%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP190^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:07 AM UTC 2026
% Result : Theorem 95.49s 68.47s
% Output : Refutation 96.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 300
% Syntax : Number of formulae : 602 ( 300 unt; 0 typ; 0 def)
% Number of atoms : 1871 ( 571 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 10465 ( 279 ~; 7 |; 88 &;9265 @)
% ( 0 <=>; 826 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 252 ( 252 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 52 usr; 21 con; 0-5 aty)
% Number of variables : 2443 ( 20 ^;2393 !; 30 ?;2443 :)
% Comments :
%------------------------------------------------------------------------------
thf(late_residual_Rep_type,type,
late_residual_Rep: $tType ).
thf(late_subject_Rep_type,type,
late_subject_Rep: $tType ).
thf(late_freeRes_Rep_type,type,
late_freeRes_Rep: $tType ).
thf(late_residual_type,type,
late_residual: $tType ).
thf(late_subject_type,type,
late_subject: $tType ).
thf(late_freeRes_type,type,
late_freeRes: $tType ).
thf(pi_Rep_type,type,
pi_Rep: $tType ).
thf(name_type,type,
name: $tType ).
thf(pi_type,type,
pi: $tType ).
thf(fs_name_decl,type,
fs_name:
!>[TA: $tType] : $o ).
thf(pt_name_decl,type,
pt_name:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(cp_name_name_decl,type,
cp_name_name:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(input_decl,type,
input: name > name > pi > pi ).
thf(par_decl,type,
par: pi > pi > pi ).
thf(res_decl,type,
res: name > pi > pi ).
thf(name_prm_name_decl,type,
name_prm_name: ( list @ ( product_prod @ name @ name ) ) > name > name ).
thf(swap_name_decl,type,
swap_name: ( product_prod @ name @ name ) > name > name ).
thf(subs_decl,type,
subs: pi > name > name > pi ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(late_OutputR_decl,type,
late_OutputR: name > name > late_freeRes ).
thf(late_TauR_decl,type,
late_TauR: late_freeRes ).
thf(late_BoundR_decl,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(late_FreeR_decl,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(late_r347633188eR_Rep_decl,type,
late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).
thf(late_BoundOutputS_decl,type,
late_BoundOutputS: name > late_subject ).
thf(late_InputS_decl,type,
late_InputS: name > late_subject ).
thf(late_transitions_decl,type,
late_transitions: pi > late_residual > $o ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(product_lists_decl,type,
product_lists:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(abs_fun_decl,type,
abs_fun:
!>[TA: $tType,TB: $tType] : ( TB > TA > TB > ( noption @ TA ) ) ).
thf(fresh_decl,type,
fresh:
!>[TA: $tType,TB: $tType] : ( TB > TA > $o ) ).
thf(perm_decl,type,
perm:
!>[TA: $tType,TB: $tType] : ( ( list @ ( product_prod @ TB @ TB ) ) > TA > TA ) ).
thf(supports_decl,type,
supports:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > TA > $o ) ).
thf(swap_decl,type,
swap:
!>[TA: $tType] : ( ( product_prod @ TA @ TA ) > TA > TA ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_rec_prod_decl,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(eqvt_decl,type,
eqvt:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(strong2129052853vative_decl,type,
strong2129052853vative: pi > pi > late_subject > name > ( set @ ( product_prod @ pi @ pi ) ) > $o ).
thf(strong743114133lation_decl,type,
strong743114133lation: pi > ( set @ ( product_prod @ pi @ pi ) ) > pi > $o ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_decl,type,
p: pi ).
thf(p2_decl,type,
p2: pi ).
thf(pxQ_decl,type,
pxQ: pi ).
thf(q_decl,type,
q: pi ).
thf(q2_decl,type,
q2: pi ).
thf(q_a_decl,type,
q_a: pi ).
thf(rel_decl,type,
rel: set @ ( product_prod @ pi @ pi ) ).
thf(alpha_decl,type,
alpha: late_freeRes ).
thf(aa_decl,type,
aa: name ).
thf(b_decl,type,
b: name ).
thf(x_decl,type,
x: name ).
thf(y_decl,type,
y: name ).
thf(z_decl,type,
z: name ).
thf(298,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_135_prod__induct6) ).
thf(1454,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)],[298]) ).
thf(22,axiom,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_subject_Oexhaust) ).
thf(347,plain,
! [A: late_subject] :
( ! [B: name] :
( A
!= ( late_InputS @ B ) )
=> ~ ! [B: name] :
( A
!= ( late_BoundOutputS @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(191,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_106_freshBoundDerivative_I1_J) ).
thf(893,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)],[191]) ).
thf(276,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA ),B: $o,C: $o] :
( ( perm @ TA @ $o @ A
@ ( B
& C ) )
= ( ( perm @ TA @ $o @ A @ B )
& ( perm @ TA @ $o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_conj__eqvt) ).
thf(1315,plain,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA ),B: $o,C: $o] :
( ( perm @ TA @ $o @ A
@ ( B
& C ) )
= ( ( perm @ TA @ $o @ A @ B )
& ( perm @ TA @ $o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(74,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_101_transitions_OResB) ).
thf(468,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)],[74]) ).
thf(238,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_230_transitions_OComm1) ).
thf(1110,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)],[238]) ).
thf(154,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: TA,C: set @ TA] :
( ( perm @ name @ $o @ A @ ( member @ TA @ B @ C ) )
= ( member @ TA @ ( perm @ name @ TA @ A @ B ) @ ( perm @ name @ ( set @ TA ) @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_in__eqvt) ).
thf(762,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: TA,C: set @ TA] :
( ( perm @ name @ $o @ A @ ( member @ TA @ B @ C ) )
= ( member @ TA @ ( perm @ name @ TA @ A @ B ) @ ( perm @ name @ ( set @ TA ) @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(289,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_min__list_Oinduct) ).
thf(1406,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(131,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_51_freeRes_Ostrong__inducts) ).
thf(683,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)],[131]) ).
thf(220,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_127_prod__cases3) ).
thf(994,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)],[220]) ).
thf(37,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(379,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(272,axiom,
fresh @ name @ pi @ y @ ( res @ x @ q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_cClose1_Ohyps_I4_J) ).
thf(1305,plain,
fresh @ name @ pi @ y @ ( res @ x @ q ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(181,axiom,
! [A: list @ ( product_prod @ name @ name ),B: name] :
( ( perm @ name @ late_subject @ A @ ( late_InputS @ B ) )
= ( late_InputS @ ( perm @ name @ name @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_subject_Operm_I1_J) ).
thf(861,plain,
! [A: list @ ( product_prod @ name @ name ),B: name] :
( ( perm @ name @ late_subject @ A @ ( late_InputS @ B ) )
= ( late_InputS @ ( perm @ name @ name @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(258,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_194_Par2F) ).
thf(1173,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)],[258]) ).
thf(144,axiom,
! [A: name] :
( ( name_prm_name @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_name__prm__name_Osimps_I1_J) ).
thf(730,plain,
! [A: name] :
( ( name_prm_name @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(267,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_209_resInputBoundOutputTrans) ).
thf(1290,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)],[267]) ).
thf(185,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_52_freeRes_Ostrong__induct_H) ).
thf(873,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)],[185]) ).
thf(68,axiom,
! [A: name,B: pi,C: name,D: pi] :
( ( fresh @ name @ pi @ A @ B )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ A @ ( res @ C @ ( par @ B @ D ) ) ) @ ( res @ C @ ( par @ B @ ( res @ A @ D ) ) ) ) @ rel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_ScopeExt) ).
thf(449,plain,
! [A: name,B: pi,C: name,D: pi] :
( ( fresh @ name @ pi @ A @ B )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ A @ ( res @ C @ ( par @ B @ D ) ) ) @ ( res @ C @ ( par @ B @ ( res @ A @ D ) ) ) ) @ rel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(232,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_207_inputBoundOutputTrans) ).
thf(1078,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)],[232]) ).
thf(41,axiom,
alpha = late_TauR,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_cClose1_Ohyps_I14_J) ).
thf(385,plain,
alpha = late_TauR,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(40,axiom,
cp_name_name @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Agent_Ocp__name__name_6) ).
thf(384,plain,
cp_name_name @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(247,axiom,
! [A: list @ ( product_prod @ name @ name )] :
( ( perm @ name @ late_freeRes @ A @ late_TauR )
= late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_freeRes_Operm_I2_J) ).
thf(1137,plain,
! [A: list @ ( product_prod @ name @ name )] :
( ( perm @ name @ late_freeRes @ A @ late_TauR )
= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(95,axiom,
! [A: name,B: pi,C: late_subject,D: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( late_BoundR @ C @ D @ B )
= ( late_BoundR @ C @ A @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ D @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_alphaBoundResidual) ).
thf(533,plain,
! [A: name,B: pi,C: late_subject,D: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( late_BoundR @ C @ D @ B )
= ( late_BoundR @ C @ A @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ D @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(255,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( ( eqvt @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: product_prod @ TA @ TA,C: list @ ( product_prod @ name @ name )] :
( ( member @ ( product_prod @ TA @ TA ) @ B @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( perm @ name @ ( product_prod @ TA @ TA ) @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_eqvt__def) ).
thf(1164,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( ( eqvt @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: product_prod @ TA @ TA,C: list @ ( product_prod @ name @ name )] :
( ( member @ ( product_prod @ TA @ TA ) @ B @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( perm @ name @ ( product_prod @ TA @ TA ) @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: TA > TB,C: TA] :
( ( perm @ name @ TB @ A @ ( B @ C ) )
= ( perm @ name @ ( TA > TB ) @ A @ B @ ( perm @ name @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_perm__app) ).
thf(472,plain,
! [TA: $tType,TB: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: TA > TB,C: TA] :
( ( perm @ name @ TB @ A @ ( B @ C ) )
= ( perm @ name @ ( TA > TB ) @ A @ B @ ( perm @ name @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(168,axiom,
! [TA: $tType,TB: $tType,A: list @ ( product_prod @ TB @ TB ),B: $o,C: TA,D: TA] :
( ( ( perm @ TB @ $o @ A @ B )
=> ( ( perm @ TB @ TA @ A @ ( if @ TA @ B @ C @ D ) )
= ( perm @ TB @ TA @ A @ C ) ) )
& ( ~ ( perm @ TB @ $o @ A @ B )
=> ( ( perm @ TB @ TA @ A @ ( if @ TA @ B @ C @ D ) )
= ( perm @ TB @ TA @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_if__eqvt) ).
