TSTP Solution File: ITP181^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP181^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:35 EDT 2024
% Result : Theorem 54.18s 36.34s
% Output : Refutation 54.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 232
% Syntax : Number of formulae : 429 ( 234 unt; 37 typ; 0 def)
% Number of atoms : 1182 ( 394 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 6050 ( 240 ~; 8 |; 82 &;5228 @)
% ( 0 <=>; 492 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 130 ( 130 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 13 con; 0-5 aty)
% Number of variables : 1903 ( 8 ^1854 !; 26 ?;1903 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
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(fs_name_type,type,
fs_name:
!>[TA: $tType] : $o ).
thf(input_type,type,
input: 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_type,type,
abs_fun:
!>[TA: $tType,TB: $tType] : ( TB > TA > TB > ( noption @ TA ) ) ).
thf(fresh_type,type,
fresh:
!>[TA: $tType,TB: $tType] : ( TB > TA > $o ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(produc2004651681e_prod_type,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_rec_prod_type,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(eqvt_type,type,
eqvt:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(strong2129052853vative_type,type,
strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
thf(strong743114133lation_type,type,
strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_type,type,
p: pi ).
thf(pq_type,type,
pq: pi ).
thf(q_type,type,
q: pi ).
thf(a_type,type,
a: late_subject ).
thf(x_type,type,
x: name ).
thf(y_type,type,
y: name ).
thf(134,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Pair__inject) ).
thf(760,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_internal__case__prod__conv) ).
thf(909,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( abs_fun @ TB @ TA @ A @ B )
= ( abs_fun @ TB @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_abs__fun__eq1) ).
thf(468,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( abs_fun @ TB @ TA @ A @ B )
= ( abs_fun @ TB @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(13,axiom,
! [A: pi,B: late_freeRes,C: pi,D: late_freeRes > pi > $o] :
( ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ B @ C ) )
=> ( ( ( B = late_TauR )
=> ( ( A = C )
=> ( D @ late_TauR @ A ) ) )
=> ( D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_tauCases) ).
thf(234,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)],[13]) ).
thf(139,axiom,
( ( fresh @ name @ name )
= ( != @ name ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_name__fresh) ).
thf(777,plain,
( ( fresh @ name @ name )
= ( ^ [A: name,B: name] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(92,axiom,
! [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_BoundR @ A @ B @ C )
!= ( late_FreeR @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_residual_Odistinct_I1_J) ).
thf(523,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)],[92]) ).
thf(192,axiom,
fresh @ name @ pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Bound_Ohyps_I2_J) ).
thf(1005,plain,
fresh @ name @ pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(23,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( sum @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_pi_Odistinct_I41_J) ).
thf(276,plain,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( sum @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(169,axiom,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: TA] :
~ ! [B: name] :
~ ( fresh @ name @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_name__exists__fresh) ).
thf(873,plain,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: TA] :
~ ! [B: name] :
~ ( fresh @ name @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(16,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_pi_Odistinct_I85_J) ).
thf(247,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(118,axiom,
! [A: name,B: pi,C: name,D: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( subs @ ( subs @ B @ C @ A ) @ A @ D )
= ( subs @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_substTrans) ).
thf(655,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)],[118]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_old_Oprod_Oinducts) ).
thf(597,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC,C: TA] :
( ( fresh @ TB @ ( product_prod @ TC @ TA ) @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( ( fresh @ TB @ TC @ A @ B )
& ( fresh @ TB @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_fresh__prod) ).
thf(861,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC,C: TA] :
( ( fresh @ TB @ ( product_prod @ TC @ TA ) @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( ( fresh @ TB @ TC @ A @ B )
& ( fresh @ TB @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(95,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_Late__Semantics1_OfreeRes_Oinject) ).
thf(533,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)],[95]) ).
thf(86,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_Late__Semantics_OComm1) ).
thf(500,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)],[86]) ).
thf(190,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 @ name @ late_subject @ 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 @ name @ late_subject @ H @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_parCasesB_H) ).
thf(945,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 @ name @ late_subject @ 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 @ name @ late_subject @ H @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(38,axiom,
! [A: late_residual > $o,B: late_residual] :
( ! [C: late_subject,D: name,E: pi] : ( A @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [C: late_freeRes,D: pi] : ( A @ ( late_FreeR @ C @ D ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_residual_Oinducts) ).
thf(340,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)],[38]) ).
thf(187,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( input @ A @ B @ C ) @ D )
=> ~ ! [E: name,F: name,G: pi] :
( ( ( A = F )
& ( ( abs_fun @ name @ pi @ B @ C )
= ( abs_fun @ name @ pi @ E @ G ) ) )
=> ( ( D
= ( late_BoundR @ ( late_InputS @ F ) @ E @ G ) )
=> ( E = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_inputCases_H) ).
thf(930,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)],[187]) ).
thf(141,axiom,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh @ name @ pi @ D @ A )
=> ( fresh @ name @ pi @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_freshFreeDerivative_I2_J) ).
thf(782,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)],[141]) ).
thf(160,axiom,
! [A: name,B: pi,C: name,D: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( A != C )
=> ( fresh @ name @ pi @ A @ ( subs @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_fresh__fact1) ).
thf(841,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)],[160]) ).
thf(26,axiom,
! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
( ( ( late_FreeR @ A @ B )
= ( late_FreeR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_residual_Oinject_I2_J) ).
thf(288,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)],[26]) ).
thf(36,axiom,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: name,D: pi,E: TA] :
( ( 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 ) )
& ( member @ ( product_prod @ 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 @ name @ late_subject @ C @ G )
=> ( ( C != H )
=> ( ( fresh @ name @ TA @ 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 @ name @ late_freeRes @ C @ G )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
& ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ H @ ( res @ C @ F ) ) @ A ) ) ) )
=> ( strong743114133lation @ D @ A @ ( res @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_resSimCases) ).
thf(320,plain,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: name,D: pi,E: TA] :
( ( 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 ) )
& ( member @ ( product_prod @ 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 @ name @ late_subject @ C @ G )
=> ( ( C != H )
=> ( ( fresh @ name @ TA @ 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 @ name @ late_freeRes @ C @ G )
=> ? [H: pi] :
( ( late_transitions @ D @ ( late_FreeR @ G @ H ) )
& ( member @ ( product_prod @ 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)],[36]) ).
thf(53,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_Late__Semantics1_Osubject_Odistinct_I1_J) ).
thf(389,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(108,axiom,
! [A: name,B: pi,C: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( subs @ ( res @ C @ B ) @ C @ A )
= ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_substRes3) ).
thf(570,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)],[108]) ).
thf(142,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_prod__cases6) ).
thf(785,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(148,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 @ name @ late_subject @ E @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_freshBoundDerivative_I1_J) ).
thf(802,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 @ name @ late_subject @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(43,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_pi_Odistinct_I71_J) ).
thf(357,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( sum @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(179,axiom,
! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_resInputBoundOutputTrans) ).
