%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP182^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 08:07:05 AM UTC 2026
% Result : Theorem 78.49s 53.61s
% Output : Refutation 79.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 289
% Syntax : Number of formulae : 580 ( 264 unt; 0 typ; 0 def)
% Number of atoms : 1879 ( 465 equ; 2 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 9545 ( 235 ~; 7 |; 78 &;8471 @)
% ( 0 <=>; 754 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 270 ( 270 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 46 usr; 16 con; 0-5 aty)
% Number of variables : 2307 ( 42 ^;2235 !; 30 ?;2307 :)
% 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(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(input_decl,type,
input: name > name > pi > pi ).
thf(res_decl,type,
res: name > pi > pi ).
thf(sum_decl,type,
sum: pi > pi > pi ).
thf(bNF_Greatest_shift_decl,type,
bNF_Greatest_shift:
!>[TA: $tType,TB: $tType] : ( ( ( list @ TB ) > TA ) > TB > ( list @ TB ) > TA ) ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(late_OutputR_decl,type,
late_OutputR: name > name > 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(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(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
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(id_decl,type,
id:
!>[TA: $tType] : ( set @ ( product_prod @ TA @ TA ) ) ).
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(pq_decl,type,
pq: pi ).
thf(p2_decl,type,
p2: pi ).
thf(q_decl,type,
q: pi ).
thf(rel_decl,type,
rel: set @ ( product_prod @ pi @ pi ) ).
thf(a_decl,type,
a: late_subject ).
thf(aa_decl,type,
aa: name ).
thf(x_decl,type,
x: name ).
thf(y_decl,type,
y: name ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(365,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(252,axiom,
late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_cOpen_Ohyps_I1_J) ).
thf(1168,plain,
late_transitions @ p @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_le__funE) ).
thf(479,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(20,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_equalityE) ).
thf(347,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(210,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA ),B: $o] :
( ( perm @ TA @ $o @ A @ ~ B )
= ( ~ ( perm @ TA @ $o @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_neg__eqvt) ).
thf(1031,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)],[210]) ).
thf(287,axiom,
fs_name @ name,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Oname___Agent_Ofs__name_19) ).
thf(1315,plain,
fs_name @ name,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(178,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_list_OdiscI) ).
thf(941,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)],[178]) ).
thf(72,axiom,
cp_name_name @ late_residual,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_31) ).
thf(481,plain,
cp_name_name @ late_residual,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(225,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/sandbox/benchmark/theBenchmark.p',fact_21_subject_Operm_I2_J) ).
thf(1083,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)],[225]) ).
thf(66,axiom,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ( cp_name_name @ ( list @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Agent_Ocp__name__name_14) ).
thf(468,plain,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ( cp_name_name @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(41,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_4) ).
thf(408,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',fact_44_prod__induct6) ).
thf(762,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)],[142]) ).
thf(202,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_not__Cons__self2) ).
thf(1005,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',fact_52_prod__cases7) ).
thf(1290,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)],[281]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',fact_43_prod__induct7) ).
thf(1068,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)],[221]) ).
thf(10,axiom,
pt_name @ late_freeRes_Rep,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_35) ).
thf(308,plain,
pt_name @ late_freeRes_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_le__funD) ).
thf(379,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(55,axiom,
pt_name @ late_subject,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject___Agent_Opt__name_29) ).
thf(440,plain,
pt_name @ late_subject,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',fact_223_residual_Ostrong__inducts) ).
thf(1078,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)],[224]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(384,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(244,axiom,
! [TA: $tType,TB: $tType] :
( ( ( pt_name @ TB )
& ( pt_name @ TA ) )
=> ( pt_name @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Agent_Opt__name_23) ).
thf(1137,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)],[244]) ).
thf(81,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_ord__le__eq__trans) ).
thf(500,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(250,axiom,
fresh @ name @ pi @ y @ q,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062) ).
thf(1164,plain,
fresh @ name @ pi @ y @ q,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',fact_184_residual_Operm_I1_J) ).
thf(747,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)],[138]) ).
thf(179,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/sandbox/benchmark/theBenchmark.p',fact_116_pt__bij3) ).
thf(945,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)],[179]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',fact_98_eqvtRelI) ).
thf(538,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)],[95]) ).
thf(159,axiom,
! [TA: $tType,A: $o,B: list @ ( product_prod @ TA @ TA )] :
( A
=> ( perm @ TA @ $o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_perm__boolI) ).
thf(814,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)],[159]) ).
thf(290,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/sandbox/benchmark/theBenchmark.p',fact_79_min__list_Oinduct) ).
thf(1327,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)],[290]) ).
thf(166,axiom,
cp_name_name @ name,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Oname___Agent_Ocp__name__name_17) ).
thf(829,plain,
cp_name_name @ name,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',fact_247_inputIneqTrans) ).
thf(1196,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)],[258]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',fact_57_Pair__inject) ).
thf(1046,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)],[215]) ).
thf(7,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_eq__refl) ).
thf(301,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(273,axiom,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: TA] :
~ ! [B: name] :
~ ( fresh @ name @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_name__exists__fresh) ).
thf(1254,plain,
! [TA: $tType] :
( ( fs_name @ TA )
=> ! [A: TA] :
~ ! [B: name] :
~ ( fresh @ name @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',fact_61_cp__name__name1) ).
thf(1055,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)],[217]) ).
thf(279,axiom,
fresh @ name @ pi @ y @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93__092_060open_062y_A_092_060sharp_062_AP_092_060close_062) ).
thf(1287,plain,
fresh @ name @ pi @ y @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(82,axiom,
cp_name_name @ late_subject_Rep,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_36) ).
thf(504,plain,
cp_name_name @ late_subject_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(22,axiom,
fs_name @ late_residual,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual___Agent_Ofs__name_33) ).
