_133_parCasesB_H) ).
thf(1167,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)],[175]) ).
thf(83,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_230_residual_Oinject_I1_J) ).
thf(718,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)],[83]) ).
thf(109,axiom,
! [A: set_Pr1834926343_pi_pi,B: pi] :
~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_nilSim_I1_J) ).
thf(856,plain,
! [A: set_Pr1834926343_pi_pi,B: pi] :
~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(76,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_199_outputCases) ).
thf(689,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)],[76]) ).
thf(41,axiom,
! [A: pi,B: set_Pr1834926343_pi_pi] : ( strong743114133lation @ A @ B @ piNil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_nilSimRight) ).
thf(444,plain,
! [A: pi,B: set_Pr1834926343_pi_pi] : ( strong743114133lation @ A @ B @ piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(206,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_subject_Ofresh_I2_J) ).
thf(1374,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(87,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_231_pi_Odistinct_I21_J) ).
thf(733,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)],[87]) ).
thf(50,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_240_inputIneqTrans) ).
thf(513,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)],[50]) ).
thf(38,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_211_pi_Ofresh_I9_J) ).
thf(430,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)],[38]) ).
thf(101,axiom,
! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ( ( ( late_transitions @ C @ D )
=> ( ( A = B )
=> ( E @ A @ A ) ) )
=> ( E @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_matchCases) ).
thf(819,plain,
! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ( ( ( late_transitions @ C @ D )
=> ( ( A = B )
=> ( E @ A @ A ) ) )
=> ( E @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(161,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_163_Open) ).
thf(1125,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)],[161]) ).
thf(211,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_178_resTauOutputTrans) ).
thf(1388,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)],[211]) ).
thf(81,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_nilCases_H) ).
thf(711,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(12,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_169_simE_I2_J) ).
thf(291,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)],[12]) ).
thf(35,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_170_simCases) ).
thf(413,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)],[35]) ).
thf(165,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_41_subject_Oinducts) ).
thf(1139,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)],[165]) ).
thf(205,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_72_Late__Semantics_OClose1) ).
thf(1371,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)],[205]) ).
thf(186,axiom,
( fresh_name_name
= ( != @ name ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_name__fresh) ).
thf(1312,plain,
( fresh_name_name
= ( ^ [A: name,B: name] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(46,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_214_pi_Odistinct_I55_J) ).
thf(498,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)],[46]) ).
thf(181,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_53_residual_Ostrong__induct) ).
thf(1239,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)],[181]) ).
thf(193,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_184_pi_Ofresh_I2_J) ).
thf(1332,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)],[193]) ).
thf(79,axiom,
! [A: name > pi > $o,B: name,C: pi] :
( ! [D: name] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: name] :
( ( fresh_name_name @ D @ F )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_pi_Ostrong__inducts) ).
thf(704,plain,
! [A: name > pi > $o,B: name,C: pi] :
( ! [D: name] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: name] :
( ( fresh_name_name @ D @ F )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(176,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_56_residual_Ostrong__induct) ).
thf(1224,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)],[176]) ).
thf(200,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_239_inputBoundOutputTrans) ).
thf(1356,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)],[200]) ).
thf(218,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_20_pi_Ofresh_I8_J) ).
thf(1408,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)],[218]) ).
thf(159,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_152_transitions_OComm2) ).
thf(1117,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)],[159]) ).
thf(143,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_23_resCasesF_H) ).
thf(1011,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)],[143]) ).
thf(198,axiom,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cClose1_Ohyps_I6_J) ).
thf(1349,plain,
y != z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(25,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_113_prod__cases) ).
thf(362,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)],[25]) ).
thf(88,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( match @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_pi_Odistinct_I61_J) ).
thf(737,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( match @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(14,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_241_parZeroRight) ).
thf(303,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)],[14]) ).
thf(49,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_pi_Odistinct_I25_J) ).
thf(509,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(114,axiom,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_subst__identity) ).
thf(880,plain,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(27,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_pi_Odistinct_I79_J) ).