thf(814,plain,
! [TA: $tType,TB: $tType,A: list @ ( product_prod @ TB @ TB ),B: $o,C: TA,D: TA] :
( ( ( perm @ TB @ $o @ A @ B )
=> ( ( perm @ TB @ TA @ A @ ( if @ TA @ B @ C @ D ) )
= ( perm @ TB @ TA @ A @ C ) ) )
& ( ~ ( perm @ TB @ $o @ A @ B )
=> ( ( perm @ TB @ TA @ A @ ( if @ TA @ B @ C @ D ) )
= ( perm @ TB @ TA @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(135,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: TA,C: name] :
( ( fresh @ name @ TA @ A @ B )
=> ( ( fresh @ name @ TA @ C @ B )
=> ( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_name__fresh__fresh) ).
thf(698,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: TA,C: name] :
( ( fresh @ name @ TA @ A @ B )
=> ( ( fresh @ name @ TA @ C @ B )
=> ( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(149,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: product_prod @ ( TA > TB ) @ ( list @ TA )] :
( ! [B: TA > TB,C: TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [B: TA > TB,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ~ ! [B: TA > TB] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_arg__min__list_Ocases) ).
thf(747,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: product_prod @ ( TA > TB ) @ ( list @ TA )] :
( ! [B: TA > TB,C: TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [B: TA > TB,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
=> ~ ! [B: TA > TB] :
( A
!= ( product_Pair @ ( TA > TB ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(299,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] :
~ ( perm @ TA @ $o @ A @ $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_false__eqvt) ).
thf(1458,plain,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] :
~ ( perm @ TA @ $o @ A @ $false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(125,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_124_surj__pair) ).
thf(670,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)],[125]) ).
thf(263,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_list__induct2_H) ).
thf(1222,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(201,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_130_prod__cases6) ).
thf(930,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)],[201]) ).
thf(243,axiom,
! [TA: $tType,TB: $tType] :
( ( supports @ TA @ TB )
= ( ^ [A: set @ TA,B: TB] :
! [C: TA,D: TA] :
( ( ~ ( member @ TA @ C @ A )
& ~ ( member @ TA @ D @ A ) )
=> ( ( perm @ TA @ TB @ ( cons @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ ( nil @ ( product_prod @ TA @ TA ) ) ) @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_supports__def) ).
thf(1127,plain,
! [TA: $tType,TB: $tType] :
( ( supports @ TA @ TB )
= ( ^ [A: set @ TA,B: TB] :
! [C: TA,D: TA] :
( ( ~ ( member @ TA @ C @ A )
& ~ ( member @ TA @ D @ A ) )
=> ( ( perm @ TA @ TB @ ( cons @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ ( nil @ ( product_prod @ TA @ TA ) ) ) @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(283,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_175_pi_Ofresh_I8_J) ).
thf(1391,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)],[283]) ).
thf(160,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_229_transitions_OComm2) ).
thf(782,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)],[160]) ).
thf(139,axiom,
! [A: product_prod @ name @ name,B: list @ ( product_prod @ name @ name ),C: name] :
( ( name_prm_name @ ( cons @ ( product_prod @ name @ name ) @ A @ B ) @ C )
= ( swap_name @ A @ ( name_prm_name @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_name__prm__name_Osimps_I2_J) ).
thf(709,plain,
! [A: product_prod @ name @ name,B: list @ ( product_prod @ name @ name ),C: name] :
( ( name_prm_name @ ( cons @ ( product_prod @ name @ name ) @ A @ B ) @ C )
= ( swap_name @ A @ ( name_prm_name @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(212,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_list_Oexhaust) ).
thf(973,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(281,axiom,
late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_cClose1_Ohyps_I1_J) ).
thf(1386,plain,
late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(62,axiom,
fresh @ name @ pi @ z @ ( res @ x @ q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_cClose1_Ohyps_I9_J) ).
thf(436,plain,
fresh @ name @ pi @ z @ ( res @ x @ q ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(9,axiom,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ( cp_name_name @ ( noption @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nominal_Onoption___Agent_Ocp__name__name_18) ).
thf(320,plain,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ( cp_name_name @ ( noption @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(102,axiom,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_cClose1_Ohyps_I6_J) ).
thf(565,plain,
y != z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(266,axiom,
! [A: pi,B: late_residual,C: list @ ( product_prod @ name @ name )] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( perm @ name @ pi @ C @ A ) @ ( perm @ name @ late_residual @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_eqvt) ).
thf(1287,plain,
! [A: pi,B: late_residual,C: list @ ( product_prod @ name @ name )] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( perm @ name @ pi @ C @ A ) @ ( perm @ name @ late_residual @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(270,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_84_freeRes_Ofresh_I1_J) ).
thf(1298,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)],[270]) ).
thf(196,axiom,
fresh @ name @ pi @ z @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_cClose1_Ohyps_I8_J) ).
thf(917,plain,
fresh @ name @ pi @ z @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(203,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_72_old_Oprod_Oinject) ).
thf(934,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)],[203]) ).
thf(301,axiom,
! [A: list @ ( product_prod @ name @ name ),B: name,C: name] :
( ( perm @ name @ late_freeRes @ A @ ( late_OutputR @ B @ C ) )
= ( late_OutputR @ ( perm @ name @ name @ A @ B ) @ ( perm @ name @ name @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_freeRes_Operm_I1_J) ).
thf(1462,plain,
! [A: list @ ( product_prod @ name @ name ),B: name,C: name] :
( ( perm @ name @ late_freeRes @ A @ ( late_OutputR @ B @ C ) )
= ( late_OutputR @ ( perm @ name @ name @ A @ B ) @ ( perm @ name @ name @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: list @ TA] :
( ( fresh @ TB @ ( list @ TA ) @ A @ ( cons @ TA @ B @ C ) )
= ( ( fresh @ TB @ TA @ A @ B )
& ( fresh @ TB @ ( list @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_fresh__list__cons) ).
thf(638,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: list @ TA] :
( ( fresh @ TB @ ( list @ TA ) @ A @ ( cons @ TA @ B @ C ) )
= ( ( fresh @ TB @ TA @ A @ B )
& ( fresh @ TB @ ( list @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(184,axiom,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_product__lists_Osimps_I1_J) ).
thf(870,plain,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(211,axiom,
! [A: name,B: pi,C: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= ( subs @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_injPermSubst) ).
thf(969,plain,
! [A: name,B: pi,C: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= ( subs @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(8,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_215_simps_I9_J) ).
thf(316,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)],[8]) ).
thf(285,axiom,
fs_name @ pi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Agent_Opi___Agent_Ofs__name) ).
thf(1398,plain,
fs_name @ pi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType] :
( ( ( pt_name @ TB )
& ( pt_name @ TA ) )
=> ( pt_name @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Agent_Opt__name) ).
thf(416,plain,
! [TA: $tType,TB: $tType] :
( ( ( pt_name @ TB )
& ( pt_name @ TA ) )
=> ( pt_name @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(76,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: set @ ( product_prod @ pi @ pi ),F: list @ ( product_prod @ name @ name )] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( eqvt @ pi @ E )
=> ( strong2129052853vative @ ( perm @ name @ pi @ F @ A ) @ ( perm @ name @ pi @ F @ B ) @ ( perm @ name @ late_subject @ F @ C ) @ ( perm @ name @ name @ F @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_derivativeEqvtI) ).
thf(475,plain,
! [A: pi,B: pi,C: late_subject,D: name,E: set @ ( product_prod @ pi @ pi ),F: list @ ( product_prod @ name @ name )] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( eqvt @ pi @ E )
=> ( strong2129052853vative @ ( perm @ name @ pi @ F @ A ) @ ( perm @ name @ pi @ F @ B ) @ ( perm @ name @ late_subject @ F @ C ) @ ( perm @ name @ name @ F @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(152,axiom,
! [A: name,B: name] :
( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_swap__simps_I1_J) ).
thf(756,plain,
! [A: name,B: name] :
( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(162,axiom,
! [A: name,B: pi] : ( fresh @ name @ pi @ A @ ( res @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_freshRes) ).
thf(789,plain,
! [A: name,B: pi] : ( fresh @ name @ pi @ A @ ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(107,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_198_inputIneqTrans) ).
thf(591,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)],[107]) ).
thf(66,axiom,
! [A: list @ ( product_prod @ name @ name ),B: late_subject,C: name,D: pi] :
( ( perm @ name @ late_residual @ A @ ( late_BoundR @ B @ C @ D ) )
= ( late_BoundR @ ( perm @ name @ late_subject @ A @ B ) @ ( perm @ name @ name @ A @ C ) @ ( perm @ name @ pi @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_residual_Operm_I1_J) ).
thf(443,plain,
! [A: list @ ( product_prod @ name @ name ),B: late_subject,C: name,D: pi] :
( ( perm @ name @ late_residual @ A @ ( late_BoundR @ B @ C @ D ) )
= ( late_BoundR @ ( perm @ name @ late_subject @ A @ B ) @ ( perm @ name @ name @ A @ C ) @ ( perm @ name @ pi @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(117,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_200_Late__Semantics_OPar1B) ).
thf(646,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)],[117]) ).
thf(24,axiom,
pt_name @ late_subject_Rep,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_35) ).
thf(353,plain,
pt_name @ late_subject_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(78,axiom,
b != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_cOpen_Ohyps_I2_J) ).
thf(480,plain,
b != x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(246,axiom,
fresh @ name @ pi @ z @ q,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__092_060open_062z_A_092_060sharp_062_AQ_092_060close_062) ).
thf(1136,plain,
fresh @ name @ pi @ z @ q,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(173,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_20_Late__Semantics1_OfreeRes_Oinject) ).
thf(834,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)],[173]) ).
thf(252,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_243_simCases) ).
thf(1151,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)],[252]) ).
thf(204,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_list_Odistinct_I1_J) ).
thf(937,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(261,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_222_substRes2) ).
thf(1215,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)],[261]) ).
thf(241,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).
thf(1119,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(284,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_132_prod__induct3) ).
thf(1394,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)],[284]) ).
thf(46,axiom,
! [TA: $tType] :
( ( fs_name @ TA )
=> ( fs_name @ ( list @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_List_Olist___Agent_Ofs__name_12) ).
thf(396,plain,
! [TA: $tType] :
( ( fs_name @ TA )
=> ( fs_name @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(53,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Late__Semantics1_Osubject_Odistinct_I1_J) ).
thf(411,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(6,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_183_pi_Oinject_I7_J) ).
thf(312,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)],[6]) ).
thf(69,axiom,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_sorted__wrt_Ocases) ).
thf(452,plain,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(38,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(380,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(129,axiom,
! [A: late_residual_Rep] :
( ( perm @ name @ late_residual_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_residual__perm__empty) ).
thf(678,plain,
! [A: late_residual_Rep] :
( ( perm @ name @ late_residual_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(121,axiom,
late_transitions @ ( res @ x @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_cClose1_Ohyps_I2_J) ).
thf(661,plain,
late_transitions @ ( res @ x @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(199,axiom,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_freeRes_Oexhaust) ).