thf(357,plain,
fs_name @ late_residual,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(180,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ ( sum @ B @ C ) @ A @ ( sum @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_sumSym) ).
thf(949,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ ( sum @ B @ C ) @ A @ ( sum @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',fact_33_successively_Ocases) ).
thf(542,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)],[97]) ).
thf(156,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_list_Oexhaust) ).
thf(802,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)],[156]) ).
thf(19,axiom,
! [A: name,B: name,C: pi,D: late_freeRes,E: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_FreeR @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_inputFreeTrans) ).
thf(344,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)],[19]) ).
thf(270,axiom,
fs_name @ pi,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Opi___Agent_Ofs__name) ).
thf(1247,plain,
fs_name @ pi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(188,axiom,
! [TA: $tType,A: product_prod @ TA @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( id @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( product_Pair @ TA @ TA @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_IdE) ).
thf(969,plain,
! [TA: $tType,A: product_prod @ TA @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( id @ TA ) )
=> ~ ! [B: TA] :
( A
!= ( product_Pair @ TA @ TA @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(145,axiom,
! [A: pi_Rep] :
( ( perm @ name @ pi_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_pi__perm__empty) ).
thf(770,plain,
! [A: pi_Rep] :
( ( perm @ name @ pi_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(237,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_subrelI) ).
thf(1115,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',fact_193_freshResidual) ).
thf(1232,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)],[265]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType,A: TB] : ( fresh @ TB @ ( list @ TA ) @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_fresh__list__nil) ).
thf(881,plain,
! [TA: $tType,TB: $tType,A: TB] : ( fresh @ TB @ ( list @ TA ) @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(44,axiom,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ( cp_name_name @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Agent_Ocp__name__name_2) ).
thf(416,plain,
! [TA: $tType] :
( ( cp_name_name @ TA )
=> ( cp_name_name @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(76,axiom,
cp_name_name @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Agent_Ocp__name__name_9) ).
thf(492,plain,
cp_name_name @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(151,axiom,
late_transitions @ ( res @ x @ p ) @ ( late_BoundR @ a @ y @ pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_cSum1_Ohyps) ).
thf(789,plain,
late_transitions @ ( res @ x @ p ) @ ( late_BoundR @ a @ y @ pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',fact_127_eqvtRelE) ).
thf(1040,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)],[213]) ).
thf(106,axiom,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Late__Semantics_Osubject_Odistinct_I1_J) ).
thf(623,plain,
! [A: name,B: name] :
( ( late_InputS @ A )
!= ( late_BoundOutputS @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',fact_117_abs__fun__if) ).
thf(646,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)],[113]) ).
thf(74,axiom,
cp_name_name @ pi_Rep,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Opi__Rep___Agent_Ocp__name__name_20) ).
thf(485,plain,
cp_name_name @ pi_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(86,axiom,
! [A: name,B: name,C: pi,D: late_residual] :
~ ( late_transitions @ ( res @ A @ ( input @ A @ B @ C ) ) @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_resTrans_I2_J) ).
thf(514,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)],[86]) ).
thf(187,axiom,
! [A: name,B: name] :
( ( fresh @ name @ late_subject @ A @ ( late_BoundOutputS @ B ) )
= ( fresh @ name @ name @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_subject_Ofresh_I2_J) ).
thf(966,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)],[187]) ).
thf(143,axiom,
fresh @ name @ pi @ y @ ( res @ x @ ( sum @ p @ q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_Bound_Ohyps_I2_J) ).
thf(766,plain,
fresh @ name @ pi @ y @ ( res @ x @ ( sum @ p @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',fact_253_subject_Operm_I1_J) ).
thf(1169,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)],[253]) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',fact_5_perm__swap_I1_J) ).
thf(877,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)],[173]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',fact_40_fresh__aux) ).
thf(956,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)],[183]) ).
thf(238,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ ( sum @ B @ B ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_sumIdempRight) ).
thf(1119,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ ( sum @ B @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(233,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/sandbox/benchmark/theBenchmark.p',fact_75_sorted__wrt_Oinduct) ).
thf(1104,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)],[233]) ).
thf(84,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_set__eq__subset) ).
thf(507,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(222,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_strict__sorted_Ocases) ).
thf(1072,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)],[222]) ).
thf(58,axiom,
pt_name @ late_subject_Rep,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_37) ).
thf(453,plain,
pt_name @ late_subject_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(9,axiom,
pt_name @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Agent_Opt__name_12) ).
thf(307,plain,
pt_name @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(292,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',fact_29_fresh__bij) ).
thf(678,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)],[118]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_55_prod__cases4) ).
thf(529,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)],[92]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',fact_211_freeRes_Ofresh_I1_J) ).
thf(793,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)],[153]) ).
thf(259,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/sandbox/benchmark/theBenchmark.p',fact_95_derivativeEqvtI) ).
thf(1199,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)],[259]) ).
thf(247,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/sandbox/benchmark/theBenchmark.p',fact_70_map__tailrec__rev_Oinduct) ).
thf(1153,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)],[247]) ).
thf(31,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(381,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',fact_72_successively_Oinduct) ).
thf(714,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)],[127]) ).
thf(14,axiom,
fs_name @ late_subject,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject___Agent_Ofs__name_30) ).
thf(334,plain,
fs_name @ late_subject,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(262,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi,D: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ ( sum @ B @ ( sum @ C @ D ) ) @ A @ ( sum @ ( sum @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_sumAssocRight) ).
thf(1223,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi,D: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ ( sum @ B @ ( sum @ C @ D ) ) @ A @ ( sum @ ( sum @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(162,axiom,
! [A: pi,B: set @ ( product_prod @ pi @ pi ),C: pi,D: set @ ( product_prod @ pi @ pi )] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ B @ D )
=> ( strong743114133lation @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_monotonic) ).