thf(367,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(100,axiom,
! [A: name,B: pi,C: late_residual] :
~ ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_mismatchTrans) ).
thf(816,plain,
! [A: name,B: pi,C: late_residual] :
~ ( late_transitions @ ( mismatch @ A @ A @ B ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(95,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_221_abs__fun__eq1) ).
thf(799,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)],[95]) ).
thf(78,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_matchTrans) ).
thf(700,plain,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( match @ A @ B @ C ) @ D )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(169,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Late__Semantics_Osubject_Oinject_I2_J) ).
thf(1149,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(121,axiom,
! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ( ( ( late_transitions @ C @ D )
=> ( ( A != B )
=> ( E @ A @ B ) ) )
=> ( E @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_mismatchCases) ).
thf(915,plain,
! [A: name,B: name,C: pi,D: late_residual,E: name > name > $o] :
( ( late_transitions @ ( mismatch @ A @ B @ C ) @ D )
=> ( ( ( late_transitions @ C @ D )
=> ( ( A != B )
=> ( E @ A @ B ) ) )
=> ( E @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(209,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_192_resTrans_I1_J) ).
thf(1381,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)],[209]) ).
thf(129,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_200_outputTauTrans) ).
thf(959,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)],[129]) ).
thf(71,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( mismatch @ A @ B @ C )
= ( mismatch @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_pi_Oinject_I5_J) ).
thf(636,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( mismatch @ A @ B @ C )
= ( mismatch @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(229,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_27_Late__Semantics_OPar1B) ).
thf(1445,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)],[229]) ).
thf(115,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( input @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_pi_Odistinct_I51_J) ).
thf(883,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( input @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(15,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_164_resSimCases) ).
thf(306,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)],[15]) ).
thf(140,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_69_transitions_OClose2) ).
thf(1000,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)],[140]) ).
thf(243,axiom,
late_transitions @ q @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_cClose1_Ohyps_I2_J) ).
thf(1496,plain,
late_transitions @ q @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(154,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_98_substRes2) ).
thf(1102,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)],[154]) ).
thf(48,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_213_pi_Odistinct_I57_J) ).
thf(505,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)],[48]) ).
thf(122,axiom,
! [A: set_Pr1834926343_pi_pi,B: name,C: pi] : ( strong743114133lation @ piNil @ A @ ( mismatch @ B @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_mismatchNilLeft) ).
thf(922,plain,
! [A: set_Pr1834926343_pi_pi,B: name,C: pi] : ( strong743114133lation @ piNil @ A @ ( mismatch @ B @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(29,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( match @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_pi_Odistinct_I63_J) ).
thf(374,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( match @ A @ B @ C )
!= ( sum @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(3,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_306_sumCases) ).
thf(255,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)],[3]) ).
thf(51,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_215_pi_Oinject_I8_J) ).
thf(516,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)],[51]) ).
thf(144,axiom,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Late__Semantics1_Osubject_Oinject_I1_J) ).
thf(1018,plain,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(23,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_315_pi_Odistinct_I27_J) ).
thf(355,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)],[23]) ).
thf(45,axiom,
! [A: name > pi > $o,B: name,C: pi] :
( ! [D: name] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: name] :
( ( fresh_name_name @ D @ F )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_pi_Ostrong__induct) ).
thf(458,plain,
! [A: name > pi > $o,B: name,C: pi] :
( ! [D: name] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ( fresh_name_name @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: name] :
( ! [H: name] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: name] :
( ! [G: name] : ( A @ G @ D )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: name] :
( ( fresh_name_name @ D @ F )
=> ( ! [G: name] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: name] :
( ! [F: name] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(54,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_pi_Odistinct_I35_J) ).
thf(525,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(13,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_176_simCasesCont) ).
thf(295,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)],[13]) ).
thf(171,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_235_inputFreeTrans) ).
thf(1156,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)],[171]) ).
thf(215,axiom,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( par @ A @ ( bang @ A ) ) @ B )
=> ( late_transitions @ ( bang @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_Bang) ).