thf(902,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)],[179]) ).
thf(104,axiom,
! [A: name,B: late_freeRes,C: pi] :
( ( fresh @ name @ late_residual @ A @ ( late_FreeR @ B @ C ) )
= ( ( fresh @ name @ late_freeRes @ A @ B )
& ( fresh @ name @ pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_residual_Ofresh_I2_J) ).
thf(559,plain,
! [A: name,B: late_freeRes,C: pi] :
( ( fresh @ name @ late_residual @ A @ ( late_FreeR @ B @ C ) )
= ( ( fresh @ name @ late_freeRes @ A @ B )
& ( fresh @ name @ pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(168,axiom,
! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_BoundR @ ( late_InputS @ E ) @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_resOutputInputTrans) ).
thf(870,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)],[168]) ).
thf(35,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh @ name @ pi @ F @ A )
=> ( ( fresh @ name @ pi @ F @ E )
=> ( ( fresh @ name @ pi @ C @ A )
=> ( ( fresh @ name @ pi @ C @ E )
=> ( ( F != B )
=> ( ( fresh @ name @ pi @ F @ D )
=> ( ( C != B )
=> ( ( fresh @ name @ pi @ C @ G )
=> ( ( F != C )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_transitions_OClose2) ).
thf(316,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)],[35]) ).
thf(25,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_pi_Odistinct_I5_J) ).
thf(284,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( input @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_old_Oprod_Oexhaust) ).
thf(770,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(79,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( output @ A @ B @ C )
= ( output @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_pi_Oinject_I1_J) ).
thf(475,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)],[79]) ).
thf(6,axiom,
! [A: name] : ( fresh @ name @ late_freeRes @ A @ late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_freeRes_Ofresh_I2_J) ).
thf(211,plain,
! [A: name] : ( fresh @ name @ late_freeRes @ A @ late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(109,axiom,
! [A: name,B: late_subject,C: name,D: pi] :
( ( fresh @ name @ late_residual @ A @ ( late_BoundR @ B @ C @ D ) )
= ( ( fresh @ name @ late_subject @ A @ B )
& ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_residual_Ofresh_I1_J) ).
thf(574,plain,
! [A: name,B: late_subject,C: name,D: pi] :
( ( fresh @ name @ late_residual @ A @ ( late_BoundR @ B @ C @ D ) )
= ( ( fresh @ name @ late_subject @ A @ B )
& ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(180,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh @ name @ late_subject @ E @ B )
=> ( ( E != C )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_Late__Semantics_OResB) ).
thf(905,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh @ name @ late_subject @ E @ B )
=> ( ( E != C )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(24,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( mismatch @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_pi_Odistinct_I9_J) ).
thf(280,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( mismatch @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(171,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_old_Oprod_Orec) ).
thf(877,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(55,axiom,
! [A: name,B: name,C: name] :
( ( fresh @ name @ late_freeRes @ A @ ( late_OutputR @ B @ C ) )
= ( ( fresh @ name @ name @ A @ B )
& ( fresh @ name @ name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_freeRes_Ofresh_I1_J) ).
thf(396,plain,
! [A: name,B: name,C: name] :
( ( fresh @ name @ late_freeRes @ A @ ( late_OutputR @ B @ C ) )
= ( ( fresh @ name @ name @ A @ B )
& ( fresh @ name @ name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(15,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( mismatch @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_pi_Odistinct_I73_J) ).
thf(243,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)],[15]) ).
thf(20,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_Late__Semantics_Osubject_Oinject_I2_J) ).
thf(265,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(88,axiom,
fs_name @ late_subject,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject___Agent_Ofs__name_11) ).
thf(507,plain,
fs_name @ late_subject,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(93,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: pi] :
~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_nilSim_I1_J) ).
thf(527,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: pi] :
~ ( strong743114133lation @ piNil @ A @ ( tau @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(127,axiom,
! [A: name,B: pi,C: name,D: pi] :
( ( ( res @ A @ B )
= ( res @ C @ D ) )
= ( ( abs_fun @ name @ pi @ A @ B )
= ( abs_fun @ name @ pi @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_pi_Oinject_I8_J) ).
thf(734,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)],[127]) ).
thf(10,axiom,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_freeRes_Oexhaust) ).
thf(221,plain,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(28,axiom,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
=> ~ ( ( fresh @ name @ late_freeRes @ A @ D )
| ( fresh @ name @ late_freeRes @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_outputFreshTrans) ).
thf(292,plain,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
=> ~ ( ( fresh @ name @ late_freeRes @ A @ D )
| ( fresh @ name @ late_freeRes @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(50,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_Late__Semantics_OfreeRes_Oinject) ).
thf(380,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)],[50]) ).
thf(185,axiom,
! [A: name,B: pi] :
( ( fresh @ name @ pi @ A @ ( tau @ B ) )
= ( fresh @ name @ pi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_pi_Ofresh_I3_J) ).
thf(925,plain,
! [A: name,B: pi] :
( ( fresh @ name @ pi @ A @ ( tau @ B ) )
= ( fresh @ name @ pi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(176,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC,C: TA] :
( ( fresh @ TB @ ( product_prod @ TC @ TA ) @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
=> ( fresh @ TB @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_fresh__prodD_I2_J) ).
thf(894,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC,C: TA] :
( ( fresh @ TB @ ( product_prod @ TC @ TA ) @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
=> ( fresh @ TB @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(155,axiom,
! [A: name,B: name,C: pi] :
( ( fresh @ name @ pi @ A @ ( res @ B @ C ) )
= ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_pi_Ofresh_I9_J) ).
thf(825,plain,
! [A: name,B: name,C: pi] :
( ( fresh @ name @ pi @ A @ ( res @ B @ C ) )
= ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(31,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ A @ C ) ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_resOutputOutputTrans) ).
thf(302,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)],[31]) ).
thf(58,axiom,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( fresh @ name @ ( name > ( noption @ TA ) ) @ A @ ( abs_fun @ name @ TA @ B @ C ) )
= ( ( A = B )
| ( fresh @ name @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_name__fresh__abs) ).
thf(407,plain,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( fresh @ name @ ( name > ( noption @ TA ) ) @ A @ ( abs_fun @ name @ TA @ B @ C ) )
= ( ( A = B )
| ( fresh @ name @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(65,axiom,
! [A: pi,B: late_freeRes,C: pi,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( late_transitions @ ( par @ A @ D ) @ ( late_FreeR @ B @ ( par @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Par1F) ).
thf(429,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)],[65]) ).
thf(143,axiom,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_resZeroTrans) ).
thf(788,plain,
! [A: name,B: late_residual] :
~ ( late_transitions @ ( res @ A @ piNil ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1,conjecture,
y != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
y != x,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(197,plain,
y != x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: name,C: name,D: pi] :
~ ( strong743114133lation @ piNil @ A @ ( output @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_nilSim_I3_J) ).