thf(820,plain,
! [A: pi,B: set @ ( product_prod @ pi @ pi ),C: pi,D: set @ ( product_prod @ pi @ pi )] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ B @ D )
=> ( strong743114133lation @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(5,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_order__trans) ).
thf(297,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(50,axiom,
! [A: name,B: name,C: name,D: pi,E: late_freeRes,F: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_FreeR @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_resInputFreeTrans) ).
thf(429,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)],[50]) ).
thf(133,axiom,
( ( fresh @ name @ name )
= ( != @ name ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_name__fresh) ).
thf(729,plain,
( ( fresh @ name @ name )
= ( ^ [A: name,B: name] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(267,axiom,
! [A: name] :
( ( perm @ name @ name @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_name__calc_I2_J) ).
thf(1238,plain,
! [A: name] :
( ( perm @ name @ name @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(137,axiom,
pt_name @ pi,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Opi___Agent_Opt__name_7) ).
thf(746,plain,
pt_name @ pi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',fact_26_fresh__perm__app) ).
thf(1091,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)],[228]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',fact_186_Late__Semantics_OResB) ).
thf(1042,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)],[214]) ).
thf(181,axiom,
! [A: name,B: name] :
( ( fresh @ name @ late_subject @ A @ ( late_InputS @ B ) )
= ( fresh @ name @ name @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_subject_Ofresh_I1_J) ).
thf(952,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)],[181]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',fact_68_strict__sorted_Oinduct) ).
thf(693,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)],[122]) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',fact_15_prod_Oinject) ).
thf(630,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)],[108]) ).
thf(65,axiom,
fs_name @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Agent_Ofs__name_13) ).
thf(467,plain,
fs_name @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(24,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_equalityD1) ).
thf(361,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType] :
( ( ( pt_name @ TB )
& ( pt_name @ TA ) )
=> ( pt_name @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Agent_Opt__name) ).
thf(435,plain,
! [TA: $tType,TB: $tType] :
( ( ( pt_name @ TB )
& ( pt_name @ TA ) )
=> ( pt_name @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',fact_49_prod__induct5) ).
thf(1178,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)],[256]) ).
thf(283,axiom,
! [A: name,B: pi,C: pi] :
( ( fresh @ name @ pi @ A @ ( sum @ B @ C ) )
= ( ( fresh @ name @ pi @ A @ B )
& ( fresh @ name @ pi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_pi_Ofresh_I7_J) ).
thf(1296,plain,
! [A: name,B: pi,C: pi] :
( ( fresh @ name @ pi @ A @ ( sum @ B @ C ) )
= ( ( fresh @ name @ pi @ A @ B )
& ( fresh @ name @ pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',fact_228_resCasesB) ).
thf(830,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)],[167]) ).
thf(62,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(461,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_le__fun__def) ).
thf(493,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',fact_82_splice_Oinduct) ).
thf(1027,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)],[209]) ).
thf(241,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ B @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_Strong__Late__Sim_Oreflexive) ).
thf(1128,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ B @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',fact_195_transitions_OResB) ).
thf(742,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)],[136]) ).
thf(227,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] : ( perm @ TA @ $o @ A @ $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_true__eqvt) ).
thf(1089,plain,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] : ( perm @ TA @ $o @ A @ $true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',fact_118_eqvt__def) ).
thf(874,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)],[172]) ).
thf(275,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/sandbox/benchmark/theBenchmark.p',fact_30_map__tailrec__rev_Ocases) ).
thf(1259,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)],[275]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',fact_188_simE_I1_J) ).
thf(1017,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)],[206]) ).
thf(235,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_min__list_Ocases) ).
thf(1111,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)],[235]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cp_name_name @ TB )
& ( cp_name_name @ TA ) )
=> ( cp_name_name @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Agent_Ocp__name__name_22) ).
thf(725,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)],[130]) ).
thf(230,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/sandbox/benchmark/theBenchmark.p',fact_240_pi_Operm_I4_J) ).
thf(1096,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)],[230]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(388,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_shift__def) ).
thf(869,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',fact_38_swap__simps_I2_J) ).
thf(610,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)],[102]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',fact_104_imp__eqvt) ).
thf(783,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)],[149]) ).
thf(80,axiom,
cp_name_name @ late_freeRes,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_25) ).
thf(499,plain,
cp_name_name @ late_freeRes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',fact_16_old_Oprod_Oinject) ).
thf(989,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)],[196]) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',fact_63_perm__compose) ).
thf(857,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)],[168]) ).
thf(68,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_le__cases) ).
thf(471,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',fact_227_resCases_H) ).
thf(884,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)],[177]) ).
thf(17,axiom,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( sum @ A @ B )
= ( sum @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_pi_Oinject_I6_J) ).
thf(339,plain,
! [A: pi,B: pi,C: pi,D: pi] :
( ( ( sum @ A @ B )
= ( sum @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(257,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/sandbox/benchmark/theBenchmark.p',fact_71_list__nonempty__induct) ).
thf(1182,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)],[257]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_old_Oprod_Oexhaust) ).
thf(526,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)],[91]) ).
thf(110,axiom,
! [A: name,B: name,C: pi,D: name,E: name,F: pi] :
~ ( late_transitions @ ( input @ A @ B @ C ) @ ( late_BoundR @ ( late_BoundOutputS @ D ) @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_inputBoundOutputTrans) ).
thf(637,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)],[110]) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',fact_119_perm__prod_Osimps) ).
thf(1075,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)],[223]) ).
thf(70,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_subset__eq) ).
thf(476,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(231,axiom,
! [A: late_subject_Rep] :
( ( perm @ name @ late_subject_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_subject__perm__empty) ).
thf(1099,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)],[231]) ).
thf(246,axiom,
! [A: pi,B: late_freeRes,C: pi,D: name] :
( ( late_transitions @ A @ ( late_FreeR @ B @ C ) )
=> ( ( fresh @ name @ pi @ D @ A )
=> ( fresh @ name @ pi @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_freshFreeDerivative_I2_J) ).