thf(1400,plain,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( par @ A @ ( bang @ A ) ) @ B )
=> ( late_transitions @ ( bang @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(116,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_196_Output) ).
thf(887,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)],[116]) ).
thf(16,axiom,
! [A: pi,B: pi,C: pi] :
( ( sum @ A @ B )
!= ( bang @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_pi_Odistinct_I83_J) ).
thf(327,plain,
! [A: pi,B: pi,C: pi] :
( ( sum @ A @ B )
!= ( bang @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(204,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_91_residual_Ofresh_I2_J) ).
thf(1368,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)],[204]) ).
thf(34,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_302_pi_Odistinct_I53_J) ).
thf(409,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)],[34]) ).
thf(240,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( mismatch @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C )
& ( fresh_name_pi @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_pi_Ofresh_I6_J) ).
thf(1484,plain,
! [A: name,B: name,C: name,D: pi] :
( ( fresh_name_pi @ A @ ( mismatch @ B @ C @ D ) )
= ( ( fresh_name_name @ A @ B )
& ( fresh_name_name @ A @ C )
& ( fresh_name_pi @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(6,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_242_parZeroLeft) ).
thf(263,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)],[6]) ).
thf(153,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_100_Late__Semantics_OResB) ).
thf(1098,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)],[153]) ).
thf(246,axiom,
fresh_name_name @ y @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_cClose1_Ohyps_I12_J) ).
thf(1499,plain,
fresh_name_name @ y @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(17,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_225_name__fresh__abs) ).
thf(331,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)],[17]) ).
thf(40,axiom,
! [A: pi,B: name,C: name] :
( ( subs @ ( bang @ A ) @ B @ C )
= ( bang @ ( subs @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_simps_I10_J) ).
thf(441,plain,
! [A: pi,B: name,C: name] :
( ( subs @ ( bang @ A ) @ B @ C )
= ( bang @ ( subs @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(60,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_212_pi_Ofresh_I4_J) ).
thf(585,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)],[60]) ).
thf(47,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_217_pi_Oinject_I3_J) ).
thf(502,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)],[47]) ).
thf(24,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_297_simps_I7_J) ).
thf(359,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)],[24]) ).
thf(73,axiom,
! [A: pi,B: pi] :
( ( ( bang @ A )
= ( bang @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_pi_Oinject_I9_J) ).
thf(643,plain,
! [A: pi,B: pi] :
( ( ( bang @ A )
= ( bang @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(90,axiom,
! [A: name,B: pi,C: pi] :
( ( res @ A @ B )
!= ( bang @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_pi_Odistinct_I89_J) ).
thf(744,plain,
! [A: name,B: pi,C: pi] :
( ( res @ A @ B )
!= ( bang @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(64,axiom,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_freeRes_Ofresh_I2_J) ).
thf(600,plain,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(249,axiom,
y != aa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_cClose1_Ohyps_I5_J) ).
thf(1504,plain,
y != aa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(134,axiom,
! [A: name] : ( fresh_name_pi @ A @ piNil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_pi_Ofresh_I1_J) ).
thf(978,plain,
! [A: name] : ( fresh_name_pi @ A @ piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(142,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_44_Par1F) ).
thf(1008,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)],[142]) ).
thf(42,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_pi_Odistinct_I73_J) ).
thf(446,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( par @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(110,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_89_simps_I8_J) ).
thf(859,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)],[110]) ).
thf(43,axiom,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_pi_Odistinct_I15_J) ).
thf(450,plain,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(233,axiom,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_subject_Ofresh_I1_J) ).
thf(1459,plain,
! [A: name,B: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ B ) )
= ( fresh_name_name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(59,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_pi_Odistinct_I5_J) ).
thf(581,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(94,axiom,
! [A: late_subject > pi > $o,B: late_subject,C: pi] :
( ! [D: late_subject] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_subject] :
( ( fresh_717452603ubject @ D @ F )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_pi_Ostrong__induct) ).