thf(361,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: name,C: name,D: pi] :
~ ( strong743114133lation @ piNil @ A @ ( output @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(67,axiom,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_FreeR @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_inputFreeTrans) ).
thf(435,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)],[67]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_prod__cases7) ).
thf(665,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(157,axiom,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh @ name @ late_freeRes @ D @ B )
=> ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_ResF) ).
thf(830,plain,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh @ name @ late_freeRes @ D @ B )
=> ( late_transitions @ ( res @ D @ A ) @ ( late_FreeR @ B @ ( res @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(75,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_pi_Odistinct_I29_J) ).
thf(461,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)],[75]) ).
thf(101,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_BoundOutputS @ D ) @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_inputBoundOutputTrans) ).
thf(551,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)],[101]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_prod__cases4) ).
thf(725,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(57,axiom,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_pi_Odistinct_I43_J) ).
thf(403,plain,
! [A: pi,B: pi,C: pi] :
( ( tau @ A )
!= ( par @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(193,axiom,
fresh @ name @ ( product_prod @ name @ ( product_prod @ pi @ pi ) ) @ y @ ( product_Pair @ name @ ( product_prod @ pi @ pi ) @ x @ ( product_Pair @ pi @ pi @ p @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Bound_Ohyps_I5_J) ).
thf(1006,plain,
fresh @ name @ ( product_prod @ name @ ( product_prod @ pi @ pi ) ) @ y @ ( product_Pair @ name @ ( product_prod @ pi @ pi ) @ x @ ( product_Pair @ pi @ pi @ p @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(164,axiom,
! [A: pi,B: set @ ( product_prod @ 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 ) )
& ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ F @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_simE_I2_J) ).
thf(857,plain,
! [A: pi,B: set @ ( product_prod @ 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 ) )
& ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ F @ E ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(78,axiom,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_pi_Odistinct_I45_J) ).
thf(471,plain,
! [A: pi,B: name,C: pi] :
( ( tau @ A )
!= ( res @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(11,axiom,
! [A: late_freeRes > $o,B: late_freeRes] :
( ! [C: name,D: name] : ( A @ ( late_OutputR @ C @ D ) )
=> ( ( A @ late_TauR )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_freeRes_Oinducts) ).
thf(225,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)],[11]) ).
thf(114,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_pi_Odistinct_I81_J) ).
thf(590,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(102,axiom,
! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_Late__Semantics_OInput) ).
thf(554,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)],[102]) ).
thf(131,axiom,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_sumCases_H) ).
thf(753,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)],[131]) ).
thf(159,axiom,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: TA > late_residual > $o,B: TA,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: TA] :
( ( fresh @ name @ TA @ E @ G )
=> ( ( fresh @ name @ late_subject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: TA] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_residual_Ostrong__induct) ).
thf(837,plain,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: TA > late_residual > $o,B: TA,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: TA] :
( ( fresh @ name @ TA @ E @ G )
=> ( ( fresh @ name @ late_subject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: TA] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(54,axiom,
! [A: pi,B: pi,C: name,D: name] :
( ( subs @ ( sum @ A @ B ) @ C @ D )
= ( sum @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_simps_I7_J) ).
thf(393,plain,
! [A: pi,B: pi,C: name,D: name] :
( ( subs @ ( sum @ A @ B ) @ C @ D )
= ( sum @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(123,axiom,
! [A: name,B: pi,C: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( subs @ B @ A @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_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)],[123]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_surj__pair) ).
thf(1002,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(140,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh @ name @ pi @ A @ ( sum @ B @ C ) )
= ( ( fresh @ name @ pi @ A @ B )
& ( fresh @ name @ pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_pi_Ofresh_I7_J) ).
thf(779,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)],[140]) ).
thf(47,axiom,
! [A: pi,B: name,C: name] :
( ( subs @ ( tau @ A ) @ B @ C )
= ( tau @ ( subs @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_simps_I2_J) ).
thf(371,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)],[47]) ).
thf(87,axiom,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_pi_Odistinct_I1_J) ).
thf(503,plain,
! [A: name,B: name,C: pi] :
( piNil
!= ( output @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(39,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
=> ( ( fresh @ name @ pi @ F @ A )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_Late__Semantics_OClose1) ).
thf(343,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)],[39]) ).
thf(89,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
( ( late_transitions @ ( output @ A @ B @ C ) @ D )
=> ~ ! [E: name,F: name,G: pi] :
( ( ( A = E )
& ( B = F )
& ( C = G ) )
=> ( D
!= ( late_FreeR @ ( late_OutputR @ E @ F ) @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_outputCases_H) ).
thf(508,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)],[89]) ).
thf(33,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( par @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_pi_Odistinct_I55_J) ).
thf(311,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)],[33]) ).
thf(135,axiom,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_BoundR @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_resTauBoundTrans) ).
thf(765,plain,
! [A: name,B: pi,C: late_subject,D: name,E: pi] :
~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_BoundR @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(94,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( fresh @ name @ pi @ A @ ( input @ B @ C @ D ) )
= ( ( fresh @ name @ name @ A @ B )
& ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_pi_Ofresh_I4_J) ).
thf(530,plain,
! [A: name,B: name,C: name,D: pi] :
( ( fresh @ name @ pi @ A @ ( input @ B @ C @ D ) )
= ( ( fresh @ name @ name @ A @ B )
& ( fresh @ name @ ( name > ( noption @ pi ) ) @ A @ ( abs_fun @ name @ pi @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(120,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 @ name @ late_subject @ C @ B )
=> ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_transitions_OPar2B) ).
thf(662,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 @ name @ late_subject @ C @ B )
=> ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(149,axiom,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Sum2) ).
thf(805,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)],[149]) ).
thf(4,axiom,
! [TA: $tType,A: TA > late_freeRes > $o,B: TA,C: late_freeRes] :
( ! [D: name,E: name,F: TA] : ( A @ F @ ( late_OutputR @ D @ E ) )
=> ( ! [D: TA] : ( A @ D @ late_TauR )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_freeRes_Ostrong__induct_H) ).
thf(205,plain,
! [TA: $tType,A: TA > late_freeRes > $o,B: TA,C: late_freeRes] :
( ! [D: name,E: name,F: TA] : ( A @ F @ ( late_OutputR @ D @ E ) )
=> ( ! [D: TA] : ( A @ D @ late_TauR )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(138,axiom,
! [A: pi,B: set @ ( product_prod @ pi @ pi ),C: pi,D: late_subject,E: name,F: pi] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( late_transitions @ C @ ( late_BoundR @ D @ E @ F ) )
=> ( ( fresh @ name @ pi @ E @ A )
=> ? [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ D @ E @ G ) )
& ( strong2129052853vative @ G @ F @ D @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_simE_I1_J) ).
thf(773,plain,
! [A: pi,B: set @ ( product_prod @ 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)],[138]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_prod__induct7) ).