thf(1150,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)],[246]) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',fact_97_old_Oprod_Orec) ).
thf(1131,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)],[242]) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',fact_230_simulation__def) ).
thf(1002,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)],[200]) ).
thf(289,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id @ TA ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_IdD) ).
thf(1324,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id @ TA ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(236,axiom,
late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_Aa_091x_093_A_092_060prec_062_AP_H_092_060close_062) ).
thf(1114,plain,
late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(260,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/sandbox/benchmark/theBenchmark.p',fact_229_resSimCases) ).
thf(1202,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)],[260]) ).
thf(226,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/sandbox/benchmark/theBenchmark.p',fact_64_perm__bij) ).
thf(1086,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)],[226]) ).
thf(268,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_neq__Nil__conv) ).
thf(1241,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)],[268]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_58_prod__cases) ).
thf(633,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)],[109]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',fact_115_if__eqvt) ).
thf(805,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)],[157]) ).
thf(12,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_le__cases3) ).
thf(311,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(146,axiom,
! [A: name,B: pi] : ( fresh @ name @ pi @ A @ ( res @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_freshRes) ).
thf(773,plain,
! [A: name,B: pi] : ( fresh @ name @ pi @ A @ ( res @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',fact_74_remdups__adj_Oinduct) ).
thf(662,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)],[117]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',fact_41_old_Oprod_Oinducts) ).
thf(718,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)],[128]) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',fact_225_simE_I2_J) ).
thf(750,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)],[139]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',fact_10_perm__swap_I2_J) ).
thf(1251,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)],[272]) ).
thf(261,axiom,
! [A: pi,B: late_subject,C: name,D: pi,E: name] :
( ( late_transitions @ A @ ( late_BoundR @ B @ C @ D ) )
=> ( ( fresh @ name @ pi @ E @ A )
=> ( ( E != C )
=> ( fresh @ name @ pi @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_freshBoundDerivative_I2_J) ).
thf(1219,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)],[261]) ).
thf(164,axiom,
( a
= ( late_BoundOutputS @ aa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cOpen_Ohyps_I3_J) ).
thf(824,plain,
( a
= ( late_BoundOutputS @ aa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(161,axiom,
fresh @ name @ pi @ y @ p2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__092_060open_062y_A_092_060sharp_062_AP_H_092_060close_062) ).
thf(819,plain,
fresh @ name @ pi @ y @ p2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(190,axiom,
aa != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_cOpen_Ohyps_I2_J) ).
thf(975,plain,
aa != x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(48,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Collect__mono) ).
thf(423,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',fact_92_fresh__prod) ).
thf(1125,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)],[240]) ).
thf(1,conjecture,
strong2129052853vative @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( strong2129052853vative @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(291,plain,
~ ( strong2129052853vative @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',fact_77_transpose_Ocases) ).
thf(826,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)],[165]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',fact_120_cons__eqvt) ).
thf(711,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)],[126]) ).
thf(274,axiom,
! [A: pi,B: set @ ( product_prod @ pi @ pi ),C: pi,D: set @ ( product_prod @ pi @ pi ),E: list @ ( product_prod @ name @ name )] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ B @ D )
=> ( ( eqvt @ pi @ D )
=> ( strong743114133lation @ ( perm @ name @ pi @ E @ A ) @ D @ ( perm @ name @ pi @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_eqvtI) ).
thf(1256,plain,
! [A: pi,B: set @ ( product_prod @ pi @ pi ),C: pi,D: set @ ( product_prod @ pi @ pi ),E: list @ ( product_prod @ name @ name )] :
( ( strong743114133lation @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ B @ D )
=> ( ( eqvt @ pi @ D )
=> ( strong743114133lation @ ( perm @ name @ pi @ E @ A ) @ D @ ( perm @ name @ pi @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(263,axiom,
! [A: name,B: name,C: name,D: pi,E: name,F: name,G: pi] :
~ ( late_transitions @ ( res @ A @ ( input @ B @ C @ D ) ) @ ( late_BoundR @ ( late_BoundOutputS @ E ) @ F @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_resInputBoundOutputTrans) ).
thf(1226,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)],[263]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',fact_217_ResF) ).
thf(545,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)],[98]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_ord__eq__le__subst) ).
thf(445,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(286,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/sandbox/benchmark/theBenchmark.p',fact_32_arg__min__list_Ocases) ).
thf(1312,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)],[286]) ).
thf(79,axiom,
pt_name @ late_residual_Rep,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_39) ).
thf(498,plain,
pt_name @ late_residual_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',fact_204_alphaBoundResidual) ).
thf(1058,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)],[218]) ).
thf(64,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_11) ).
thf(466,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(15,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_in__mono) ).
thf(335,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(96,axiom,
! [TA: $tType,A: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( id @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_IdI) ).
thf(540,plain,
! [TA: $tType,A: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( id @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',fact_237_residual__Rep_Oinject_I2_J) ).
thf(391,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)],[35]) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',fact_206_simCasesCont) ).
thf(1139,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)],[245]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',fact_53_prod__cases6) ).
thf(979,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)],[192]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',fact_50_prod__induct4) ).
thf(681,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)],[119]) ).
thf(174,axiom,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ x @ p2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181__092_060open_062_060_092_060nu_062x_062_IP_A_092_060oplus_062_AQ_J_A_092_060longmapsto_062_Aa_060_092_060nu_062x_062_A_092_060prec_062_AP_H_092_060close_062) ).
thf(880,plain,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ x @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(239,axiom,
! [A: pi,B: name,C: name,D: pi] :
( ( late_transitions @ A @ ( late_FreeR @ ( late_OutputR @ B @ C ) @ D ) )
=> ( ( B != C )
=> ( late_transitions @ ( res @ C @ A ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Open) ).