thf(759,plain,
! [A: late_subject > pi > $o,B: late_subject,C: pi] :
( ! [D: late_subject] : ( A @ D @ piNil )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( output @ D @ E @ F ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( tau @ D ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ( fresh_717452603ubject @ E @ G )
=> ( ( fresh_name_name @ E @ D )
=> ( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( input @ D @ E @ F ) ) ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( match @ D @ E @ F ) ) )
=> ( ! [D: name,E: name,F: pi,G: late_subject] :
( ! [H: late_subject] : ( A @ H @ F )
=> ( A @ G @ ( mismatch @ D @ E @ F ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( sum @ D @ E ) ) ) )
=> ( ! [D: pi,E: pi,F: late_subject] :
( ! [G: late_subject] : ( A @ G @ D )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( par @ D @ E ) ) ) )
=> ( ! [D: name,E: pi,F: late_subject] :
( ( fresh_717452603ubject @ D @ F )
=> ( ! [G: late_subject] : ( A @ G @ E )
=> ( A @ F @ ( res @ D @ E ) ) ) )
=> ( ! [D: pi,E: late_subject] :
( ! [F: late_subject] : ( A @ F @ D )
=> ( A @ E @ ( bang @ D ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(230,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_179_resOutputTauTrans) ).
thf(1448,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)],[230]) ).
thf(156,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_234_resTrans_I2_J) ).
thf(1108,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)],[156]) ).
thf(191,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_35_pi_Oinject_I7_J) ).
thf(1326,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)],[191]) ).
thf(61,axiom,
! [A: pi,B: late_residual,C: name,D: name] :
( ( late_transitions @ A @ B )
=> ( ( C != D )
=> ( late_transitions @ ( mismatch @ C @ D @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_Mismatch) ).
thf(588,plain,
! [A: pi,B: late_residual,C: name,D: name] :
( ( late_transitions @ A @ B )
=> ( ( C != D )
=> ( late_transitions @ ( mismatch @ C @ D @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(99,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_201_tauOutputTrans) ).
thf(813,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)],[99]) ).
thf(251,axiom,
fresh_name_name @ z @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_cClose1_Ohyps_I13_J) ).
thf(1508,plain,
fresh_name_name @ z @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(239,axiom,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_name__exists__fresh) ).
thf(1481,plain,
! [A: late_freeRes] :
~ ! [B: name] :
~ ( fresh_1641682979reeRes @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(70,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_95_fresh__fact1) ).
thf(632,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)],[70]) ).
thf(182,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_155_resCasesB_H) ).
thf(1244,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)],[182]) ).
thf(119,axiom,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Tau) ).
thf(896,plain,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(91,axiom,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_pi_Odistinct_I13_J) ).
thf(748,plain,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(148,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_150_resCases_H) ).
thf(1030,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)],[148]) ).
thf(30,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_313_pi_Oinject_I6_J) ).
thf(378,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)],[30]) ).
thf(39,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_174_simCasesCont) ).
thf(433,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)],[39]) ).
thf(103,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( match @ A @ B @ C )
= ( match @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_pi_Oinject_I4_J) ).
thf(832,plain,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( match @ A @ B @ C )
= ( match @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(185,axiom,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_resZeroTrans) ).
thf(1309,plain,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(163,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_153_Late__Semantics_OComm1) ).
thf(1133,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)],[163]) ).
thf(92,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( mismatch @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_pi_Odistinct_I9_J) ).
thf(752,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( mismatch @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(104,axiom,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_pi_Oinject_I2_J) ).
thf(835,plain,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(177,axiom,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_freshRes) ).
thf(1229,plain,
! [A: name,B: pi] : ( fresh_name_pi @ A @ ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(208,axiom,
fresh_name_pi @ z @ p2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_cClose1_Ohyps_I11_J) ).
thf(1380,plain,
fresh_name_pi @ z @ p2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(168,axiom,
fresh_name_pi @ y @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_cClose1_Ohyps_I3_J) ).
thf(1148,plain,
fresh_name_pi @ y @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(37,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_173_simCasesCont) ).
thf(422,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)],[37]) ).
thf(187,axiom,
fresh_name_pi @ z @ q,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_cClose1_Ohyps_I9_J) ).