thf(925,plain,
! [A: late_freeRes] :
( ! [B: name,C: name] :
( A
!= ( late_OutputR @ B @ C ) )
=> ( A = late_TauR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(273,axiom,
! [A: list @ ( product_prod @ name @ name ),B: name,C: pi] :
( ( perm @ name @ pi @ A @ ( res @ B @ C ) )
= ( res @ ( perm @ name @ name @ A @ B ) @ ( perm @ name @ pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_pi_Operm_I9_J) ).
thf(1306,plain,
! [A: list @ ( product_prod @ name @ name ),B: name,C: pi] :
( ( perm @ name @ pi @ A @ ( res @ B @ C ) )
= ( res @ ( perm @ name @ name @ A @ B ) @ ( perm @ name @ pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(254,axiom,
fresh @ name @ pi @ z @ p2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_cClose1_Ohyps_I11_J) ).
thf(1163,plain,
fresh @ name @ pi @ z @ p2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(206,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_126_Pair__inject) ).
thf(942,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)],[206]) ).
thf(65,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_136_prod__induct7) ).
thf(439,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)],[65]) ).
thf(98,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: list @ ( product_prod @ name @ name ),C: TA] :
( ( fresh @ name @ ( list @ ( product_prod @ name @ name ) ) @ A @ B )
=> ( ( fresh @ name @ TA @ A @ C )
=> ( fresh @ name @ TA @ A @ ( perm @ name @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_fresh__perm__app) ).
thf(546,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: list @ ( product_prod @ name @ name ),C: TA] :
( ( fresh @ name @ ( list @ ( product_prod @ name @ name ) ) @ A @ B )
=> ( ( fresh @ name @ TA @ A @ C )
=> ( fresh @ name @ TA @ A @ ( perm @ name @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(164,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_list__nonempty__induct) ).
thf(793,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(17,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_192_subject_Ostrong__induct_H) ).
thf(334,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)],[17]) ).
thf(282,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_map__tailrec__rev_Oinduct) ).
thf(1387,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(159,axiom,
! [A: name,B: pi,C: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( res @ C @ B )
= ( res @ A @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_alphaRes) ).
thf(778,plain,
! [A: name,B: pi,C: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( res @ C @ B )
= ( res @ A @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1,conjecture,
late_transitions @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ z @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ q ) @ ( perm @ name @ late_residual @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ z @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( late_transitions @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ z @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ q ) @ ( perm @ name @ late_residual @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ z @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(302,plain,
~ ( late_transitions @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ z @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ q ) @ ( perm @ name @ late_residual @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ z @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(242,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_138_old_Oprod_Oinducts) ).
thf(1123,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)],[242]) ).
thf(169,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(820,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)],[169]) ).
thf(44,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(392,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(60,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: TA,C: name] :
( ( fresh @ name @ TA @ A @ B )
=> ( ( fresh @ name @ TA @ C @ B )
=> ( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_perm__fresh__fresh) ).
thf(429,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: TA,C: name] :
( ( fresh @ name @ TA @ A @ B )
=> ( ( fresh @ name @ TA @ C @ B )
=> ( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(292,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_remdups__adj_Oinduct) ).
thf(1423,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(73,axiom,
fresh @ name @ pi @ x @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_assms_I1_J) ).
thf(467,plain,
fresh @ name @ pi @ x @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(29,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( pt_name @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Agent_Opt__name_3) ).
thf(361,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( pt_name @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(187,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_not__Cons__self2) ).
thf(879,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(178,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_254_pi_Ofresh_I4_J) ).
thf(852,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)],[178]) ).
thf(15,axiom,
pt_name @ pi_Rep,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Agent_Opi__Rep___Agent_Opt__name_17) ).
thf(329,plain,
pt_name @ pi_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(92,axiom,
! [A: name] :
( ( perm @ name @ name @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_name__calc_I2_J) ).
thf(522,plain,
! [A: name] :
( ( perm @ name @ name @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(253,axiom,
! [TA: $tType,A: ( list @ TA ) > $o] :
( ! [B: list @ TA] : ( A @ B )
=> ( A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_allE__Nil) ).
thf(1159,plain,
! [TA: $tType,A: ( list @ TA ) > $o] :
( ! [B: list @ TA] : ( A @ B )
=> ( A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(82,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: TA,C: name,D: TA,E: name] :
( ( ( abs_fun @ name @ TA @ A @ B )
= ( abs_fun @ name @ TA @ C @ D ) )
=> ( ( E != A )
=> ( ( E != C )
=> ( ( fresh @ name @ TA @ E @ B )
=> ( ( fresh @ name @ TA @ E @ D )
=> ( B
= ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ E ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C @ E ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ D ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_alpha__fresh_H) ).
thf(493,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: TA,C: name,D: TA,E: name] :
( ( ( abs_fun @ name @ TA @ A @ B )
= ( abs_fun @ name @ TA @ C @ D ) )
=> ( ( E != A )
=> ( ( E != C )
=> ( ( fresh @ name @ TA @ E @ B )
=> ( ( fresh @ name @ TA @ E @ D )
=> ( B
= ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ E ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C @ E ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ D ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(100,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_min__list_Ocases) ).
thf(551,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cp_name_name @ TB )
& ( cp_name_name @ TA ) )
=> ( cp_name_name @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Agent_Ocp__name__name) ).
thf(324,plain,
! [TA: $tType,TB: $tType] :
( ( ( cp_name_name @ TB )
& ( cp_name_name @ TA ) )
=> ( cp_name_name @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(226,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_204_transitions_OPar1B) ).
thf(1012,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)],[226]) ).
thf(237,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_185_transitions_OInput) ).
thf(1106,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)],[237]) ).
thf(269,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: list @ ( product_prod @ name @ name )] :
( ( eqvt @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( perm @ name @ TA @ D @ B ) @ ( perm @ name @ TA @ D @ C ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_eqvtRelI) ).
thf(1296,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: list @ ( product_prod @ name @ name )] :
( ( eqvt @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( perm @ name @ TA @ D @ B ) @ ( perm @ name @ TA @ D @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(123,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_22) ).
thf(665,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)],[123]) ).
thf(287,axiom,
fresh @ name @ name @ z @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_cClose1_Ohyps_I13_J) ).
thf(1402,plain,
fresh @ name @ name @ z @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(207,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_strict__sorted_Oinduct) ).
thf(948,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(142,axiom,
( ( swap @ name )
= swap_name ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Agent_Oswap__name__def) ).
thf(725,plain,
( ( swap @ name )
= swap_name ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(215,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_splice_Oinduct) ).
thf(980,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(224,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_195_Par1F) ).
thf(1006,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)],[224]) ).
thf(43,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_pi_Odistinct_I85_J) ).
thf(388,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( par @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(27,axiom,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_subst__identity) ).
thf(356,plain,
! [A: pi,B: name] :
( ( subs @ A @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(57,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_201_Late__Semantics_OPar2B) ).
thf(420,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)],[57]) ).
thf(84,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA ),B: $o,C: $o] :
( ( perm @ TA @ $o @ A
@ ( B
| C ) )
= ( ( perm @ TA @ $o @ A @ B )
| ( perm @ TA @ $o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_disj__eqvt) ).
thf(499,plain,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA ),B: $o,C: $o] :
( ( perm @ TA @ $o @ A
@ ( B
| C ) )
= ( ( perm @ TA @ $o @ A @ B )
| ( perm @ TA @ $o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(189,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: TA,C: TA] :
( ( ( perm @ name @ TA @ A @ B )
= ( perm @ name @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_perm__bij) ).
thf(884,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: TA,C: TA] :
( ( ( perm @ name @ TA @ A @ B )
= ( perm @ name @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(19,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_193_subject_Ostrong__inducts) ).
thf(339,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)],[19]) ).
thf(202,axiom,
pt_name @ pi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Agent_Opi___Agent_Opt__name_5) ).
thf(933,plain,
pt_name @ pi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(101,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_248_simCasesCont) ).
thf(554,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)],[101]) ).
thf(96,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C )
= ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_name__swap) ).
thf(537,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C )
= ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
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_125_prod__cases) ).
thf(642,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(81,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_221_Agent_OsubstRes3) ).
thf(489,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)],[81]) ).
thf(138,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_57_freshFreeDerivative_I2_J) ).
thf(706,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)],[138]) ).
thf(291,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_108_residual_Odistinct_I1_J) ).
thf(1419,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)],[291]) ).
thf(174,axiom,
! [A: pi_Rep] :
( ( perm @ name @ pi_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_pi__perm__empty) ).
thf(837,plain,
! [A: pi_Rep] :
( ( perm @ name @ pi_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(221,axiom,
! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
( ( ( late_FreeR @ A @ B )
= ( late_FreeR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_residual_Oinject_I2_J) ).
thf(997,plain,
! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
( ( ( late_FreeR @ A @ B )
= ( late_FreeR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(136,axiom,
! [A: list @ ( product_prod @ name @ name ),B: pi,C: pi] :
( ( perm @ name @ pi @ A @ ( par @ B @ C ) )
= ( par @ ( perm @ name @ pi @ A @ B ) @ ( perm @ name @ pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_pi_Operm_I8_J) ).
thf(701,plain,
! [A: list @ ( product_prod @ name @ name ),B: pi,C: pi] :
( ( perm @ name @ pi @ A @ ( par @ B @ C ) )
= ( par @ ( perm @ name @ pi @ A @ B ) @ ( perm @ name @ pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(297,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ ( product_prod @ TB @ TB ),B: TC,C: TA] :
( ( perm @ TB @ ( product_prod @ TC @ TA ) @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( product_Pair @ TC @ TA @ ( perm @ TB @ TC @ A @ B ) @ ( perm @ TB @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_perm__prod_Osimps) ).
thf(1451,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ ( product_prod @ TB @ TB ),B: TC,C: TA] :
( ( perm @ TB @ ( product_prod @ TC @ TA ) @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( product_Pair @ TC @ TA @ ( perm @ TB @ TC @ A @ B ) @ ( perm @ TB @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(71,axiom,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi,G: late_subject > name > pi > $o] :
( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
=> ( ( E != A )
=> ( ( E != B )
=> ( ( fresh @ name @ pi @ E @ C )
=> ( ( ( D
= ( late_InputS @ A ) )
=> ( ( F
= ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B @ E ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) )
=> ( G @ ( late_InputS @ A ) @ E @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B @ E ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) ) ) )
=> ( G @ D @ E @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_inputCases) ).
thf(457,plain,
! [A: name,B: name,C: pi,D: late_subject,E: name,F: pi,G: late_subject > name > pi > $o] :
( ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ D @ E @ F ) )
=> ( ( E != A )
=> ( ( E != B )
=> ( ( fresh @ name @ pi @ E @ C )
=> ( ( ( D
= ( late_InputS @ A ) )
=> ( ( F
= ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B @ E ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) )
=> ( G @ ( late_InputS @ A ) @ E @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B @ E ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) ) ) )
=> ( G @ D @ E @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(279,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_110_resCases_H) ).