thf(1122,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)],[239]) ).
thf(255,axiom,
! [TA: $tType] :
( ( perm @ TA @ $o )
= ( ^ [A: list @ ( product_prod @ TA @ TA ),B: $o] : B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_perm__bool__def) ).
thf(1175,plain,
! [TA: $tType] :
( ( perm @ TA @ $o )
= ( ^ [A: list @ ( product_prod @ TA @ TA ),B: $o] : B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(204,axiom,
! [A: pi,B: pi,C: late_subject,D: name,E: set @ ( product_prod @ pi @ pi ),F: set @ ( product_prod @ pi @ pi )] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ E @ F )
=> ( strong2129052853vative @ A @ B @ C @ D @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_derivativeMonotonic) ).
thf(1011,plain,
! [A: pi,B: pi,C: late_subject,D: name,E: set @ ( product_prod @ pi @ pi ),F: set @ ( product_prod @ pi @ pi )] :
( ( strong2129052853vative @ A @ B @ C @ D @ E )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ E @ F )
=> ( strong2129052853vative @ A @ B @ C @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(46,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Late__Semantics_OfreeRes_Oinject) ).
thf(419,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)],[46]) ).
thf(29,axiom,
! [TA: $tType] :
( ( fs_name @ TA )
=> ( fs_name @ ( list @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Agent_Ofs__name_16) ).
thf(377,plain,
! [TA: $tType] :
( ( fs_name @ TA )
=> ( fs_name @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(198,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id @ TA ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_pair__in__Id__conv) ).
thf(996,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id @ TA ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',fact_39_swap__simps_I3_J) ).
thf(758,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)],[141]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',fact_22_perm__fresh__fresh) ).
thf(535,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)],[94]) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',fact_210_freeRes_Operm_I1_J) ).
thf(816,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)],[160]) ).
thf(155,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: set @ TA,C: set @ TA] :
( ( perm @ name @ $o @ A @ ( ord_less_eq @ ( set @ TA ) @ B @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ ( perm @ name @ ( set @ TA ) @ A @ B ) @ ( perm @ name @ ( set @ TA ) @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_subseteq__eqvt) ).
thf(799,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: list @ ( product_prod @ name @ name ),B: set @ TA,C: set @ TA] :
( ( perm @ name @ $o @ A @ ( ord_less_eq @ ( set @ TA ) @ B @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ ( perm @ name @ ( set @ TA ) @ A @ B ) @ ( perm @ name @ ( set @ TA ) @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(88,axiom,
cp_name_name @ late_subject,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_28) ).
thf(520,plain,
cp_name_name @ late_subject,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(207,axiom,
y != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062) ).
thf(1022,plain,
y != x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(282,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/sandbox/benchmark/theBenchmark.p',fact_76_remdups__adj_Ocases) ).
thf(1293,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)],[282]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',fact_54_prod__cases5) ).
thf(811,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)],[158]) ).
thf(33,axiom,
cp_name_name @ late_freeRes_Rep,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_34) ).
thf(387,plain,
cp_name_name @ late_freeRes_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_subset__iff) ).
thf(367,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',fact_51_prod__induct3) ).
thf(552,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)],[100]) ).
thf(194,axiom,
! [TA: $tType,TB: $tType,A: list @ ( product_prod @ TB @ TB )] :
( ( perm @ TB @ ( list @ TA ) @ A @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_nil__eqvt) ).
thf(983,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)],[194]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA,C: set @ TB] :
( ( supports @ TB @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TB ) @ A @ C )
=> ( supports @ TB @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_supports__subset) ).
thf(399,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA,C: set @ TB] :
( ( supports @ TB @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TB ) @ A @ C )
=> ( supports @ TB @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(184,axiom,
late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_BoundR @ a @ y @ pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Bound_Ohyps_I1_J) ).
thf(959,plain,
late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_BoundR @ a @ y @ pq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(148,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/sandbox/benchmark/theBenchmark.p',fact_28_fresh__eqvt) ).
thf(780,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)],[148]) ).
thf(6,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_order__refl) ).
thf(299,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',fact_121_fresh__prodD_I1_J) ).
thf(1102,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)],[232]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',fact_78_shuffles_Oinduct) ).
thf(685,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)],[120]) ).
thf(89,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_ord__eq__le__trans) ).
thf(521,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(60,axiom,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_pi_Odistinct_I81_J) ).
thf(455,plain,
! [A: pi,B: pi,C: name,D: pi] :
( ( sum @ A @ B )
!= ( res @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(176,axiom,
fresh @ name @ pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Bound_Ohyps_I3_J) ).
thf(883,plain,
fresh @ name @ pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(36,axiom,
cp_name_name @ late_residual_Rep,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_38) ).
thf(394,plain,
cp_name_name @ late_residual_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(195,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_list_Odistinct_I1_J) ).
thf(986,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(83,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_linear) ).
thf(505,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(54,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_subsetD) ).
thf(438,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(69,axiom,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_Sum2) ).
thf(473,plain,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(129,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/sandbox/benchmark/theBenchmark.p',fact_213_residual_Ofresh_I2_J) ).
thf(722,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)],[129]) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',fact_110_pt__set__bij3) ).
thf(1034,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)],[211]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',fact_83_list__induct2_H) ).
thf(548,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)],[99]) ).
thf(28,axiom,
! [A: late_freeRes,B: pi,C: late_freeRes,D: pi] :
( ( ( late_FreeR @ A @ B )
= ( late_FreeR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_residual_Oinject_I2_J) ).
thf(374,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)],[28]) ).
thf(243,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/sandbox/benchmark/theBenchmark.p',fact_194_eqvt) ).
thf(1134,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)],[243]) ).
thf(104,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: late_subject,D: name] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong2129052853vative @ B @ B @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_derivativeReflexive) ).