thf(1314,plain,
fresh_name_pi @ z @ q,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(20,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_229_abs__fresh_I1_J) ).
thf(341,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)],[20]) ).
thf(194,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_28_Late__Semantics_OPar2B) ).
thf(1335,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)],[194]) ).
thf(102,axiom,
! [A: name,B: name,C: set_Pr1834926343_pi_pi,D: pi] :
( ( A != B )
=> ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_matchNilLeft) ).
thf(828,plain,
! [A: name,B: name,C: set_Pr1834926343_pi_pi,D: pi] :
( ( A != B )
=> ( strong743114133lation @ piNil @ C @ ( match @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(237,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_52_residual_Ostrong__inducts) ).
thf(1473,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)],[237]) ).
thf(77,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_88_simps_I9_J) ).
thf(696,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)],[77]) ).
thf(128,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_pi_Odistinct_I75_J) ).
thf(955,plain,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( res @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(197,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_180_resOutputInputTrans) ).
thf(1346,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)],[197]) ).
thf(124,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_197_outputIneqTrans) ).
thf(928,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)],[124]) ).
thf(151,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_237_Late__Semantics_OInput) ).
thf(1093,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)],[151]) ).
thf(199,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_Late__Semantics1_Osubject_Odistinct_I1_J) ).
thf(1352,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(170,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_40_residual_Odistinct_I1_J) ).
thf(1152,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)],[170]) ).
thf(210,axiom,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( bang @ A ) @ B )
=> ~ ! [C: pi] :
( ( ( bang @ A )
= ( bang @ C ) )
=> ~ ( late_transitions @ ( par @ C @ ( bang @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_bangCases) ).
thf(1384,plain,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( bang @ A ) @ B )
=> ~ ! [C: pi] :
( ( ( bang @ A )
= ( bang @ C ) )
=> ~ ( late_transitions @ ( par @ C @ ( bang @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(63,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_189_pi_Odistinct_I29_J) ).
thf(596,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)],[63]) ).
thf(138,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_203_tauCases_H) ).
thf(992,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)],[138]) ).
thf(247,axiom,
late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ xPQ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Free_Ohyps) ).
thf(1500,plain,
late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ xPQ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(8,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_131_old_Oprod_Oinducts) ).
thf(277,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)],[8]) ).
thf(225,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_195_resTauBoundTrans) ).
thf(1431,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)],[225]) ).
thf(141,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_238_transitions_OInput) ).
thf(1004,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)],[141]) ).
thf(189,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_68_fresh__prod) ).
thf(1320,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)],[189]) ).
thf(19,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_172_parSym) ).
thf(337,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)],[19]) ).
thf(126,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_198_outputCases_H) ).
thf(940,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)],[126]) ).
thf(242,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_58_parCasesB) ).
thf(1490,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)],[242]) ).
thf(72,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_188_pi_Odistinct_I31_J) ).
thf(639,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)],[72]) ).
thf(62,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Late__Semantics_OfreeRes_Odistinct_I1_J) ).
thf(592,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(44,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).
thf(454,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(80,axiom,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_simps_I1_J) ).
thf(708,plain,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1589,plain,
$false,
inference(cvc4,[status(thm)],[1501,1411,365,1454,846,628,893,1315,962,1024,1469,1422,741,1142,1437,1497,1426,384,533,1164,1507,1095,898,1391,1441,288,1359,257,934,1462,949,1323,619,838,802,344,853,870,284,1362,1415,924,756,1418,646,1136,348,806,966,602,866,1394,988,1405,1377,280,529,1306,810,1338,381,714,1163,334,1343,1021,729,1238,260,862,392,1487,252,1365,625,522,889,1159,1027,1128,842,974,1106,1402,519,1143,1121,1111,725,420,1397,1089,1234,980,1498,1329,537,686,1414,970,622,1114,997,1478,1297,1451,1231,984,721,371,1434,1086,266,541,1466,1167,718,856,689,444,1374,733,513,430,819,1125,1388,711,291,413,1139,1371,1312,498,1239,1332,704,1224,1356,1408,1117,1011,1349,362,737,303,509,880,367,816,799,700,1149,915,1381,959,636,1445,883,306,1000,1496,1102,505,922,374,255,516,1018,355,458,525,295,1156,1400,887,327,1368,409,1484,263,1098,1499,331,441,585,502,359,643,744,600,1504,978,1008,446,859,450,1459,581,759,1448,1108,1326,588,813,1508,1481,632,1244,896,748,1030,378,433,832,1309,1133,752,835,1229,1380,1148,422,1314,341,1335,828,1473,696,955,1346,928,1093,1352,1152,1384,596,992,1500,277,1431,1004,1320,337,940,1490,639,592,454,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP192^1 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 6 14:43:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.02/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.66/1.17 % [INFO] Parsing done (274ms).