thf(794,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(60,axiom,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_pi_Oinject_I2_J) ).
thf(412,plain,
! [A: pi,B: pi] :
( ( ( tau @ A )
= ( tau @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(64,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ F @ G ) )
=> ( ( fresh @ name @ pi @ C @ A )
=> ( ( fresh @ name @ pi @ C @ E )
=> ( ( fresh @ name @ pi @ F @ A )
=> ( ( fresh @ name @ pi @ F @ E )
=> ( ( C != B )
=> ( ( fresh @ name @ pi @ C @ G )
=> ( ( F != B )
=> ( ( fresh @ name @ pi @ F @ D )
=> ( ( C != F )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ F @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_transitions_OClose1) ).
thf(425,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)],[64]) ).
thf(29,axiom,
! [A: name,B: name,C: name,D: pi,E: late_freeRes,F: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_FreeR @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_resInputFreeTrans) ).
thf(296,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)],[29]) ).
thf(113,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: pi,F: pi > $o] :
( ( late_transitions @ ( par @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ( fresh @ name @ pi @ D @ A )
=> ( ( fresh @ name @ pi @ D @ B )
=> ( ! [G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ C @ D @ G ) )
=> ( F @ ( par @ G @ B ) ) )
=> ( ! [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
=> ( F @ ( par @ A @ G ) ) )
=> ( F @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_parCasesB) ).
thf(584,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)],[113]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_prod__cases3) ).
thf(819,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(105,axiom,
fs_name @ late_freeRes,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_10) ).
thf(562,plain,
fs_name @ late_freeRes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType] :
( ( ( fs_name @ TB )
& ( fs_name @ TA ) )
=> ( fs_name @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Agent_Ofs__name_9) ).
thf(423,plain,
! [TA: $tType,TB: $tType] :
( ( ( fs_name @ TB )
& ( fs_name @ TA ) )
=> ( fs_name @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(194,axiom,
fresh @ name @ late_subject @ y @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Bound_Ohyps_I4_J) ).
thf(1007,plain,
fresh @ name @ late_subject @ y @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(130,axiom,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi,D: TA] :
( ( 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 @ name @ late_subject @ F @ E )
=> ( ( fresh @ name @ TA @ 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 ) )
& ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ G @ F ) @ A ) ) )
=> ( strong743114133lation @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_simCasesCont) ).
thf(743,plain,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi,D: TA] :
( ( 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 @ name @ late_subject @ F @ E )
=> ( ( fresh @ name @ TA @ 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 ) )
& ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ G @ F ) @ A ) ) )
=> ( strong743114133lation @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(170,axiom,
! [A: name] : ( fresh @ name @ pi @ A @ piNil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_pi_Ofresh_I1_J) ).
thf(875,plain,
! [A: name] : ( fresh @ name @ pi @ A @ piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_prod__induct3) ).
thf(577,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TA,C: TC] :
( ( fresh @ TB @ ( product_prod @ TA @ TC ) @ A @ ( product_Pair @ TA @ TC @ B @ C ) )
=> ( fresh @ TB @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_fresh__prodD_I1_J) ).
thf(579,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TA,C: TC] :
( ( fresh @ TB @ ( product_prod @ TA @ TC ) @ A @ ( product_Pair @ TA @ TC @ B @ C ) )
=> ( fresh @ TB @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(27,axiom,
fs_name @ name,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Agent_Oname___Agent_Ofs__name_8) ).
thf(291,plain,
fs_name @ name,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(70,axiom,
! [TA: $tType,A: TA > late_subject > $o,B: TA,C: late_subject] :
( ! [D: name,E: TA] : ( A @ E @ ( late_InputS @ D ) )
=> ( ! [D: name,E: TA] : ( A @ E @ ( late_BoundOutputS @ D ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_subject_Ostrong__induct_H) ).
thf(445,plain,
! [TA: $tType,A: TA > late_subject > $o,B: TA,C: late_subject] :
( ! [D: name,E: TA] : ( A @ E @ ( late_InputS @ D ) )
=> ( ! [D: name,E: TA] : ( A @ E @ ( late_BoundOutputS @ D ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(183,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh @ name @ pi @ E @ A )
=> ( ( E != C )
=> ( fresh @ name @ pi @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_freshBoundDerivative_I2_J) ).
thf(919,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)],[183]) ).
thf(41,axiom,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_pi_Odistinct_I19_J) ).
thf(350,plain,
! [A: name,B: name,C: pi,D: pi] :
( ( output @ A @ B @ C )
!= ( tau @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(97,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( mismatch @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_pi_Odistinct_I39_J) ).
thf(540,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( mismatch @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(9,axiom,
! [TA: $tType,A: TA > late_freeRes > $o,B: TA,C: late_freeRes] :
( ! [D: name,E: name,F: TA] : ( A @ F @ ( late_OutputR @ D @ E ) )
=> ( ! [D: TA] : ( A @ D @ late_TauR )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_freeRes_Ostrong__inducts) ).
thf(219,plain,
! [TA: $tType,A: TA > late_freeRes > $o,B: TA,C: late_freeRes] :
( ! [D: name,E: name,F: TA] : ( A @ F @ ( late_OutputR @ D @ E ) )
=> ( ! [D: TA] : ( A @ D @ late_TauR )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(62,axiom,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_pi_Odistinct_I3_J) ).
thf(419,plain,
! [A: pi] :
( piNil
!= ( tau @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(49,axiom,
! [A: name,B: pi,C: name,D: name,E: pi] :
~ ( late_transitions @ ( res @ A @ ( tau @ B ) ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_resTauOutputTrans) ).
thf(377,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)],[49]) ).
thf(128,axiom,
! [A: pi,B: late_subject,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_BoundR @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_tauBoundTrans) ).
thf(737,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)],[128]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_prod_Oinject) ).
thf(880,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(117,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 @ name @ late_subject @ H @ E )
=> ( ( H != F )
=> ( ( fresh @ name @ pi @ F @ D )
=> ~ ( fresh @ name @ late_subject @ 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 @ name @ late_freeRes @ G @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_resCases_H) ).
thf(599,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 @ name @ late_subject @ H @ E )
=> ( ( H != F )
=> ( ( fresh @ name @ pi @ F @ D )
=> ~ ( fresh @ name @ late_subject @ 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 @ name @ late_freeRes @ G @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(72,axiom,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_subst__identity) ).
thf(451,plain,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(107,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_nilCases_H) ).
thf(567,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(175,axiom,
! [A: name,B: pi,C: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( res @ C @ B )
= ( res @ A @ ( subs @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_substRes2) ).
thf(890,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)],[175]) ).
thf(151,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 @ name @ late_freeRes @ A @ C )
=> ( E @ ( res @ A @ F ) ) ) )
=> ( E @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_resCasesF) ).
thf(811,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 @ name @ late_freeRes @ A @ C )
=> ( E @ ( res @ A @ F ) ) ) )
=> ( E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(84,axiom,
! [A: pi,B: name,C: name,D: pi] :
~ ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_tauOutputTrans) ).