thf(617,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: late_subject,D: name] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong2129052853vative @ B @ B @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(18,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_1) ).
thf(342,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_le__funI) ).
thf(355,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(163,axiom,
ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ rel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Id) ).
thf(823,plain,
ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ rel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(90,axiom,
pt_name @ late_freeRes,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes___Agent_Opt__name_26) ).
thf(525,plain,
pt_name @ late_freeRes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',fact_232_supports__def) ).
thf(690,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)],[121]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',fact_212_residual_Operm_I2_J) ).
thf(640,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)],[111]) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',fact_122_fresh__prodD_I2_J) ).
thf(1025,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)],[208]) ).
thf(171,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] :
~ ( perm @ TA @ $o @ A @ $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_perm__boolE) ).
thf(872,plain,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] :
~ ( perm @ TA @ $o @ A @ $false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(124,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Late__Semantics_Osubject_Oinject_I2_J) ).
thf(705,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',fact_66_in__eqvt) ).
thf(739,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)],[135]) ).
thf(56,axiom,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( sum @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_pi_Odistinct_I53_J) ).
thf(441,plain,
! [A: name,B: name,C: pi,D: pi,E: pi] :
( ( input @ A @ B @ C )
!= ( sum @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(27,axiom,
! [A: name,B: name,C: pi,D: name,E: pi] :
( ( input @ A @ B @ C )
!= ( res @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_pi_Odistinct_I57_J) ).
thf(370,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)],[27]) ).
thf(67,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(470,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(112,axiom,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_Late__Semantics1_Osubject_Oinject_I2_J) ).
thf(643,plain,
! [A: name,B: name] :
( ( ( late_BoundOutputS @ A )
= ( late_BoundOutputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',fact_81_induct__list012) ).
thf(1262,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)],[276]) ).
thf(266,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/sandbox/benchmark/theBenchmark.p',fact_236_perm__residual__Rep_Osimps_I2_J) ).
thf(1235,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)],[266]) ).
thf(123,axiom,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] :
~ ( perm @ TA @ $o @ A @ $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_false__eqvt) ).
thf(703,plain,
! [TA: $tType,A: list @ ( product_prod @ TA @ TA )] :
~ ( perm @ TA @ $o @ A @ $false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',fact_23_name__fresh__fresh) ).
thf(656,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)],[115]) ).
thf(103,axiom,
! [TA: $tType,A: ( list @ TA ) > $o] :
( ! [B: list @ TA] : ( A @ B )
=> ( A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_allE__Nil) ).
thf(613,plain,
! [TA: $tType,A: ( list @ TA ) > $o] :
( ! [B: list @ TA] : ( A @ B )
=> ( A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',fact_103_name__bij) ).
thf(1284,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)],[278]) ).
thf(216,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ! [A: TA] :
( ( perm @ name @ TA @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_pt__name1) ).
thf(1052,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)],[216]) ).
thf(131,axiom,
fresh @ name @ ( product_prod @ name @ ( product_prod @ pi @ pi ) ) @ y @ ( product_Pair @ name @ ( product_prod @ pi @ pi ) @ x @ ( product_Pair @ pi @ pi @ p @ q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Bound_Ohyps_I5_J) ).
thf(727,plain,
fresh @ name @ ( product_prod @ name @ ( product_prod @ pi @ pi ) ) @ y @ ( product_Pair @ name @ ( product_prod @ pi @ pi ) @ x @ ( product_Pair @ pi @ pi @ p @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(191,axiom,
fresh @ name @ late_subject @ y @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Bound_Ohyps_I4_J) ).
thf(978,plain,
fresh @ name @ late_subject @ y @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',fact_65_perm__app) ).
thf(1008,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)],[203]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',fact_35_shuffles_Ocases) ).
thf(627,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)],[107]) ).
thf(288,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/sandbox/benchmark/theBenchmark.p',fact_218_resCasesF_H) ).
thf(1316,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)],[288]) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',fact_226_resCasesB_H) ).
thf(556,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)],[101]) ).
thf(73,axiom,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Late__Semantics1_Osubject_Oinject_I1_J) ).
thf(482,plain,
! [A: name,B: name] :
( ( ( late_InputS @ A )
= ( late_InputS @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',fact_73_arg__min__list_Oinduct) ).
thf(1157,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)],[248]) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',fact_8_name__swap__bij) ).
thf(1108,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)],[234]) ).
thf(277,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/sandbox/benchmark/theBenchmark.p',fact_231_simCases) ).
thf(1276,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)],[277]) ).
thf(219,axiom,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_product__lists_Osimps_I1_J) ).
thf(1062,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)],[219]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',fact_238_alphaInput) ).
thf(652,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)],[114]) ).
thf(39,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_equalityD2) ).
thf(401,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(269,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/sandbox/benchmark/theBenchmark.p',fact_107_disj__eqvt) ).
thf(1244,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)],[269]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',fact_221_freshFreeDerivative_I1_J) ).
thf(963,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)],[186]) ).
thf(87,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_subset__antisym) ).
thf(517,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',fact_219_resCasesF) ).
thf(731,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)],[134]) ).
thf(45,axiom,
pt_name @ late_residual,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_Oresidual___Agent_Opt__name_32) ).
thf(418,plain,
pt_name @ late_residual,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',fact_185_freshBoundDerivative_I1_J) ).
thf(786,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)],[150]) ).
thf(85,axiom,
! [A: late_subject,B: name,C: pi,D: late_freeRes,E: pi] :
( ( late_BoundR @ A @ B @ C )
!= ( late_FreeR @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_residual_Odistinct_I1_J) ).
thf(510,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)],[85]) ).
thf(285,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/sandbox/benchmark/theBenchmark.p',fact_14_list_Oinject) ).
thf(1309,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)],[285]) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',fact_106_conj__eqvt) ).
thf(1161,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)],[249]) ).