thf(1324,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)],[279]) ).
thf(239,axiom,
( ( fresh @ name @ name )
= ( != @ name ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_name__fresh) ).
thf(1114,plain,
( ( fresh @ name @ name )
= ( ^ [A: name,B: name] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(216,axiom,
! [A: list @ ( product_prod @ name @ name ),B: name,C: name] :
( ( ( perm @ name @ name @ A @ B )
= ( perm @ name @ name @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_name__bij) ).
thf(984,plain,
! [A: list @ ( product_prod @ name @ name ),B: name,C: name] :
( ( ( perm @ name @ name @ A @ B )
= ( perm @ name @ name @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(194,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_successively_Oinduct) ).
thf(911,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(87,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: set @ ( product_prod @ TA @ TA ),B: list @ ( product_prod @ name @ name ),C: TA,D: TA] :
( ( eqvt @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( perm @ name @ TA @ B @ C ) @ ( perm @ name @ TA @ B @ D ) ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_eqvtRelE) ).
thf(508,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: set @ ( product_prod @ TA @ TA ),B: list @ ( product_prod @ name @ name ),C: TA,D: TA] :
( ( eqvt @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( perm @ name @ TA @ B @ C ) @ ( perm @ name @ TA @ B @ D ) ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(198,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_217_substTrans) ).
thf(921,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)],[198]) ).
thf(120,axiom,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Late__Semantics_OfreeRes_Odistinct_I1_J) ).
thf(657,plain,
! [A: name,B: name] :
( ( late_OutputR @ A @ B )
!= late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(155,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_perm__swap_I2_J) ).
thf(765,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(257,axiom,
! [A: name,B: name,C: list @ ( product_prod @ name @ name ),D: name] :
( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ C ) @ D )
= ( swap @ name @ ( product_Pair @ name @ name @ A @ B ) @ ( perm @ name @ name @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_name__calc_I1_J) ).
thf(1170,plain,
! [A: name,B: name,C: list @ ( product_prod @ name @ name ),D: name] :
( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ C ) @ D )
= ( swap @ name @ ( product_Pair @ name @ name @ A @ B ) @ ( perm @ name @ name @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(47,axiom,
pt_name @ late_residual_Rep,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_37) ).
thf(398,plain,
pt_name @ late_residual_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(256,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_83_residual_Ofresh_I2_J) ).
thf(1167,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)],[256]) ).
thf(122,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: TA,C: name,D: TA] :
( ( ( abs_fun @ name @ TA @ A @ B )
= ( abs_fun @ name @ TA @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A != C )
& ( B
= ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ D ) )
& ( fresh @ name @ TA @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_name__abs__eq) ).
thf(662,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: TA,C: name,D: TA] :
( ( ( abs_fun @ name @ TA @ A @ B )
= ( abs_fun @ name @ TA @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A != C )
& ( B
= ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ D ) )
& ( fresh @ name @ TA @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(21,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(343,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(277,axiom,
! [TA: $tType] :
( ( perm @ TA @ $o )
= ( ^ [A: list @ ( product_prod @ TA @ TA ),B: $o] : B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_perm__bool__def) ).
thf(1318,plain,
! [TA: $tType] :
( ( perm @ TA @ $o )
= ( ^ [A: list @ ( product_prod @ TA @ TA ),B: $o] : B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cp_name_name @ TB )
& ( cp_name_name @ TA ) )
=> ( cp_name_name @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Agent_Ocp__name__name_20) ).
thf(750,plain,
! [TA: $tType,TB: $tType] :
( ( ( cp_name_name @ TB )
& ( cp_name_name @ TA ) )
=> ( cp_name_name @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(89,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_218_forget) ).
thf(513,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)],[89]) ).
thf(236,axiom,
! [TA: $tType,TB: $tType,A: list @ ( product_prod @ TB @ TB ),B: TA,C: list @ TA] :
( ( perm @ TB @ ( list @ TA ) @ A @ ( cons @ TA @ B @ C ) )
= ( cons @ TA @ ( perm @ TB @ TA @ A @ B ) @ ( perm @ TB @ ( list @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_cons__eqvt) ).
thf(1103,plain,
! [TA: $tType,TB: $tType,A: list @ ( product_prod @ TB @ TB ),B: TA,C: list @ TA] :
( ( perm @ TB @ ( list @ TA ) @ A @ ( cons @ TA @ B @ C ) )
= ( cons @ TA @ ( perm @ TB @ TA @ A @ B ) @ ( perm @ TB @ ( list @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(271,axiom,
! [A: name,B: pi,C: name,D: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( subs @ B @ C @ D )
= ( subs @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B ) @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_renaming) ).
thf(1301,plain,
! [A: name,B: pi,C: name,D: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( subs @ B @ C @ D )
= ( subs @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(262,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: TA] :
( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_name__id) ).
thf(1219,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: TA] :
( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(170,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_70_fresh__prod) ).
thf(824,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)],[170]) ).
thf(35,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Late__Semantics_Osubject_Oinject_I2_J) ).
thf(375,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(145,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_sorted__wrt_Oinduct) ).
thf(733,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(58,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_123_freshFreeDerivative_I1_J) ).
thf(423,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)],[58]) ).
thf(49,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_182_pi_Odistinct_I55_J) ).
thf(402,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)],[49]) ).
thf(157,axiom,
! [A: list @ ( product_prod @ name @ name ),B: pi,C: name,D: name] :
( ( perm @ name @ pi @ A @ ( subs @ B @ C @ D ) )
= ( subs @ ( perm @ name @ pi @ A @ B ) @ ( perm @ name @ name @ A @ C ) @ ( perm @ name @ name @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_eqvt__subs) ).
thf(772,plain,
! [A: list @ ( product_prod @ name @ name ),B: pi,C: name,D: name] :
( ( perm @ name @ pi @ A @ ( subs @ B @ C @ D ) )
= ( subs @ ( perm @ name @ pi @ A @ B ) @ ( perm @ name @ name @ A @ C ) @ ( perm @ name @ name @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(186,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_219_fresh__fact1) ).
thf(875,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)],[186]) ).
thf(264,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_199_inputFreeTrans) ).
thf(1226,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)],[264]) ).
thf(208,axiom,
pt_name @ late_residual,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual___Agent_Opt__name_30) ).
thf(958,plain,
pt_name @ late_residual,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(288,axiom,
! [A: name,B: name] :
( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_swap__simps_I2_J) ).
thf(1403,plain,
! [A: name,B: name] :
( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(115,axiom,
late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_Free_Ohyps) ).
thf(641,plain,
late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(104,axiom,
y != aa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_cClose1_Ohyps_I5_J) ).
thf(572,plain,
y != aa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(275,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_128_prod__cases4) ).
thf(1312,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)],[275]) ).
thf(72,axiom,
cp_name_name @ pi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Agent_Opi___Agent_Ocp__name__name_4) ).
thf(466,plain,
cp_name_name @ pi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(137,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] :
~ ( perm @ TA @ $o @ A @ $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_perm__boolE) ).
thf(704,plain,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] :
~ ( perm @ TA @ $o @ A @ $false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: $o,B: list @ ( product_prod @ TB @ TB ),C: TA,D: TA] :
( ( A
=> ( ( perm @ TB @ TA @ B @ ( if @ TA @ A @ C @ D ) )
= ( perm @ TB @ TA @ B @ C ) ) )
& ( ~ A
=> ( ( perm @ TB @ TA @ B @ ( if @ TA @ A @ C @ D ) )
= ( perm @ TB @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_abs__fun__if) ).
thf(540,plain,
! [TA: $tType,TB: $tType,A: $o,B: list @ ( product_prod @ TB @ TB ),C: TA,D: TA] :
( ( A
=> ( ( perm @ TB @ TA @ B @ ( if @ TA @ A @ C @ D ) )
= ( perm @ TB @ TA @ B @ C ) ) )
& ( ~ A
=> ( ( perm @ TB @ TA @ B @ ( if @ TA @ A @ C @ D ) )
= ( perm @ TB @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(214,axiom,
fresh @ name @ pi @ y @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_cClose1_Ohyps_I3_J) ).
thf(979,plain,
fresh @ name @ pi @ y @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(50,axiom,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Late__Semantics1_Osubject_Oinject_I1_J) ).
thf(406,plain,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(130,axiom,
( ( perm @ name @ name )
= name_prm_name ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Agent_Oname__prm__name__def) ).
thf(681,plain,
( ( perm @ name @ name )
= name_prm_name ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(218,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_137_old_Oprod_Oexhaust) ).
thf(990,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)],[218]) ).
thf(146,axiom,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: list @ ( product_prod @ name @ name ),C: TA] :
( ( perm @ name @ TA @ A @ ( perm @ name @ TA @ B @ C ) )
= ( perm @ name @ TA @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ A @ B ) @ ( perm @ name @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_cp__name__name1) ).
thf(737,plain,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: list @ ( product_prod @ name @ name ),C: TA] :
( ( perm @ name @ TA @ A @ ( perm @ name @ TA @ B @ C ) )
= ( perm @ name @ TA @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ A @ B ) @ ( perm @ name @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(118,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_231_transitions_OClose2) ).
thf(649,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)],[118]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(303,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(293,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: name,C: TA,D: name] :
( ( A != B )
=> ( ( fresh @ name @ TA @ B @ C )
=> ( ( fresh @ name @ TA @ A @ C )
=> ( fresh @ name @ TA @ A @ ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B @ D ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_fresh__aux) ).
thf(1439,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: name,C: TA,D: name] :
( ( A != B )
=> ( ( fresh @ name @ TA @ B @ C )
=> ( ( fresh @ name @ TA @ A @ C )
=> ( fresh @ name @ TA @ A @ ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ B @ D ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(11,axiom,
pt_name @ late_freeRes,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes___Agent_Opt__name_24) ).
thf(323,plain,
pt_name @ late_freeRes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(108,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi,D: pi] :
( ! [E: pi,F: pi,G: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ E @ F ) @ G ) @ ( par @ E @ ( par @ F @ G ) ) ) @ A )
=> ( ! [E: pi,F: pi,G: name] :
( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ E @ F ) @ A )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ G @ E ) @ ( res @ G @ F ) ) @ A ) )
=> ( ! [E: pi,F: pi,G: pi,H: name] :
( ( fresh @ name @ pi @ H @ E )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ H @ ( par @ ( par @ E @ F ) @ G ) ) @ ( par @ E @ ( res @ H @ ( par @ F @ G ) ) ) ) @ A ) )
=> ( ! [E: pi,F: pi,G: pi,H: name] :
( ( fresh @ name @ pi @ H @ G )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ H @ ( par @ E @ F ) ) @ G ) @ ( res @ H @ ( par @ E @ ( par @ F @ G ) ) ) ) @ A ) )
=> ( strong743114133lation @ ( par @ ( par @ B @ C ) @ D ) @ A @ ( par @ B @ ( par @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_parAssocLeft) ).