thf(494,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)],[84]) ).
thf(133,axiom,
! [A: name,B: pi] : ( fresh @ name @ pi @ A @ ( res @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_freshRes) ).
thf(758,plain,
! [A: name,B: pi] : ( fresh @ name @ pi @ A @ ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(46,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( output @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_pi_Odistinct_I27_J) ).
thf(367,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)],[46]) ).
thf(152,axiom,
! [A: pi,B: late_residual,C: name] :
( ( late_transitions @ A @ B )
=> ( ( fresh @ name @ pi @ C @ A )
=> ( fresh @ name @ late_residual @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_freshResidual) ).
thf(816,plain,
! [A: pi,B: late_residual,C: name] :
( ( late_transitions @ A @ B )
=> ( ( fresh @ name @ pi @ C @ A )
=> ( fresh @ name @ late_residual @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(115,axiom,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh @ name @ pi @ D @ A )
=> ( fresh @ name @ late_freeRes @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_freshFreeDerivative_I1_J) ).
thf(594,plain,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh @ name @ pi @ D @ A )
=> ( fresh @ name @ late_freeRes @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(17,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_InputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_FreeR @ ( late_OutputR @ B @ F ) @ G ) )
=> ( ( fresh @ name @ pi @ C @ A )
=> ( ( fresh @ name @ pi @ C @ E )
=> ( ( C != B )
=> ( ( C != F )
=> ( ( fresh @ name @ pi @ C @ G )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ D @ C @ F ) @ G ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_transitions_OComm1) ).
thf(251,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)],[17]) ).
thf(189,axiom,
( strong743114133lation
= ( ^ [A: pi,B: set @ ( product_prod @ 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 ) )
& ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ F @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_simulation__def) ).
thf(943,plain,
( strong743114133lation
= ( ^ [A: pi,B: set @ ( product_prod @ 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 ) )
& ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ F @ E ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(122,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 @ name @ late_subject @ J @ G )
=> ( ( J != H )
=> ( ( fresh @ name @ pi @ H @ F )
=> ~ ( fresh @ name @ late_subject @ H @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_resCasesB_H) ).
thf(668,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 @ name @ late_subject @ J @ G )
=> ( ( J != H )
=> ( ( fresh @ name @ pi @ H @ F )
=> ~ ( fresh @ name @ late_subject @ H @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(147,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh @ name @ pi @ C @ E )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Late__Semantics_OPar1B) ).
thf(799,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)],[147]) ).
thf(7,axiom,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_Tau) ).
thf(213,plain,
! [A: pi] : ( late_transitions @ ( tau @ A ) @ ( late_FreeR @ late_TauR @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(162,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 @ name @ late_freeRes @ H @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_resCasesF_H) ).
thf(848,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 @ name @ late_freeRes @ H @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(91,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( par @ A @ B )
= ( par @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_pi_Oinject_I7_J) ).
thf(520,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)],[91]) ).
thf(182,axiom,
! [A: pi,B: pi,C: set @ ( product_prod @ 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 ) )
& ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ F @ E ) @ C ) ) )
=> ( strong743114133lation @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_simCases) ).
thf(912,plain,
! [A: pi,B: pi,C: set @ ( product_prod @ 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 ) )
& ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ F @ E ) @ C ) ) )
=> ( strong743114133lation @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(56,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( input @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_pi_Odistinct_I57_J) ).
thf(399,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)],[56]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_prod__induct4) ).
thf(768,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(173,axiom,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: TA > late_residual > $o,B: TA,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: TA] :
( ( fresh @ name @ TA @ E @ G )
=> ( ( fresh @ name @ late_subject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: TA] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_residual_Ostrong__inducts) ).
thf(883,plain,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: TA > late_residual > $o,B: TA,C: late_residual] :
( ! [D: late_subject,E: name,F: pi,G: TA] :
( ( fresh @ name @ TA @ E @ G )
=> ( ( fresh @ name @ late_subject @ E @ D )
=> ( A @ G @ ( late_BoundR @ D @ E @ F ) ) ) )
=> ( ! [D: late_freeRes,E: pi,F: TA] : ( A @ F @ ( late_FreeR @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(106,axiom,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_pi_Odistinct_I15_J) ).
thf(563,plain,
! [A: name,B: pi] :
( piNil
!= ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(30,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: name,C: name,D: pi] :
~ ( strong743114133lation @ piNil @ A @ ( input @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_nilSim_I2_J) ).
thf(299,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: name,C: name,D: pi] :
~ ( strong743114133lation @ piNil @ A @ ( input @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(68,axiom,
! [A: late_subject > $o,B: late_subject] :
( ! [C: name] : ( A @ ( late_InputS @ C ) )
=> ( ! [C: name] : ( A @ ( late_BoundOutputS @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_subject_Oinducts) ).
thf(438,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)],[68]) ).
thf(14,axiom,
! [TA: $tType,A: TA > late_subject > $o,B: TA,C: late_subject] :
( ! [D: name,E: TA] : ( A @ E @ ( late_InputS @ D ) )
=> ( ! [D: name,E: TA] : ( A @ E @ ( late_BoundOutputS @ D ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_subject_Ostrong__inducts) ).
thf(241,plain,
! [TA: $tType,A: TA > late_subject > $o,B: TA,C: late_subject] :
( ! [D: name,E: TA] : ( A @ E @ ( late_InputS @ D ) )
=> ( ! [D: name,E: TA] : ( A @ E @ ( late_BoundOutputS @ D ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(83,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( A != B )
=> ( ( A != C )
=> ( ( subs @ ( res @ A @ D ) @ B @ C )
= ( res @ A @ ( subs @ D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_simps_I9_J) ).
thf(490,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)],[83]) ).
thf(99,axiom,
fs_name @ pi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Agent_Opi___Agent_Ofs__name) ).
thf(548,plain,
fs_name @ pi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(48,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( B != C )
=> ( late_transitions @ ( res @ C @ A ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_Open) ).
thf(374,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)],[48]) ).
thf(18,axiom,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( fresh @ name @ ( name > ( noption @ TA ) ) @ A @ ( abs_fun @ name @ TA @ B @ C ) )
= ( ( A = B )
| ( fresh @ name @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_abs__fresh_I1_J) ).
thf(255,plain,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( fresh @ name @ ( name > ( noption @ TA ) ) @ A @ ( abs_fun @ name @ TA @ B @ C ) )
= ( ( A = B )
| ( fresh @ name @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(188,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh @ name @ late_subject @ E @ B )
=> ( ( E != C )
=> ( ( fresh @ name @ pi @ C @ A )
=> ( ( fresh @ name @ late_subject @ C @ B )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_transitions_OResB) ).