% 1.66/1.17 % [INFO] Running in sequential loop mode.
% 2.79/1.39 % [INFO] eprover registered as external prover.
% 2.79/1.39 % [INFO] cvc4 registered as external prover.
% 2.79/1.39 % [INFO] Scanning for conjecture ...
% 3.06/1.49 % [INFO] Found a conjecture and 321 axioms. Running axiom selection ...
% 3.17/1.59 % [INFO] Axiom selection finished. Selected 249 axioms (removed 72 axioms).
% 4.22/1.81 % [INFO] Problem is higher-order (TPTP THF).
% 4.22/1.84 % [INFO] Type checking passed.
% 4.22/1.84 % [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 ...
% 23.59/6.58 % External prover 'cvc4' found a proof!
% 23.59/6.58 % [INFO] Killing All external provers ...
% 23.59/6.58 % Time passed: 6060ms (effective reasoning time: 5401ms)
% 23.59/6.58 % 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)>
% 23.59/6.58 % Axioms used in derivation (249): fact_80_old_Oprod_Oinject, fact_36_residual_Oinject_I2_J, fact_263_mismatchCases, fact_49_residual_Ostrong__inducts, fact_275_Match, fact_56_residual_Ostrong__induct, fact_254_nilSimRight, fact_280_pi_Odistinct_I37_J, fact_198_outputCases_H, fact_170_simCases, fact_281_pi_Odistinct_I23_J, fact_306_sumCases, fact_133_parCasesB_H, fact_12_cRes_Ohyps_I2_J, fact_178_resTauOutputTrans, fact_92_subject_Ofresh_I2_J, fact_278_matchCases, fact_19_freeRes_Ofresh_I2_J, fact_247_pi_Odistinct_I5_J, fact_304_pi_Odistinct_I89_J, fact_300_bangCases, fact_289_pi_Ostrong__induct, fact_153_Late__Semantics_OComm1, fact_207_residual_Ofresh_I1_J, fact_293_pi_Ostrong__inducts, fact_284_pi_Odistinct_I49_J, fact_34_name__exists__fresh, fact_22_resCasesF, fact_261_nilCases_H, fact_4_cClose1_Ohyps_I12_J, fact_317_pi_Odistinct_I41_J, fact_305_pi_Odistinct_I87_J, fact_51_residual_Ostrong__inducts, fact_302_pi_Odistinct_I53_J, fact_23_resCasesF_H, fact_161_freeRes_Oexhaust, fact_159_freeRes_Oinducts, fact_273_pi_Odistinct_I61_J, fact_272_pi_Ofresh_I5_J, fact_283_pi_Odistinct_I67_J, fact_183_simps_I2_J, fact_251_pi_Odistinct_I15_J, fact_90_substTrans, fact_7_cClose1_Ohyps_I11_J, fact_314_pi_Odistinct_I83_J, fact_94_forget, fact_5_cClose1_Ohyps_I5_J, fact_194_tauBoundTrans, fact_135_transitions_OPar2B, fact_303_pi_Odistinct_I59_J, fact_98_substRes2, fact_257_pi_Odistinct_I3_J, fact_168_simE_I1_J, fact_50_residual_Ostrong__inducts, fact_214_pi_Odistinct_I55_J, fact_307_sumCases_H, fact_32_name__exists__fresh, fact_242_parZeroLeft, fact_204_tauCases, fact_238_transitions_OInput, fact_33_name__exists__fresh, fact_58_parCasesB, fact_189_pi_Odistinct_I29_J, fact_231_pi_Odistinct_I21_J, fact_270_nilSim_I1_J, fact_311_pi_Odistinct_I79_J, fact_29_Late