thf(594,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi,D: pi] :
( ! [E: pi,F: pi,G: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( par @ E @ F ) @ G ) @ ( par @ E @ ( par @ F @ G ) ) ) @ A )
=> ( ! [E: pi,F: pi,G: name] :
( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ E @ F ) @ A )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ G @ E ) @ ( res @ G @ F ) ) @ A ) )
=> ( ! [E: pi,F: pi,G: pi,H: name] :
( ( fresh @ name @ pi @ H @ E )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ H @ ( par @ ( par @ E @ F ) @ G ) ) @ ( par @ E @ ( res @ H @ ( par @ F @ G ) ) ) ) @ A ) )
=> ( ! [E: pi,F: pi,G: pi,H: name] :
( ( fresh @ name @ pi @ H @ G )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ ( res @ H @ ( par @ E @ F ) ) @ G ) @ ( res @ H @ ( par @ E @ ( par @ F @ G ) ) ) ) @ A ) )
=> ( strong743114133lation @ ( par @ ( par @ B @ C ) @ D ) @ A @ ( par @ B @ ( par @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(79,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_19_Late__Semantics_OfreeRes_Oinject) ).
thf(483,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)],[79]) ).
thf(210,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_121_residual_Ostrong__induct) ).
thf(964,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)],[210]) ).
thf(195,axiom,
! [TA: $tType,TB: $tType,A: TB] : ( fresh @ TB @ ( list @ TA ) @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_fresh__list__nil) ).
thf(915,plain,
! [TA: $tType,TB: $tType,A: TB] : ( fresh @ TB @ ( list @ TA ) @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(300,axiom,
aa = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062a_A_061_Ab_092_060close_062) ).
thf(1460,plain,
aa = b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(229,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_116_resCasesB_H) ).
thf(1022,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)],[229]) ).
thf(268,axiom,
z != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062z_A_092_060noteq_062_Ax_092_060close_062) ).
thf(1293,plain,
z != x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(280,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi] :
( ! [D: pi,E: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ D @ E ) @ ( par @ E @ D ) ) @ A )
=> ( ! [D: pi,E: pi,F: name] :
( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ D @ E ) @ A )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ F @ D ) @ ( res @ F @ E ) ) @ A ) )
=> ( strong743114133lation @ ( par @ B @ C ) @ A @ ( par @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_parSym) ).
thf(1381,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi] :
( ! [D: pi,E: pi] : ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( par @ D @ E ) @ ( par @ E @ D ) ) @ A )
=> ( ! [D: pi,E: pi,F: name] :
( ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ D @ E ) @ A )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ F @ D ) @ ( res @ F @ E ) ) @ A ) )
=> ( strong743114133lation @ ( par @ B @ C ) @ A @ ( par @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(16,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_187_pi_Odistinct_I57_J) ).
thf(330,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)],[16]) ).
thf(167,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_117_Open) ).
thf(811,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)],[167]) ).
thf(42,axiom,
cp_name_name @ late_subject,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_26) ).
thf(387,plain,
cp_name_name @ late_subject,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType,A: list @ ( product_prod @ TB @ TB )] :
( ( perm @ TB @ ( list @ TA ) @ A @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_nil__eqvt) ).
thf(858,plain,
! [TA: $tType,TB: $tType,A: list @ ( product_prod @ TB @ TB )] :
( ( perm @ TB @ ( list @ TA ) @ A @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(32,axiom,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ( cp_name_name @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Agent_Ocp__name__name_1) ).
thf(367,plain,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ( cp_name_name @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(177,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_list_OdiscI) ).
thf(848,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(91,axiom,
! [TA: $tType,A: $o,B: list @ ( product_prod @ TA @ TA )] :
( A
=> ( perm @ TA @ $o @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_perm__boolI) ).
thf(520,plain,
! [TA: $tType,A: $o,B: list @ ( product_prod @ TA @ TA )] :
( A
=> ( perm @ TA @ $o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(132,axiom,
! [A: late_subject_Rep] :
( ( perm @ name @ late_subject_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_subject__perm__empty) ).
thf(685,plain,
! [A: late_subject_Rep] :
( ( perm @ name @ late_subject_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(399,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(209,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_241_simE_I1_J) ).
thf(959,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)],[209]) ).
thf(295,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_remdups__adj_Ocases) ).
thf(1445,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(70,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] : ( perm @ TA @ $o @ A @ $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_true__eqvt) ).
thf(455,plain,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] : ( perm @ TA @ $o @ A @ $true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(227,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_list_Oinject) ).
thf(1015,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(259,axiom,
! [A: name,B: pi,C: late_subject,D: name,E: pi,F: late_subject > pi > $o] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ( D != A )
=> ( ( fresh @ name @ pi @ D @ B )
=> ( ! [G: name,H: pi] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ A ) @ H ) )
=> ( ( G != A )
=> ( ( C
= ( late_BoundOutputS @ G ) )
=> ( F @ ( late_BoundOutputS @ G ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ D @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ H ) ) ) ) )
=> ( ! [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
=> ( ( fresh @ name @ late_subject @ A @ C )
=> ( F @ C @ ( res @ A @ G ) ) ) )
=> ( F @ C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_resCasesB) ).
thf(1176,plain,
! [A: name,B: pi,C: late_subject,D: name,E: pi,F: late_subject > pi > $o] :
( ( late_transitions @ ( res @ A @ B ) @ ( late_BoundR @ C @ D @ E ) )
=> ( ( D != A )
=> ( ( fresh @ name @ pi @ D @ B )
=> ( ! [G: name,H: pi] :
( ( late_transitions @ B @ ( late_FreeR @ ( late_OutputR @ G @ A ) @ H ) )
=> ( ( G != A )
=> ( ( C
= ( late_BoundOutputS @ G ) )
=> ( F @ ( late_BoundOutputS @ G ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ D @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ H ) ) ) ) )
=> ( ! [G: pi] :
( ( late_transitions @ B @ ( late_BoundR @ C @ D @ G ) )
=> ( ( fresh @ name @ late_subject @ A @ C )
=> ( F @ C @ ( res @ A @ G ) ) ) )
=> ( F @ C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(306,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(222,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) )] :
( ! [B: TB > TA,C: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ C ) ) )
=> ~ ! [B: TB > TA,C: TB,D: list @ TB,E: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( cons @ TB @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_map__tailrec__rev_Ocases) ).
thf(1000,plain,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) )] :
( ! [B: TB > TA,C: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( nil @ TB ) @ C ) ) )
=> ~ ! [B: TB > TA,C: TB,D: list @ TB,E: list @ TA] :
( A
!= ( product_Pair @ ( TB > TA ) @ ( product_prod @ ( list @ TB ) @ ( list @ TA ) ) @ B @ ( product_Pair @ ( list @ TB ) @ ( list @ TA ) @ ( cons @ TB @ C @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(119,axiom,
! [A: name,B: name,C: name] :
( ( A != B )
=> ( ( C != B )
=> ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_swap__simps_I3_J) ).
thf(653,plain,
! [A: name,B: name,C: name] :
( ( A != B )
=> ( ( C != B )
=> ( ( perm @ name @ name @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ C ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_arg__min__list_Oinduct) ).
thf(768,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(171,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_shuffles_Oinduct) ).
thf(827,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(86,axiom,
y != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062) ).
thf(505,plain,
y != x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(64,axiom,
fresh @ name @ name @ y @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_cClose1_Ohyps_I12_J) ).
thf(438,plain,
fresh @ name @ name @ y @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(230,axiom,
pt_name @ name,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Agent_Oname___Agent_Opt__name_14) ).
thf(1076,plain,
pt_name @ name,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(141,axiom,
! [TA: $tType,TB: $tType,A: list @ ( product_prod @ TB @ TB ),B: TA,C: set @ TA] :
( ( perm @ TB @ $o @ A @ ( member @ TA @ B @ C ) )
= ( member @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_pt__set__bij3) ).
thf(722,plain,
! [TA: $tType,TB: $tType,A: list @ ( product_prod @ TB @ TB ),B: TA,C: set @ TA] :
( ( perm @ TB @ $o @ A @ ( member @ TA @ B @ C ) )
= ( member @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(127,axiom,
fs_name @ name,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Agent_Oname___Agent_Ofs__name_15) ).
thf(675,plain,
fs_name @ name,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(59,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_strict__sorted_Ocases) ).
thf(426,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(260,axiom,
! [A: name,B: name,C: name] :
( ( ( A = B )
=> ( ( swap_name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= C ) )
& ( ( A != B )
=> ( ( ( C = B )
=> ( ( swap_name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= A ) )
& ( ( C != B )
=> ( ( swap_name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_swap__name_Osimps) ).
thf(1203,plain,
! [A: name,B: name,C: name] :
( ( ( A = B )
=> ( ( swap_name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= C ) )
& ( ( A != B )
=> ( ( ( C = B )
=> ( ( swap_name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= A ) )
& ( ( C != B )
=> ( ( swap_name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(99,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_131_prod__cases7) ).
thf(548,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)],[99]) ).
thf(34,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(374,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(233,axiom,
! [A: list @ ( product_prod @ name @ name ),B: name] :
( ( perm @ name @ late_subject @ A @ ( late_BoundOutputS @ B ) )
= ( late_BoundOutputS @ ( perm @ name @ name @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_subject_Operm_I2_J) ).
thf(1081,plain,
! [A: list @ ( product_prod @ name @ name ),B: name] :
( ( perm @ name @ late_subject @ A @ ( late_BoundOutputS @ B ) )
= ( late_BoundOutputS @ ( perm @ name @ name @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(26,axiom,
fs_name @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Agent_Ofs__name_9) ).
thf(355,plain,
fs_name @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(250,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_168_old_Oprod_Orec) ).
thf(1145,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)],[250]) ).
thf(228,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: list @ ( product_prod @ TB @ TB )] :
( ( A = B )
=> ( ( perm @ TB @ TA @ C @ A )
= ( perm @ TB @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_pt__bij3) ).
thf(1018,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: list @ ( product_prod @ TB @ TB )] :
( ( A = B )
=> ( ( perm @ TB @ TA @ C @ A )
= ( perm @ TB @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(93,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_129_prod__cases5) ).
thf(525,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)],[93]) ).
thf(179,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_228_Late__Semantics_OComm2) ).
thf(855,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)],[179]) ).
thf(134,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_104_resCasesF_H) ).
thf(690,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)],[134]) ).