thf(939,plain,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh @ name @ late_subject @ E @ B )
=> ( ( E != C )
=> ( ( fresh @ name @ pi @ C @ A )
=> ( ( fresh @ name @ late_subject @ C @ B )
=> ( late_transitions @ ( res @ E @ A ) @ ( late_BoundR @ B @ C @ ( res @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(74,axiom,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_zeroTrans) ).
thf(458,plain,
! [A: late_residual] :
~ ( late_transitions @ piNil @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(163,axiom,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_sumCases) ).
thf(855,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)],[163]) ).
thf(174,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( output @ A @ B @ C ) ) @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_resTrans_I1_J) ).
thf(887,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)],[174]) ).
thf(144,axiom,
! [A: name,B: name] :
( ( fresh @ name @ late_subject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh @ name @ name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_subject_Ofresh_I2_J) ).
thf(791,plain,
! [A: name,B: name] :
( ( fresh @ name @ late_subject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh @ name @ name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(69,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( input @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_pi_Odistinct_I51_J) ).
thf(441,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)],[69]) ).
thf(150,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( sum @ A @ B )
= ( sum @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_pi_Oinject_I6_J) ).
thf(808,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)],[150]) ).
thf(98,axiom,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_subject_Oexhaust) ).
thf(544,plain,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(37,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Late__Semantics_Osubject_Odistinct_I1_J) ).
thf(336,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(166,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 @ name @ late_subject @ C @ B )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_transitions_OPar1B) ).
thf(864,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 @ name @ late_subject @ C @ B )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_BoundR @ B @ C @ ( par @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(52,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_Late__Semantics_OComm2) ).
thf(386,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)],[52]) ).
thf(195,axiom,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ a @ y @ pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Bound_Ohyps_I1_J) ).
thf(1008,plain,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ a @ y @ pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(85,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh @ name @ pi @ C @ E )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( res @ C @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_Late__Semantics_OClose2) ).
thf(497,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)],[85]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',fact_248_pi_Ofresh_I6_J) ).
thf(845,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)],[161]) ).
thf(103,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/sandbox2/benchmark/theBenchmark.p',fact_254_pi_Oinject_I5_J) ).
thf(556,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)],[103]) ).
thf(81,axiom,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh @ name @ pi @ F @ A )
=> ( ( fresh @ name @ pi @ F @ E )
=> ( ( F != B )
=> ( ( F != C )
=> ( ( fresh @ name @ pi @ F @ D )
=> ( late_transitions @ ( par @ A @ E ) @ ( late_FreeR @ late_TauR @ ( par @ D @ ( subs @ G @ F @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_transitions_OComm2) ).
thf(482,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)],[81]) ).
thf(112,axiom,
! [A: name,B: name] :
( ( fresh @ name @ late_subject @ A @ ( late_InputS @ B ) )
= ( fresh @ name @ name @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_subject_Ofresh_I1_J) ).
thf(581,plain,
! [A: name,B: name] :
( ( fresh @ name @ late_subject @ A @ ( late_InputS @ B ) )
= ( fresh @ name @ name @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(76,axiom,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_simps_I1_J) ).
thf(465,plain,
! [A: name,B: name] :
( ( subs @ piNil @ A @ B )
= piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(12,axiom,
! [A: name,B: name,C: pi,D: pi] :
~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ late_TauR @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_outputTauTrans) ).
thf(231,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)],[12]) ).
thf(90,axiom,
! [A: pi,B: late_freeRes,C: pi,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( late_transitions @ ( par @ D @ A ) @ ( late_FreeR @ B @ ( par @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Par2F) ).
thf(517,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)],[90]) ).
thf(177,axiom,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi] :
~ ( late_transitions @ ( output @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_outputBoundTrans) ).
thf(896,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)],[177]) ).
thf(19,axiom,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi,F: late_freeRes > pi > $o] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ D @ E ) )
=> ( ( ( D
= ( late_OutputR @ A @ B ) )
=> ( ( C = E )
=> ( F @ ( late_OutputR @ A @ B ) @ C ) ) )
=> ( F @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_outputCases) ).
thf(258,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)],[19]) ).
thf(126,axiom,
! [A: late_subject,B: name,C: pi,D: late_subject,E: name,F: pi] :
( ( ( late_BoundR @ A @ B @ C )
= ( late_BoundR @ D @ E @ F ) )
= ( ( A = D )
& ( ( abs_fun @ name @ pi @ B @ C )
= ( abs_fun @ name @ pi @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_residual_Oinject_I1_J) ).
thf(731,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)],[126]) ).
thf(5,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_Late__Semantics_OfreeRes_Odistinct_I1_J) ).
thf(207,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(80,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_pi_Odistinct_I35_J) ).
thf(478,plain,
! [A: pi,B: name,C: name,D: pi] :
( ( tau @ A )
!= ( input @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(22,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_pi_Odistinct_I53_J) ).
thf(272,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)],[22]) ).
thf(51,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_Late__Semantics1_Osubject_Oinject_I2_J) ).
thf(383,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(178,axiom,
! [A: name,B: name,C: name,D: pi] :
( ( fresh @ name @ pi @ A @ ( output @ B @ C @ D ) )
= ( ( fresh @ name @ name @ A @ B )
& ( fresh @ name @ name @ A @ C )
& ( fresh @ name @ pi @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_pi_Ofresh_I2_J) ).
thf(899,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)],[178]) ).
thf(40,axiom,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_pi_Odistinct_I13_J) ).
thf(346,plain,
! [A: pi,B: pi] :
( piNil
!= ( par @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(100,axiom,
! [A: pi,B: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ A @ B @ piNil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_nilSimRight) ).
thf(549,plain,
! [A: pi,B: set @ ( product_prod @ pi @ pi )] : ( strong743114133lation @ A @ B @ piNil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(96,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( input @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_pi_Odistinct_I21_J) ).
thf(536,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)],[96]) ).
thf(71,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( output @ A @ B @ C )
!= ( mismatch @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_pi_Odistinct_I25_J) ).
thf(447,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)],[71]) ).
thf(34,axiom,
fs_name @ late_residual,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual___Agent_Ofs__name_12) ).
thf(315,plain,
fs_name @ late_residual,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(66,axiom,
! [A: pi,B: pi,C: name,D: name] :
( ( subs @ ( par @ A @ B ) @ C @ D )
= ( par @ ( subs @ A @ C @ D ) @ ( subs @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_simps_I8_J) ).
thf(432,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)],[66]) ).
thf(167,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh @ name @ pi @ A @ ( par @ B @ C ) )
= ( ( fresh @ name @ pi @ A @ B )
& ( fresh @ name @ pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_pi_Ofresh_I8_J) ).
thf(867,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)],[167]) ).
thf(158,axiom,
! [A: name,B: name,C: pi] :
( ( A != B )
=> ( fresh @ name @ pi @ A @ ( subs @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_fresh__fact2) ).
thf(833,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)],[158]) ).
thf(59,axiom,
! [A: name,B: name,C: pi] : ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Output) ).