__Semantics_Osubject_Oinject_I2_J, fact_125_old_Oprod_Oexhaust, fact_40_residual_Odistinct_I1_J, fact_63_fresh__prod, fact_21_freshFreeDerivative_I1_J, fact_97_freshResidual, fact_296_simps_I10_J, fact_64_fresh__prod, fact_188_pi_Odistinct_I31_J, fact_174_simCasesCont, fact_89_simps_I8_J, fact_312_pi_Oinject_I9_J, fact_288_pi_Ostrong__induct, fact_157_Late__Semantics_OfreeRes_Oinject, fact_225_name__fresh__abs, fact_14_cClose1_Ohyps_I14_J, fact_38_freshRes, fact_279_pi_Oinject_I4_J, fact_16_cClose1_Ohyps_I9_J, fact_191_pi_Odistinct_I43_J, fact_260_pi_Odistinct_I9_J, fact_113_prod__cases, fact_177_parAssocLeft, fact_234_resTrans_I2_J, fact_264_mismatchTrans, fact_200_outputTauTrans, fact_237_Late__Semantics_OInput, fact_42_Late__Semantics_Osubject_Odistinct_I1_J, fact_221_abs__fun__eq1, fact_101_freshBoundDerivative_I1_J, fact_181_resOutputOutputTrans, fact_175_simCasesCont, fact_292_pi_Ostrong__inducts, fact_20_pi_Ofresh_I8_J, fact_282_pi_Odistinct_I65_J, fact_87_subst__identity, fact_53_residual_Ostrong__induct, fact_119_Pair__inject, fact_252_pi_Odistinct_I13_J, fact_134_transitions_OPar1B, fact_246_pi_Ofresh_I6_J, fact_233_inputCases_H, fact_186_pi_Oinject_I1_J, fact_160_Late__Semantics_OfreeRes_Odistinct_I1_J, fact_315_pi_Odistinct_I27_J, fact_232_pi_Odistinct_I35_J, fact_6_cClose1_Ohyps_I4_J, fact_68_fresh__prod, fact_291_pi_Ostrong__inducts, fact_72_Late__Semantics_OClose1, fact_27_Late__Semantics_OPar1B, fact_239_inputBoundOutputTrans, fact_99_Agent_OsubstRes3, fact_15_cClose1_Ohyps_I2_J, fact_213_pi_Odistinct_I57_J, fact_301_Bang, fact_60_fresh__prod, fact_39_residual_Oinducts, fact_236_resInputFreeTrans, fact_70_transitions_OClose1, fact_299_pi_Odistinct_I69_J, fact_66_fresh__prod, fact_285_matchNilLeft, fact_244_pi_Ofresh_I1_J, fact_96_fresh__fact2, fact_35_pi_Oinject_I7_J, fact_1_cClose1_Ohyps_I7_J, fact_197_outputIneqTrans, fact_176_simCasesCont, fact_167_resSimCases, fact_162_Late__Semantics1_OfreeRes_Odistinct_I1_J, fact_309_Sum2, fact_205_outputFreshTrans, fact_249_pi_Odistinct_I75_J, fact_182_pi_Ofresh_I3_J, fact_43_Par2F, fact_215_pi_Oinject_I8_J, fact_201_tauOutputTrans, fact_156_Late__Semantics1_OfreeRes_Oinject, fact_149_subject_Oexhaust, fact_199_outputCases, fact_202_Tau, fact_2_cClose1_Ohyps_I6_J, fact_74_Late__Semantics1_Osubject_Oinject_I2_J, fact_250_pi_Odistinct_I73_J, fact_196_Output, fact_17_Free_Ohyps, fact_91_residual_Ofresh_I2_J, fact_44_Par1F, fact_45_freshBoundDerivative_I2_J, fact_185_pi_Oinject_I2_J, fact_262_zeroTrans, fact_276_matchCases_H, fact_267_resZeroTrans, fact_57_freshFreeDerivative_I2_J, fact_217_pi_Oinject_I3