thf(190,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_54_freeRes_Oinducts) ).
thf(887,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)],[190]) ).
thf(14,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( pt_name @ ( list @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_List_Olist___Agent_Opt__name_11) ).
thf(327,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( pt_name @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(51,axiom,
fs_name @ late_freeRes,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_25) ).
thf(409,plain,
fs_name @ late_freeRes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(235,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_240_simE_I2_J) ).
thf(1098,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)],[235]) ).
thf(219,axiom,
late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_cOpen_Ohyps_I1_J) ).
thf(993,plain,
late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(140,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_list_Oinducts) ).
thf(712,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(223,axiom,
! [A: late_freeRes_Rep] :
( ( perm @ name @ late_freeRes_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_freeRes__perm__empty) ).
thf(1003,plain,
! [A: late_freeRes_Rep] :
( ( perm @ name @ late_freeRes_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType] :
( ( ( pt_name @ TB )
& ( pt_name @ TA ) )
=> ( pt_name @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Agent_Opt__name_21) ).
thf(673,plain,
! [TA: $tType,TB: $tType] :
( ( ( pt_name @ TB )
& ( pt_name @ TA ) )
=> ( pt_name @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(163,axiom,
! [A: name] : ( fresh @ name @ late_freeRes @ A @ late_TauR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_freeRes_Ofresh_I2_J) ).
thf(791,plain,
! [A: name] : ( fresh @ name @ late_freeRes @ A @ late_TauR ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(85,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_neq__Nil__conv) ).
thf(502,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(175,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_109_residual_Oinducts) ).
thf(840,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)],[175]) ).
thf(166,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_211_Late__Semantics_OClose2) ).
thf(808,plain,
! [A: pi,B: name,C: name,D: pi,E: pi,F: name,G: pi] :
( ( late_transitions @ A @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) )
=> ( ( late_transitions @ E @ ( late_BoundR @ ( late_InputS @ B ) @ F @ G ) )
=> ( ( fresh @ name @ pi @ 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)],[166]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(359,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(244,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_perm__swap_I1_J) ).
thf(1130,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(148,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_253_pi_Ofresh_I9_J) ).
thf(744,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)],[148]) ).
thf(18,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_216_simps_I8_J) ).
thf(336,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)],[18]) ).
thf(249,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_96_Late__Semantics_OResB) ).
thf(1141,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)],[249]) ).
thf(182,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_178_subject_Ofresh_I1_J) ).
thf(864,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)],[182]) ).
thf(143,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_105_ResF) ).
thf(727,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)],[143]) ).
thf(248,axiom,
eqvt @ pi @ rel,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_EqvtRel) ).
thf(1140,plain,
eqvt @ pi @ rel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(67,axiom,
! [A: list @ ( product_prod @ name @ name ),B: late_freeRes,C: pi] :
( ( perm @ name @ late_residual @ A @ ( late_FreeR @ B @ C ) )
= ( late_FreeR @ ( perm @ name @ late_freeRes @ A @ B ) @ ( perm @ name @ pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_residual_Operm_I2_J) ).
thf(446,plain,
! [A: list @ ( product_prod @ name @ name ),B: late_freeRes,C: pi] :
( ( perm @ name @ late_residual @ A @ ( late_FreeR @ B @ C ) )
= ( late_FreeR @ ( perm @ name @ late_freeRes @ A @ B ) @ ( perm @ name @ pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(176,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_name__swap__bij) ).
thf(845,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: name,B: name,C: TA] :
( ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ ( perm @ name @ TA @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ A @ B ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(112,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_103_resCasesF) ).
thf(627,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)],[112]) ).
thf(234,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_induct__list012) ).
thf(1084,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(30,axiom,
cp_name_name @ pi_Rep,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Agent_Opi__Rep___Agent_Ocp__name__name_16) ).
thf(363,plain,
cp_name_name @ pi_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(278,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_73_prod_Oinject) ).
thf(1321,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)],[278]) ).
thf(153,axiom,
z != aa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cClose1_Ohyps_I10_J) ).
thf(759,plain,
z != aa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(296,axiom,
! [A: name,B: pi,C: name] :
( ( subs @ ( res @ A @ B ) @ C @ A )
= ( res @ C @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Strong__Late__Sim__SC__Mirabelle__dtpyqonsky_OsubstRes3) ).
thf(1448,plain,
! [A: name,B: pi,C: name] :
( ( subs @ ( res @ A @ B ) @ C @ A )
= ( res @ C @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ C @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(213,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh @ name @ pi @ A @ B )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ A @ ( par @ B @ C ) ) @ ( par @ B @ ( res @ A @ C ) ) ) @ rel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_Res) ).
thf(976,plain,
! [A: name,B: pi,C: pi] :
( ( fresh @ name @ pi @ A @ B )
=> ( member @ ( product_prod @ pi @ pi ) @ ( product_Pair @ pi @ pi @ ( res @ A @ ( par @ B @ C ) ) @ ( par @ B @ ( res @ A @ C ) ) ) @ rel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(133,axiom,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: TA] :
~ ! [B: name] :
~ ( fresh @ name @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_name__exists__fresh) ).
thf(688,plain,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: TA] :
~ ! [B: name] :
~ ( fresh @ name @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(106,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: name,C: TA] :
( ( perm @ name @ $o @ A @ ( fresh @ name @ TA @ B @ C ) )
= ( fresh @ name @ TA @ ( perm @ name @ name @ A @ B ) @ ( perm @ name @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_fresh__eqvt) ).
thf(588,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: name,C: TA] :
( ( perm @ name @ $o @ A @ ( fresh @ name @ TA @ B @ C ) )
= ( fresh @ name @ TA @ ( perm @ name @ name @ A @ B ) @ ( perm @ name @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(90,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: TA] :
( ( perm @ name @ TA @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_pt__name1) ).
thf(517,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: TA] :
( ( perm @ name @ TA @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(192,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_transpose_Ocases) ).
thf(896,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(23,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_2) ).
thf(351,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(56,axiom,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ( cp_name_name @ ( list @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_List_Olist___Agent_Ocp__name__name_10) ).
thf(418,plain,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ( cp_name_name @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(161,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_118_freshResidual) ).
thf(786,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)],[161]) ).
thf(103,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_134_prod__induct5) ).
thf(568,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)],[103]) ).
thf(36,axiom,
pt_name @ late_subject,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject___Agent_Opt__name_27) ).
thf(378,plain,
pt_name @ late_subject,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(88,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: set @ ( product_prod @ pi @ pi ),F: list @ ( product_prod @ name @ name )] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( eqvt @ pi @ E )
=> ( strong2129052853vative @ ( perm @ name @ pi @ F @ A ) @ ( perm @ name @ pi @ F @ B ) @ C @ ( perm @ name @ name @ F @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_derivativeEqvtI2) ).
thf(510,plain,
! [A: pi,B: pi,C: late_subject,D: name,E: set @ ( product_prod @ pi @ pi ),F: list @ ( product_prod @ name @ name )] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( eqvt @ pi @ E )
=> ( strong2129052853vative @ ( perm @ name @ pi @ F @ A ) @ ( perm @ name @ pi @ F @ B ) @ C @ ( perm @ name @ name @ F @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(124,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: list @ ( product_prod @ name @ name ),C: TA] :
( ( perm @ name @ TA @ A @ ( perm @ name @ TA @ B @ C ) )
= ( perm @ name @ TA @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ A @ B ) @ ( perm @ name @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_name__perm__compose) ).
thf(667,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: list @ ( product_prod @ name @ name ),C: TA] :
( ( perm @ name @ TA @ A @ ( perm @ name @ TA @ B @ C ) )
= ( perm @ name @ TA @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ A @ B ) @ ( perm @ name @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(200,axiom,
fresh @ name @ pi @ y @ q2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_cClose1_Ohyps_I7_J) ).
thf(929,plain,
fresh @ name @ pi @ y @ q2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(39,axiom,
cp_name_name @ late_residual_Rep,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_36) ).
thf(383,plain,
cp_name_name @ late_residual_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(193,axiom,
! [A: name,B: name,C: name] :
( ( ( A = B )
=> ( ( swap @ name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= C ) )
& ( ( A != B )
=> ( ( ( C = B )
=> ( ( swap @ name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= A ) )
& ( ( C != B )
=> ( ( swap @ name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_name__calc_I3_J) ).
thf(899,plain,
! [A: name,B: name,C: name] :
( ( ( A = B )
=> ( ( swap @ name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= C ) )
& ( ( A != B )
=> ( ( ( C = B )
=> ( ( swap @ name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= A ) )
& ( ( C != B )
=> ( ( swap @ name @ ( product_Pair @ name @ name @ A @ C ) @ B )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(172,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_242_simulation__def) ).
thf(832,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)],[172]) ).
thf(274,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_206_resInputFreeTrans) ).
thf(1309,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)],[274]) ).
thf(294,axiom,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ( ! [B: TA > TA > $o,C: TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_successively_Ocases) ).
thf(1442,plain,
! [TA: $tType,A: product_prod @ ( TA > TA > $o ) @ ( list @ TA )] :
( ! [B: TA > TA > $o] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ( ! [B: TA > TA > $o,C: TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ~ ! [B: TA > TA > $o,C: TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( TA > TA > $o ) @ ( list @ TA ) @ B @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(231,axiom,
fs_name @ late_residual,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual___Agent_Ofs__name_31) ).
thf(1077,plain,
fs_name @ late_residual,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(77,axiom,
( ( late_BoundOutputS @ aa )
= ( late_BoundOutputS @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_cOpen_Ohyps_I3_J) ).
thf(478,plain,
( ( late_BoundOutputS @ aa )
= ( late_BoundOutputS @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(240,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA ),B: $o,C: $o] :
( ( perm @ TA @ $o @ A
@ ( B
=> C ) )
= ( ( perm @ TA @ $o @ A @ B )
=> ( perm @ TA @ $o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_imp__eqvt) ).
thf(1116,plain,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA ),B: $o,C: $o] :
( ( perm @ TA @ $o @ A
@ ( B
=> C ) )
= ( ( perm @ TA @ $o @ A @ B )
=> ( perm @ TA @ $o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(245,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA ),B: late_freeRes,C: pi] :
( ( perm @ TA @ late_residual_Rep @ A @ ( late_r347633188eR_Rep @ B @ C ) )
= ( late_r347633188eR_Rep @ ( perm @ TA @ late_freeRes @ A @ B ) @ ( perm @ TA @ pi @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_perm__residual__Rep_Osimps_I2_J) ).
thf(1133,plain,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA ),B: late_freeRes,C: pi] :
( ( perm @ TA @ late_residual_Rep @ A @ ( late_r347633188eR_Rep @ B @ C ) )
= ( late_r347633188eR_Rep @ ( perm @ TA @ late_freeRes @ A @ B ) @ ( perm @ TA @ pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(151,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_119_freshBoundDerivative_I2_J) ).