thf(410,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)],[59]) ).
thf(32,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( late_transitions @ ( output @ A @ B @ C ) @ ( late_FreeR @ ( late_OutputR @ D @ E ) @ F ) )
=> ~ ( ( A != D )
| ( B != E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_outputIneqTrans) ).
thf(305,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)],[32]) ).
thf(21,axiom,
! [A: name,B: name,C: pi] :
( ( A != B )
=> ( late_transitions @ ( input @ B @ A @ C ) @ ( late_BoundR @ ( late_InputS @ B ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_transitions_OInput) ).
thf(268,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)],[21]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_prod__cases) ).
thf(828,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(146,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_resTrans_I2_J) ).
thf(796,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)],[146]) ).
thf(186,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_prod__induct6) ).
thf(928,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(61,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( output @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_pi_Odistinct_I31_J) ).
thf(415,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)],[61]) ).
thf(154,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_old_Oprod_Oinject) ).
thf(822,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(3,axiom,
! [A: pi,B: late_residual] :
( ( late_transitions @ ( tau @ A ) @ B )
=> ~ ! [C: pi] :
( ( ( tau @ A )
= ( tau @ C ) )
=> ( B
!= ( late_FreeR @ late_TauR @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_tauCases_H) ).
thf(200,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)],[3]) ).
thf(125,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 @ name @ late_subject @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_inputIneqTrans) ).
thf(728,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 @ name @ late_subject @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_prod__cases5) ).
thf(740,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(82,axiom,
! [A: pi,B: pi] :
( piNil
!= ( sum @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_pi_Odistinct_I11_J) ).
thf(486,plain,
! [A: pi,B: pi] :
( piNil
!= ( sum @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(42,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
( ( ( input @ A @ B @ C )
= ( input @ D @ E @ F ) )
= ( ( A = D )
& ( ( abs_fun @ name @ pi @ B @ C )
= ( abs_fun @ name @ pi @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_pi_Oinject_I3_J) ).
thf(354,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)],[42]) ).
thf(196,axiom,
fresh @ name @ pi @ y @ ( res @ x @ ( sum @ p @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Bound_Ohyps_I3_J) ).
thf(1009,plain,
fresh @ name @ pi @ y @ ( res @ x @ ( sum @ p @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_prod__induct5) ).
thf(923,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(119,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: pi] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh @ name @ pi @ C @ E )
=> ( late_transitions @ ( par @ E @ A ) @ ( late_BoundR @ B @ C @ ( par @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Late__Semantics_OPar2B) ).
thf(659,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)],[119]) ).
thf(8,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).
thf(215,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(132,axiom,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Sum1) ).
thf(755,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)],[132]) ).
thf(73,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_pi_Odistinct_I79_J) ).
thf(454,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( sum @ A @ B )
!= ( par @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(45,axiom,
! [A: name,B: name,C: name,D: pi,E: pi] :
~ ( late_transitions @ ( res @ A @ ( output @ B @ C @ D ) ) @ ( late_FreeR @ late_TauR @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_resOutputTauTrans) ).
thf(364,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)],[45]) ).
thf(1010,plain,
$false,
inference(e,[status(thm)],[760,909,468,234,777,523,1005,276,873,247,655,597,861,533,500,945,340,930,782,841,288,320,389,570,785,802,357,902,559,870,316,284,770,475,211,574,905,280,877,396,243,265,507,527,734,221,292,380,925,894,825,302,407,429,788,197,361,435,665,830,461,551,725,403,1006,857,471,225,590,554,753,837,393,721,1002,779,371,503,343,508,311,765,530,662,805,205,773,794,412,425,296,584,819,562,423,1007,743,875,577,579,291,445,919,350,540,219,419,377,737,880,599,451,567,890,811,494,758,367,816,594,251,943,668,799,213,848,520,912,399,768,883,563,299,438,241,490,548,374,255,939,458,855,887,791,441,808,544,336,864,386,1008,497,845,556,482,581,465,231,517,896,258,731,207,478,272,383,899,346,549,536,447,315,432,867,833,410,305,268,828,796,928,415,822,200,728,740,486,354,1009,923,659,215,755,454,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : ITP181^2 : TPTP v8.1.2. Released v7.5.0.
% 0.15/0.17 % Command : run_Leo-III %s %d
% 0.16/0.39 % Computer : n016.cluster.edu
% 0.16/0.39 % Model : x86_64 x86_64
% 0.16/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.39 % Memory : 8042.1875MB
% 0.16/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.39 % CPULimit : 300
% 0.16/0.39 % WCLimit : 300
% 0.16/0.39 % DateTime : Mon May 6 14:43:09 EDT 2024
% 0.16/0.39 % CPUTime :
% 0.92/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.99/1.17 % [INFO] Parsing done (261ms).
% 1.99/1.18 % [INFO] Running in sequential loop mode.
% 2.73/1.40 % [INFO] eprover registered as external prover.
% 2.73/1.40 % [INFO] cvc4 registered as external prover.
% 2.73/1.41 % [INFO] Scanning for conjecture ...
% 2.98/1.50 % [INFO] Found a conjecture and 273 axioms. Running axiom selection ...
% 3.34/1.59 % [INFO] Axiom selection finished. Selected 194 axioms (removed 79 axioms).
% 4.04/1.81 % [INFO] Problem is higher-order (TPTP THF).
% 4.24/1.83 % [INFO] Type checking passed.
% 4.24/1.83 % [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 ...
% 54.18/36.33 % External prover 'e' found a proof!
% 54.18/36.33 % [INFO] Killing All external provers ...