thf(51,axiom,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_Sum1) ).
thf(432,plain,
! [A: pi,B: late_residual,C: pi] :
( ( late_transitions @ A @ B )
=> ( late_transitions @ ( sum @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(42,axiom,
! [A: late_residual > $o,B: late_residual] :
( ! [C: late_subject,D: name,E: pi] : ( A @ ( late_BoundR @ C @ D @ E ) )
=> ( ! [C: late_freeRes,D: pi] : ( A @ ( late_FreeR @ C @ D ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_residual_Oinducts) ).
thf(410,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)],[42]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',fact_123_fresh__list__cons) ).
thf(1229,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)],[264]) ).
thf(40,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Collect__mono__iff) ).
thf(405,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(199,axiom,
! [A: late_freeRes_Rep] :
( ( perm @ name @ late_freeRes_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_freeRes__perm__empty) ).
thf(999,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)],[199]) ).
thf(105,axiom,
! [A: list @ ( product_prod @ name @ name ),B: pi,C: pi] :
( ( perm @ name @ pi @ A @ ( sum @ B @ C ) )
= ( sum @ ( perm @ name @ pi @ A @ B ) @ ( perm @ name @ pi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_pi_Operm_I7_J) ).
thf(620,plain,
! [A: list @ ( product_prod @ name @ name ),B: pi,C: pi] :
( ( perm @ name @ pi @ A @ ( sum @ B @ C ) )
= ( sum @ ( perm @ name @ pi @ A @ B ) @ ( perm @ name @ pi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(47,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(422,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(271,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/sandbox/benchmark/theBenchmark.p',fact_36_splice_Ocases) ).
thf(1248,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)],[271]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',fact_34_sorted__wrt_Ocases) ).
thf(790,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)],[152]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cp_name_name @ TB )
& ( cp_name_name @ TA ) )
=> ( cp_name_name @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Agent_Ocp__name__name) ).
thf(305,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)],[8]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_ord__le__eq__subst) ).
thf(326,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(294,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)],[4]) ).
thf(23,axiom,
! [A: name,B: name,C: name,D: name] :
( ( ( late_OutputR @ A @ B )
= ( late_OutputR @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_Late__Semantics1_OfreeRes_Oinject) ).
thf(358,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)],[23]) ).
thf(53,axiom,
pt_name @ pi_Rep,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Opi__Rep___Agent_Opt__name_21) ).
thf(437,plain,
pt_name @ pi_Rep,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(280,axiom,
! [TA: $tType,TB: $tType] :
( ( ( fs_name @ TB )
& ( fs_name @ TA ) )
=> ( fs_name @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Agent_Ofs__name_24) ).
thf(1288,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)],[280]) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',fact_250_name__calc_I1_J) ).
thf(960,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)],[185]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',fact_136_pi_Operm_I9_J) ).
thf(1165,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)],[251]) ).
thf(182,axiom,
eqvt @ pi @ rel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Eqvt) ).
thf(955,plain,
eqvt @ pi @ rel,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(154,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi,D: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ ( sum @ ( sum @ B @ C ) @ D ) @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_sumAssocLeft) ).
thf(796,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: pi,C: pi,D: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ ( sum @ ( sum @ B @ C ) @ D ) @ A @ ( sum @ B @ ( sum @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(43,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_8) ).
thf(415,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(254,axiom,
! [A: late_residual_Rep] :
( ( perm @ name @ late_residual_Rep @ ( nil @ ( product_prod @ name @ name ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_residual__perm__empty) ).
thf(1172,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)],[254]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_surj__pair) ).
thf(767,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)],[144]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',fact_67_eq__eqvt) ).
thf(532,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)],[93]) ).
thf(220,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ B @ A @ ( sum @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_sumIdempLeft) ).
thf(1065,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( strong743114133lation @ B @ A @ ( sum @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(132,axiom,
cp_name_name @ pi,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Opi___Agent_Ocp__name__name_6) ).
thf(728,plain,
cp_name_name @ pi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(63,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_subset__trans) ).
thf(464,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(49,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_subset__refl) ).
thf(427,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',fact_249_inputCases) ).
thf(860,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)],[169]) ).
thf(61,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( pt_name @ ( list @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Agent_Opt__name_15) ).
thf(459,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( pt_name @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',fact_178_alphaRes) ).
thf(992,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)],[197]) ).
thf(284,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/sandbox/benchmark/theBenchmark.p',fact_85_list_Oinducts) ).
thf(1299,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)],[284]) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',fact_56_prod__cases3) ).
thf(1093,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)],[229]) ).
thf(37,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_subsetI) ).
thf(395,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(193,axiom,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ y @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_calculation) ).
thf(982,plain,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ y @ ( perm @ name @ pi @ ( cons @ ( product_prod @ name @ name ) @ ( product_Pair @ name @ name @ y @ x ) @ ( nil @ ( product_prod @ name @ name ) ) ) @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(201,axiom,
pt_name @ name,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Agent_Oname___Agent_Opt__name_18) ).
thf(1004,plain,
pt_name @ name,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(75,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_linorder__wlog) ).
thf(486,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(16,axiom,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( pt_name @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Agent_Opt__name_5) ).
thf(337,plain,
! [TA: $tType] :
( ( pt_name @ TA )
=> ( pt_name @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',fact_62_name__perm__compose) ).
thf(755,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)],[140]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',fact_7_name__swap) ).
thf(708,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)],[125]) ).
thf(11,axiom,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_sumCases_H) ).
thf(309,plain,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(116,axiom,
! [A: set @ ( product_prod @ pi @ pi ),B: name,C: pi,D: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( ( eqvt @ pi @ A )
=> ( strong743114133lation @ ( sum @ ( res @ B @ C ) @ ( res @ B @ D ) ) @ A @ ( res @ B @ ( sum @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_sumResLeft) ).