thf(752,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)],[151]) ).
thf(7,axiom,
cp_name_name @ late_freeRes,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_23) ).
thf(315,plain,
cp_name_name @ late_freeRes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(61,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_212_transitions_OClose1) ).
thf(432,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)],[61]) ).
thf(52,axiom,
cp_name_name @ late_subject_Rep,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_34) ).
thf(410,plain,
cp_name_name @ late_subject_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(265,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_203_parCasesB_H) ).
thf(1229,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)],[265]) ).
thf(251,axiom,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_splice_Ocases) ).
thf(1148,plain,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(183,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: name,C: TA] :
( ( fresh @ name @ TA @ ( perm @ name @ name @ A @ B ) @ ( perm @ name @ TA @ A @ C ) )
= ( fresh @ name @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_fresh__bij) ).
thf(867,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: name,C: TA] :
( ( fresh @ name @ TA @ ( perm @ name @ name @ A @ B ) @ ( perm @ name @ TA @ A @ C ) )
= ( fresh @ name @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(109,axiom,
! [A: name,B: pi,C: name,D: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( input @ C @ D @ B )
= ( input @ C @ A @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ D @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_alphaInput) ).
thf(603,plain,
! [A: name,B: pi,C: name,D: name] :
( ( fresh @ name @ pi @ A @ B )
=> ( ( input @ C @ D @ B )
= ( input @ C @ A @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ D @ A ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(13,axiom,
pt_name @ late_freeRes_Rep,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_33) ).
thf(326,plain,
pt_name @ late_freeRes_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(197,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: list @ ( product_prod @ name @ name ),C: TA] :
( ( perm @ name @ TA @ A @ ( perm @ name @ TA @ B @ C ) )
= ( perm @ name @ TA @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ A @ B ) @ ( perm @ name @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_perm__compose) ).
thf(918,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: list @ ( product_prod @ name @ name ),C: TA] :
( ( perm @ name @ TA @ A @ ( perm @ name @ TA @ B @ C ) )
= ( perm @ name @ TA @ ( perm @ name @ ( list @ ( product_prod @ name @ name ) ) @ A @ B ) @ ( perm @ name @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(20,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( pt_name @ ( noption @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nominal_Onoption___Agent_Opt__name_19) ).
thf(341,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( pt_name @ ( noption @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(165,axiom,
cp_name_name @ name,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Agent_Oname___Agent_Ocp__name__name_13) ).
thf(807,plain,
cp_name_name @ name,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(63,axiom,
cp_name_name @ late_residual,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_29) ).
thf(437,plain,
cp_name_name @ late_residual,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(113,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_210_Late__Semantics_OClose1) ).
thf(635,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)],[113]) ).
thf(54,axiom,
ord @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_7) ).
thf(415,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(147,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_133_prod__induct4) ).
thf(740,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)],[147]) ).
thf(217,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: TA,C: TA] :
( ( perm @ name @ $o @ A @ ( B = C ) )
= ( ( perm @ name @ TA @ A @ B )
= ( perm @ name @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_eq__eqvt) ).
thf(987,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: TA,C: TA] :
( ( perm @ name @ $o @ A @ ( B = C ) )
= ( ( perm @ name @ TA @ A @ B )
= ( perm @ name @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(105,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_202_parCasesB) ).
thf(575,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)],[105]) ).
thf(94,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_120_residual_Ostrong__inducts) ).
thf(528,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)],[94]) ).
thf(286,axiom,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: list @ TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_shuffles_Ocases) ).
thf(1399,plain,
! [TA: $tType,A: product_prod @ ( list @ TA ) @ ( list @ TA )] :
( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ( ! [B: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: list @ TA,D: TA,E: list @ TA] :
( A
!= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(45,axiom,
cp_name_name @ late_freeRes_Rep,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_32) ).
thf(395,plain,
cp_name_name @ late_freeRes_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(111,axiom,
! [A: list @ ( product_prod @ name @ name ),B: name,C: name,D: pi] :
( ( perm @ name @ pi @ A @ ( input @ B @ C @ D ) )
= ( input @ ( perm @ name @ name @ A @ B ) @ ( perm @ name @ name @ A @ C ) @ ( perm @ name @ pi @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_pi_Operm_I4_J) ).
thf(624,plain,
! [A: list @ ( product_prod @ name @ name ),B: name,C: name,D: pi] :
( ( perm @ name @ pi @ A @ ( input @ B @ C @ D ) )
= ( input @ ( perm @ name @ name @ A @ B ) @ ( perm @ name @ name @ A @ C ) @ ( perm @ name @ pi @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(33,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_190_subject_Oinducts) ).
thf(369,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)],[33]) ).
thf(110,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_239_resSimCases) ).
thf(607,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)],[110]) ).
thf(10,axiom,
pt_name @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Agent_Opt__name_8) ).
thf(322,plain,
pt_name @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(80,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA ),B: $o] :
( ( perm @ TA @ $o @ A @ ~ B )
= ( ~ ( perm @ TA @ $o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_neg__eqvt) ).
thf(486,plain,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA ),B: $o] :
( ( perm @ TA @ $o @ A @ ~ B )
= ( ~ ( perm @ TA @ $o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(205,axiom,
! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_Late__Semantics_OInput) ).
thf(940,plain,
! [A: name,B: name,C: pi] : ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_InputS @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(25,axiom,
fs_name @ late_subject,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject___Agent_Ofs__name_28) ).
thf(354,plain,
fs_name @ late_subject,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(225,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_197_resTrans_I2_J) ).
thf(1009,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)],[225]) ).
thf(5,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Late__Semantics1_Osubject_Oinject_I2_J) ).
thf(309,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(158,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_85_subject_Ofresh_I2_J) ).
thf(775,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)],[158]) ).
thf(290,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_205_transitions_OPar2B) ).
thf(1416,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)],[290]) ).
thf(128,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_76_fresh__prodD_I2_J) ).
thf(676,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)],[128]) ).
thf(83,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_227_Late__Semantics_OComm1) ).
thf(496,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)],[83]) ).
thf(31,axiom,
! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
( ( ( late_r347633188eR_Rep @ A @ B )
= ( late_r347633188eR_Rep @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_residual__Rep_Oinject_I2_J) ).
thf(364,plain,
! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
( ( ( late_r347633188eR_Rep @ A @ B )
= ( late_r347633188eR_Rep @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(188,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_77_fresh__prodD_I1_J) ).
thf(882,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)],[188]) ).
thf(1465,plain,
$false,
inference(e,[status(thm)],[1454,347,893,1315,468,1110,762,1406,683,994,379,1305,861,1173,730,1290,873,449,1078,385,384,1137,533,1164,472,814,698,747,1458,670,1222,930,1127,1391,782,709,973,1386,436,320,565,1287,1298,917,934,1462,638,870,969,316,1398,416,475,756,789,591,443,646,353,480,1136,834,1151,937,1215,1119,1394,396,411,312,452,380,678,661,925,1306,1163,942,439,546,793,334,1387,778,302,1123,820,392,429,1423,467,361,879,852,329,522,1159,493,551,324,1012,1106,1296,665,1402,948,725,980,1006,388,356,420,499,884,339,933,554,537,642,489,706,1419,837,997,701,1451,457,1324,1114,984,911,508,921,657,765,1170,398,1167,662,343,1318,750,513,1103,1301,1219,824,375,733,423,402,772,875,1226,958,1403,641,572,1312,466,704,540,979,406,681,990,737,649,303,1439,323,594,483,964,915,1460,1022,1293,1381,330,811,387,858,367,848,520,685,399,959,1445,455,1015,1176,306,1000,653,768,827,505,438,1076,722,675,426,1203,548,374,1081,355,1145,1018,525,855,690,887,327,409,1098,993,712,1003,673,791,502,840,808,359,1130,744,336,1141,864,727,1140,446,845,627,1084,363,1321,759,1448,976,688,588,517,896,351,418,786,568,378,510,667,929,383,899,832,1309,1442,1077,478,1116,1133,752,315,432,410,1229,1148,867,603,326,918,341,807,437,635,415,740,987,575,528,1399,395,624,369,607,322,486,940,354,1009,309,775,1416,676,496,364,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP190^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n026.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 20:12:12 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.04/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.35/1.23 % [INFO] Parsing done (423ms).
% 2.35/1.24 % [INFO] Running in sequential loop mode.
% 3.70/1.62 % [INFO] eprover registered as external prover.
% 3.70/1.63 % [INFO] Scanning for conjecture ...
% 4.15/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 300 axioms. Running axiom selection ...
% 4.44/1.98 % [INFO] Axiom selection finished. Selected 299 axioms (removed 1 axioms).
% 6.07/2.41 % [INFO] Problem is higher-order (TPTP THF).
% 6.07/2.44 % [INFO] Type checking passed.
% 6.07/2.44 % [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 ...
% 95.49/68.46 % External prover 'e' found a proof!
% 95.49/68.46 % [INFO] Killing All external provers ...