_J, fact_151_transitions_OComm1, fact_180_resOutputInputTrans, fact_295_pi_Ofresh_I7_J, fact_67_fresh__prod, fact_158_freeRes_Ofresh_I1_J, fact_71_Late__Semantics_OClose2, fact_154_Late__Semantics_OComm2, fact_73_Late__Semantics1_Osubject_Oinject_I1_J, fact_30_name__fresh, fact_52_residual_Ostrong__inducts, fact_286_pi_Ostrong__induct, fact_203_tauCases_H, fact_165_resSimCases, fact_155_resCasesB_H, fact_206_resInputBoundOutputTrans, fact_28_Late__Semantics_OPar2B, fact_150_resCases_H, fact_229_abs__fresh_I1_J, fact_294_pi_Ofresh_I10_J, fact_8_cClose1_Ohyps_I1_J, fact_100_Late__Semantics_OResB, fact_88_simps_I9_J, fact_298_pi_Odistinct_I63_J, fact_269_nilSim_I3_J, fact_3_assms_I1_J, fact_268_nilSim_I2_J, fact_290_pi_Ostrong__inducts, fact_187_pi_Odistinct_I19_J, fact_241_parZeroRight, fact_173_simCasesCont, fact_18_cRes_Ohyps_I1_J, fact_253_pi_Odistinct_I25_J, fact_152_transitions_OComm2, fact_193_outputBoundTrans, fact_10_cClose1_Ohyps_I13_J, fact_258_mismatchNilLeft, fact_256_pi_Odistinct_I39_J, fact_132_transitions_OResB, fact_31_name__exists__fresh, fact_248_pi_Odistinct_I51_J, fact_212_pi_Ofresh_I4_J, fact_37_pi_Odistinct_I85_J, fact_171_simulation__def, fact_235_inputFreeTrans, fact_11_cClose1_Ohyps_I8_J, fact_297_simps_I7_J, fact_265_mismatchCases_H, fact_172_parSym, fact_308_Sum1, fact_95_fresh__fact1, fact_41_subject_Oinducts, fact_163_Open, fact_166_resSimCases, fact_55_residual_Ostrong__induct, fact_266_Mismatch, fact_54_residual_Ostrong__induct, fact_184_pi_Ofresh_I2_J, fact_9_cClose1_Ohyps_I10_J, fact_179_resOutputTauTrans, fact_245_simps_I1_J, fact_287_pi_Ostrong__induct, fact_310_pi_Odistinct_I81_J, fact_169_simE_I2_J, fact_211_pi_Ofresh_I9_J, fact_93_subject_Ofresh_I1_J, fact_69_transitions_OClose2, fact_190_pi_Odistinct_I45_J, fact_86_prod_Oinject, fact_164_resSimCases, fact_61_fresh__prod, fact_24_ResF, fact_65_fresh__prod, fact_148_Late__Semantics1_Osubject_Odistinct_I1_J, fact_192_resTrans_I1_J, fact_131_old_Oprod_Oinducts, fact_313_pi_Oinject_I6_J, fact_107_surj__pair, fact_0_cClose1_Ohyps_I3_J, fact_240_inputIneqTrans, fact_274_pi_Odistinct_I7_J, fact_259_pi_Oinject_I5_J, fact_277_matchTrans, fact_255_pi_Odistinct_I1_J, fact_316_pi_Odistinct_I33_J, fact_62_fresh__prod, fact_230_residual_Oinject_I1_J, fact_195_resTauBoundTrans
% 23.59/6.58 % No. of inferences in proof: 502
% 23.59/6.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6060 ms resp. 5401 ms w/o parsing
% 24.19/6.74 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.19/6.74 % [INFO] Killing All external provers ...
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