% 54.18/36.34 % Time passed: 35770ms (effective reasoning time: 35150ms)
% 54.18/36.34 % 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)>
% 54.18/36.34 % Axioms used in derivation (194): fact_235_outputCases_H, fact_56_residual_Oinject_I2_J, fact_62_Par2F, fact_9_freshBoundDerivative_I1_J, fact_31_prod__cases6, fact_196_resOutputOutputTrans, fact_186_Late__Semantics1_Osubject_Odistinct_I1_J, fact_19_old_Oprod_Oexhaust, fact_197_Late__Semantics_OClose1, fact_28_prod__induct4, fact_170_pi_Ofresh_I1_J, fact_232_Late__Semantics_OComm1, fact_181_nilSim_I1_J, fact_148_pi_Oinject_I3_J, fact_205_freeRes_Ofresh_I2_J, fact_249_pi_Odistinct_I25_J, fact_80_tauBoundTrans, fact_212_pi_Oinject_I1_J, fact_16_pi_Odistinct_I81_J, fact_34_prod__cases3, fact_17_freshResidual, fact_255_pi_Odistinct_I73_J, tcon_Agent_Opi___Agent_Ofs__name, fact_175_pi_Odistinct_I11_J, fact_43_transitions_OPar2B, fact_22_surj__pair, fact_136_Late__Semantics_Osubject_Oinject_I2_J, fact_179_resZeroTrans, fact_50_resTauBoundTrans, fact_32_prod__cases5, fact_219_pi_Odistinct_I1_J, fact_53_pi_Ofresh_I8_J, fact_51_residual_Ostrong__inducts, fact_15_old_Oprod_Oinject, fact_18_old_Oprod_Oinducts, tcon_Late__Semantics_Osubject___Agent_Ofs__name_11, fact_174_pi_Odistinct_I13_J, fact_195_resOutputInputTrans, fact_137_subject_Ofresh_I2_J, fact_203_simps_I2_J, fact_199_simps_I9_J, fact_172_nilCases_H, fact_82_Late__Semantics_OPar2B, fact_189_subject_Oinducts, fact_81_Late__Semantics_OPar1B, fact_204_simps_I1_J, fact_25_prod__induct7, fact_193_Late__Semantics_OInput, tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_10, fact_57_pi_Odistinct_I35_J, fact_198_subst__identity, fact_190_subject_Ostrong__induct_H, fact_206_pi_Ofresh_I2_J, fact_73_pi_Odistinct_I41_J, fact_241_tauCases_H, fact_254_pi_Oinject_I5_J, fact_70_pi_Odistinct_I57_J, fact_173_pi_Odistinct_I15_J, fact_74_resCasesF, fact_244_transitions_OClose1, fact_13_freshBoundDerivative_I2_J, fact_69_residual_Oinducts, fact_201_substTrans, fact_77_freshFreeDerivative_I2_J, fact_156_simulation__def, fact_237_outputFreshTrans, fact_208_outputTauTrans, fact_20_Pair__inject, fact_216_Late__Semantics_OfreeRes_Odistinct_I1_J, fact_6_fresh__prod, fact_157_resCasesB_H, fact_149_simE_I1_J, fact_140_pi_Ofresh_I4_J, fact_169_name__fresh, fact_234_outputIneqTrans, fact_38_sumCases_H, tcon_Agent_Oname___Agent_Ofs__name_8, fact_67_pi_Odistinct_I79_J, fact_233_Output, fact_245_Late__Semantics_OClose2, fact_75_resCasesF_H, fact_159_inputBoundOutputTrans, fact_224_Late__Semantics1_OfreeRes_Odistinct_I1_J, fact_207_resOutputTauTrans, fact_142_abs__fun__eq1, fact_211_pi_Odistinct_I27_J, fact_222_forget, fact_177_pi_Odistinct_I3_J, fact_139_pi_Ofresh_I9_J, fact_132_simCasesCont, fact_26_prod__induct6, fact_239_transitions_OComm1, fact_225_substRes3, fact_145_residual_Oinject_I1_J, fact_138_freeRes_Ofresh_I1_J, fact_55_residual_Ofresh_I2_J, fact_154_resSimCases, fact_5_Bound_Ohyps_I1_J, fact_10_Late__Semantics_OResB, fact_58_pi_Odistinct_I43_J, fact_217_pi_Odistinct_I19_J, fact_214_freeRes_Ostrong__induct_H, fact_78_freshFreeDerivative_I1_J, fact_2_Bound_Ohyps_I4_J, fact_227_resTrans_I1_J, fact_185_subject_Ofresh_I1_J, fact_151_Open, fact_180_nilSim_I2_J, fact_66_pi_Odistinct_I85_J, fact_253_pi_Odistinct_I39_J, fact_40_old_Oprod_Orec, fact_210_pi_Odistinct_I29_J, fact_153_simE_I2_J, fact_76_ResF, fact_226_substRes2, fact_231_Late__Semantics_OComm2, fact_33_prod__cases4, fact_133_residual_Ofresh_I1_J, fact_44_transitions_OPar1B, fact_131_resTauOutputTrans, fact_12_fresh__prodD_I1_J, fact_146_abs__fresh_I1_J, fact_36_Sum2, fact_252_pi_Odistinct_I51_J, fact_215_freeRes_Oinducts, fact_61_pi_Oinject_I7_J, fact_29_prod__induct3, fact_23_name__exists__fresh, fact_243_transitions_OClose2, fact_147_name__fresh__abs, fact_35_freshRes, fact_165_Late__Semantics1_Osubject_Oinject_I2_J, fact_72_pi_Odistinct_I53_J, fact_41_internal__case__prod__conv, fact_130_resInputBoundOutputTrans, fact_14_prod_Oinject, fact_1_Bound_Ohyps_I5_J, fact_223_freeRes_Oexhaust, fact_236_outputCases, fact_188_Late__Semantics_Osubject_Odistinct_I1_J, fact_83_parCasesB, fact_202_simps_I7_J, fact_65_resInputFreeTrans, fact_135_Late__Semantics_OfreeRes_Oinject, fact_191_subject_Ostrong__inducts, fact_158_tauOutputTrans, fact_134_resCases_H, fact_11_fresh__prodD_I2_J, fact_52_residual_Ostrong__induct, fact_144_pi_Oinject_I8_J, fact_27_prod__induct5, fact_4_Bound_Ohyps_I2_J, fact_79_resTrans_I2_J, fact_182_inputCases_H, fact_21_prod__cases, fact_37_Sum1, fact_59_pi_Odistinct_I55_J, fact_218_pi_Odistinct_I21_J, fact_54_pi_Ofresh_I3_J, fact_229_nilSim_I3_J, fact_7_pi_Ofresh_I7_J, fact_68_residual_Odistinct_I1_J, fact_240_Tau, fact_155_simCases, tcon_Late__Semantics_Oresidual___Agent_Ofs__name_12, fact_39_sumCases, fact_49_inputIneqTrans, fact_48_parCasesB_H, fact_238_transitions_OComm2, fact_8_transitions_OResB, fact_213_freeRes_Ostrong__inducts, fact_30_prod__cases7, tcon_Product__Type_Oprod___Agent_Ofs__name_9, fact_71_pi_Odistinct_I45_J, fact_64_inputFreeTrans, fact_176_pi_Odistinct_I5_J, fact_209_pi_Odistinct_I31_J, fact_63_Par1F, fact_242_tauCases, fact_248_pi_Ofresh_I6_J, fact_251_pi_Odistinct_I71_J, fact_221_fresh__fact1, fact_166_Late__Semantics1_OfreeRes_Oinject, fact_200_simps_I8_J, fact_187_subject_Oexhaust, fact_178_nilSimRight, fact_250_pi_Odistinct_I9_J, fact_194_transitions_OInput, fact_171_zeroTrans, fact_228_outputBoundTrans, fact_60_pi_Oinject_I2_J, fact_24_pi_Oinject_I6_J, fact_220_fresh__fact2, fact_3_Bound_Ohyps_I3_J
% 54.18/36.34 % No. of inferences in proof: 392
% 54.18/36.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 35770 ms resp. 35150 ms w/o parsing
% 54.47/36.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 54.47/36.46 % [INFO] Killing All external provers ...
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