% 95.49/68.46 % Time passed: 68099ms (effective reasoning time: 67210ms)
% 95.49/68.46 % 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)>
% 95.49/68.46 % Axioms used in derivation (299): fact_217_substTrans, tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_23, fact_192_subject_Ostrong__induct_H, fact_157_shuffles_Oinduct, fact_199_inputFreeTrans, fact_230_transitions_OComm1, fact_85_subject_Ofresh_I2_J, fact_117_Open, fact_50_name__calc_I2_J, fact_206_resInputFreeTrans, fact_51_freeRes_Ostrong__inducts, fact_248_simCasesCont, fact_244_name__prm__name_Osimps_I1_J, fact_95_perm__boolI, fact_66_perm__app, fact_96_Late__Semantics_OResB, fact_120_residual_Ostrong__inducts, fact_202_parCasesB, fact_162_arg__min__list_Oinduct, fact_8_cClose1_Ohyps_I14_J, fact_125_prod__cases, fact_190_subject_Oinducts, fact_30_pi__perm__empty, fact_161_remdups__adj_Oinduct, fact_173_Late__Semantics1_Osubject_Oinject_I1_J, fact_105_ResF, fact_251_alpha__fresh_H, fact_123_freshFreeDerivative_I1_J, fact_152_list__induct2_H, fact_44_fresh__eqvt, fact_9_cClose1_Ohyps_I13_J, fact_10_perm__swap_I1_J, tcon_Agent_Opi___Agent_Ofs__name, tcon_Agent_Opi___Agent_Ocp__name__name_4, fact_172_name__calc_I1_J, fact_182_pi_Odistinct_I55_J, fact_33_Late__Semantics_Osubject_Oinject_I2_J, fact_158_transpose_Ocases, tcon_Product__Type_Oprod___Agent_Ocp__name__name_20, fact_89_name__bij, fact_71_list_Oinject, fact_215_simps_I9_J, fact_0__092_060open_062a_A_061_Ab_092_060close_062, tcon_Agent_Oname___Agent_Opt__name_14, fact_119_freshBoundDerivative_I2_J, fact_254_pi_Ofresh_I4_J, fact_104_resCasesF_H, fact_228_Late__Semantics_OComm2, fact_204_transitions_OPar1B, tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_29, fact_108_residual_Odistinct_I1_J, fact_116_resCasesB_H, fact_226_injPermSubst, fact_171_alphaInput, fact_80_true__eqvt, tcon_fun___Orderings_Oord, tcon_Late__Semantics_OfreeRes___Agent_Opt__name_24, fact_198_inputIneqTrans, fact_115_shuffles_Ocases, fact_183_pi_Oinject_I7_J, tcon_fun___Agent_Ocp__name__name, fact_118_freshResidual, fact_178_subject_Ofresh_I1_J, fact_35_freeRes_Operm_I2_J, fact_88_residual_Operm_I1_J, tcon_List_Olist___Agent_Opt__name_11, fact_64_perm__compose, fact_34_Late__Semantics1_Osubject_Oinject_I2_J, fact_163_successively_Oinduct, fact_25_cClose1_Ohyps_I8_J, fact_87_cClose1_Ohyps_I1_J, fact_130_prod__cases6, fact_136_prod__induct7, fact_242_simulation__def, tcon_HOL_Obool___Orderings_Olinorder, fact_92_conj__eqvt, fact_191_subject_Oexhaust, fact_139_not__Cons__self2, fact_113_successively_Ocases, fact_122_resCasesB, tcon_HOL_Obool___Agent_Ofs__name_9, fact_67_in__eqvt, fact_187_pi_Odistinct_I57_J, fact_110_resCases_H, fact_106_freshBoundDerivative_I1_J, fact_167_Free_Ohyps, fact_210_Late__Semantics_OClose1, fact_131_prod__cases7, fact_29_freeRes__perm__empty, fact_22_cClose1_Ohyps_I7_J, tcon_Late__Semantics_Oresidual___Agent_Opt__name_30, fact_99_nil__eqvt, fact_193_subject_Ostrong__inducts, fact_19_Late__Semantics_OfreeRes_Oinject, fact_69_residual_Oinject_I2_J, tcon_Nominal_Onoption___Agent_Ocp__name__name_18, fact_14_pt__name1, fact_160_sorted__wrt_Oinduct, fact_28_subject__perm__empty, tcon_List_Olist___Agent_Ocp__name__name_10, fact_186_Late__Semantics_OInput, fact_133_prod__induct4, fact_26_cClose1_Ohyps_I3_J, fact_46_Collect__mem__eq, fact_233_Agent_Oswap__name__def, fact_137_old_Oprod_Oexhaust, fact_55_Late__Semantics1_OfreeRes_Odistinct_I1_J, fact_126_Pair__inject, fact_68_eq__eqvt, fact_62_cp__name__name1, fact_156_min__list_Oinduct, fact_60_swap__simps_I3_J, fact_245_derivativeEqvtI2, tcon_Agent_Oname___Agent_Ocp__name__name_13, fact_197_resTrans_I2_J, fact_235_eqvtRelE, tcon_Late__Semantics_Osubject___Agent_Ofs__name_28, fact_140_allE__Nil, tcon_Set_Oset___Orderings_Oord_2, fact_86_pi_Operm_I9_J, tcon_Set_Oset___Agent_Ocp__name__name_1, help_If_1_1_T, fact_32_subject_Operm_I2_J, fact_128_prod__cases4, fact_144_alphaRes, fact_5__092_060open_062z_A_092_060noteq_062_Ax_092_060close_062, fact_74_cClose1_Ohyps_I2_J, fact_241_simE_I1_J, fact_174_residual__Rep_Oinject_I2_J, fact_218_forget, fact_145_alphaBoundResidual, fact_11_name__id, fact_247_parSym, fact_246_Agent_Oname__prm__name__def, fact_23_cClose1_Ohyps_I12_J, fact_81_false__eqvt, fact_175_pi_Ofresh_I8_J, fact_121_residual_Ostrong__induct, fact_201_Late__Semantics_OPar2B, fact_196_name__calc_I3_J, tcon_Agent_Opi__Rep___Agent_Ocp__name__name_16, fact_154_induct__list012, fact_84_freeRes_Ofresh_I1_J, fact_134_prod__induct5, fact_177_pi_Operm_I4_J, tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_35, fact_78_cons__eqvt, fact_253_pi_Ofresh_I9_J, fact_17_eqvt, fact_203_parCasesB_H, fact_52_freeRes_Ostrong__induct_H, fact_91_neg__eqvt, fact_216_simps_I8_J, fact_15__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062, fact_40_cClose1_Ohyps_I9_J, fact_141_if__eqvt, fact_211_Late__Semantics_OClose2, fact_36_name__fresh, fact_214_subst__identity, fact_169_supports__def, fact_98_perm__bool__def, fact_185_transitions_OInput, fact_200_Late__Semantics_OPar1B, tcon_Agent_Oname___Agent_Ofs__name_15, tcon_fun___Agent_Opt__name, tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_26, fact_243_simCases, tcon_Agent_Opi___Agent_Opt__name_5, fact_16_perm__swap_I2_J, fact_227_Late__Semantics_OComm1, fact_222_substRes2, fact_45_mem__Collect__eq, fact_238_name__prm__name_Osimps_I2_J, fact_42_fresh__perm__app, fact_159_remdups__adj_Ocases, fact_41_cClose1_Ohyps_I4_J, fact_232_product__lists_Osimps_I1_J, fact_224_Strong__Late__Sim__SC__Mirabelle__dtpyqonsky_OsubstRes3, fact_132_prod__induct3, fact_112_sorted__wrt_Ocases, fact_61_fresh__aux, tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_33, fact_90_imp__eqvt, fact_213_EqvtRel, fact_27_residual__perm__empty, fact_38_perm__fresh__fresh, fact_73_prod_Oinject, fact_249_parAssocLeft, tcon_Late__Semantics_Osubject___Agent_Opt__name_27, fact_13_name__swap__bij, fact_109_residual_Oinducts, fact_24_assms_I1_J, fact_63_name__perm__compose, fact_59_swap__simps_I2_J, fact_53_freeRes_Oexhaust, fact_57_freshFreeDerivative_I2_J, fact_219_fresh__fact1, fact_212_transitions_OClose1, fact_58_swap__simps_I1_J, fact_47_Collect__cong, fact_111_arg__min__list_Ocases, fact_229_transitions_OComm2, fact_12_name__swap, help_If_3_1_T, tcon_HOL_Obool___Orderings_Oord_7, help_If_2_1_T, fact_184_pi_Odistinct_I85_J, fact_166_strict__sorted_Ocases, fact_6_cOpen_Ohyps_I1_J, fact_102_map__tailrec__rev_Ocases, fact_37_residual_Operm_I2_J, fact_43_name__exists__fresh, fact_124_surj__pair, fact_31_freeRes_Operm_I1_J, fact_135_prod__induct6, fact_147_list_Odistinct_I1_J, fact_2_cClose1_Ohyps_I10_J, tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_36, tcon_Nominal_Onoption___Agent_Opt__name_19, fact_189_Late__Semantics1_Osubject_Odistinct_I1_J, fact_188_Late__Semantics_Osubject_Odistinct_I1_J, tcon_Product__Type_Oprod___Agent_Ofs__name_22, fact_94_perm__boolE, fact_155_min__list_Ocases, tcon_Late__Semantics_Oresidual___Agent_Ofs__name_31, fact_7_cOpen_Ohyps_I3_J, fact_4_cClose1_Ohyps_I5_J, fact_101_transitions_OResB, fact_170_perm__residual__Rep_Osimps_I2_J, fact_127_prod__cases3, fact_114_splice_Ocases, tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_25, fact_56_Late__Semantics_OfreeRes_Odistinct_I1_J, fact_1_cOpen_Ohyps_I2_J, tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_34, fact_72_old_Oprod_Oinject, tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_37, fact_151_neq__Nil__conv, fact_209_resInputBoundOutputTrans, fact_149_list_Oexhaust, tcon_HOL_Obool___Agent_Opt__name_8, fact_75_fresh__list__cons, fact_79_strict__sorted_Oinduct, fact_240_simE_I2_J, fact_165_map__tailrec__rev_Oinduct, fact_168_old_Oprod_Orec, fact_207_inputBoundOutputTrans, fact_21_cClose1_Ohyps_I11_J, fact_107_freshRes, fact_176_pi_Operm_I8_J, fact_181_Res, fact_180_ScopeExt, tcon_Product__Type_Oprod___Agent_Opt__name_21, fact_142_pt__bij3, tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_32, fact_20_Late__Semantics1_OfreeRes_Oinject, fact_3_cClose1_Ohyps_I6_J, tcon_Set_Oset___Agent_Opt__name_3, fact_103_resCasesF, fact_252_name__abs__eq, fact_76_fresh__prodD_I2_J, fact_138_old_Oprod_Oinducts, fact_225_renaming, tcon_List_Olist___Agent_Ofs__name_12, fact_195_Par1F, fact_223_eqvt__subs, fact_97_pt__set__bij3, fact_205_transitions_OPar2B, fact_231_transitions_OClose2, fact_83_residual_Ofresh_I2_J, fact_54_freeRes_Oinducts, fact_93_disj__eqvt, fact_129_prod__cases5, fact_65_perm__bij, fact_143_abs__fun__if, fact_82_freeRes_Ofresh_I2_J, fact_18__092_060open_062z_A_092_060sharp_062_AQ_092_060close_062, tcon_Agent_Opi__Rep___Agent_Opt__name_17, fact_49_fresh__bij, tcon_HOL_Obool___Agent_Ocp__name__name_6, fact_146_perm__prod_Osimps, fact_194_Par2F, fact_77_fresh__prodD_I1_J, fact_100_fresh__list__nil, fact_234_swap__name_Osimps, fact_239_resSimCases, fact_221_Agent_OsubstRes3, fact_250_derivativeEqvtI, fact_164_list__nonempty__induct, fact_236_eqvtRelI, fact_208_inputCases, fact_179_subject_Operm_I1_J, fact_39_name__fresh__fresh, fact_150_list_Oinducts, fact_70_fresh__prod, fact_153_splice_Oinduct, fact_237_eqvt__def, fact_220_fresh__fact2, fact_148_list_OdiscI
% 95.49/68.46 % No. of inferences in proof: 602
% 95.49/68.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 68099 ms resp. 67210 ms w/o parsing
% 96.72/68.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 96.72/68.74 % [INFO] Killing All external provers ...
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