thf(659,plain,
! [A: set @ ( product_prod @ pi @ pi ),B: name,C: pi,D: pi] :
( ( ord_less_eq @ ( set @ ( product_prod @ pi @ pi ) ) @ ( id @ pi ) @ A )
=> ( ( eqvt @ pi @ A )
=> ( strong743114133lation @ ( sum @ ( res @ B @ C ) @ ( res @ B @ D ) ) @ A @ ( res @ B @ ( sum @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(212,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/sandbox/benchmark/theBenchmark.p',fact_37_swap__simps_I1_J) ).
thf(1037,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)],[212]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',fact_224_residual_Ostrong__induct) ).
thf(775,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)],[147]) ).
thf(78,axiom,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_sumCases) ).
thf(496,plain,
! [A: pi,B: pi,C: late_residual] :
( ( late_transitions @ ( sum @ A @ B ) @ C )
=> ( ~ ( late_transitions @ A @ C )
=> ( late_transitions @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(59,axiom,
fs_name @ late_freeRes,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_27) ).
thf(454,plain,
fs_name @ late_freeRes,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',fact_6_name__id) ).
thf(1014,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)],[205]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',fact_96_derivativeEqvtI2) ).
thf(972,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)],[189]) ).
thf(1337,plain,
$false,
inference(e,[status(thm)],[365,1168,479,347,1031,1315,941,481,1083,468,408,762,1005,1290,1068,308,379,440,1078,384,1137,500,1164,747,945,538,814,1327,829,1196,1046,301,1254,1055,1287,504,357,949,542,802,344,1247,969,770,1115,1232,881,416,492,789,1040,623,646,485,514,966,766,1169,877,956,1119,1104,507,1072,453,307,292,678,529,793,1199,1153,381,714,334,1223,820,297,429,729,1238,746,1091,1042,952,693,630,467,361,435,1178,1296,830,461,493,1027,1128,742,1089,874,1259,1017,1111,725,1096,388,869,610,783,499,989,857,471,884,339,1182,526,637,1075,476,1099,1150,1131,1002,1324,1114,1202,1086,1241,633,805,311,773,662,718,750,1251,1219,824,819,975,423,1125,291,826,711,1256,1226,545,445,1312,498,1058,466,335,540,391,1139,979,681,880,1122,1175,1011,419,377,996,758,535,816,799,520,1022,1293,811,387,367,552,983,399,959,780,299,1102,685,521,455,883,394,986,505,438,473,722,1034,548,374,1134,617,342,355,823,525,690,640,1025,872,705,739,441,370,470,643,1262,1235,703,656,613,1284,1052,727,978,1008,627,1316,556,482,1157,1108,1276,1062,652,401,1244,963,517,731,418,786,510,1309,1161,432,410,1229,405,999,620,422,1248,790,305,326,294,358,437,1288,960,1165,955,796,415,1172,767,532,1065,728,464,427,860,459,992,1299,1093,395,982,1004,486,337,755,708,309,659,1037,775,496,454,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP182^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 20:03:22 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.65/0.50 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/0.79 % [INFO] Parsing done (290ms).
% 1.94/0.80 % [INFO] Running in sequential loop mode.
% 2.37/1.00 % [INFO] eprover registered as external prover.
% 2.37/1.01 % [INFO] Scanning for conjecture ...
% 2.92/1.11 % [INFO] Found a conjecture (or negated_conjecture) and 304 axioms. Running axiom selection ...
% 3.70/1.22 % [INFO] Axiom selection finished. Selected 288 axioms (removed 16 axioms).
% 4.95/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 5.33/1.61 % [INFO] Type checking passed.
% 5.33/1.62 % [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 ...
% 78.49/53.61 % External prover 'e' found a proof!
% 78.49/53.61 % [INFO] Killing All external provers ...
% 78.49/53.61 % Time passed: 53322ms (effective reasoning time: 52803ms)
% 78.49/53.61 % 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)>
% 78.49/53.61 % Axioms used in derivation (288): fact_114_allE__Nil, fact_243_pi_Odistinct_I57_J, fact_196_monotonic, tcon_Set_Oset___Agent_Ocp__name__name_2, fact_30_map__tailrec__rev_Ocases, fact_99_Bound_Ohyps_I5_J, fact_22_perm__fresh__fresh, tcon_Agent_Oname___Agent_Ocp__name__name_17, fact_202_sumSym, fact_128_Bound_Ohyps_I3_J, fact_238_alphaInput, fact_183_cSum1_Ohyps, fact_201_sumAssocLeft, fact_42_old_Oprod_Oexhaust, fact_59_surj__pair, fact_252_subject_Ofresh_I1_J, fact_175_subset__trans, tcon_Agent_Opi___Agent_Ofs__name, fact_91_IdI, tcon_Late__Semantics_Oresidual___Agent_Ofs__name_33, fact_168_equalityE, fact_105_neg__eqvt, fact_240_pi_Operm_I4_J, fact_190_Sum1, fact_61_cp__name__name1, tcon_List_Olist___Agent_Ocp__name__name_14, fact_56_prod__cases3, fact_188_simE_I1_J, fact_21_subject_Operm_I2_J, fact_217_ResF, fact_140_le__funD, tcon_Late__Semantics_OfreeRes___Agent_Ofs__name_27, fact_205_cOpen_Ohyps_I1_J, fact_9_pt__name1, fact_244_inputFreeTrans, fact_120_cons__eqvt, fact_181__092_060open_062_060_092_060nu_062x_062_IP_A_092_060oplus_062_AQ_J_A_092_060longmapsto_062_Aa_060_092_060nu_062x_062_A_092_060prec_062_AP_H_092_060close_062, tcon_Late__Semantics_Osubject___Agent_Opt__name_29, tcon_Late__Semantics_Osubject___Agent_Ocp__name__name_28, tcon_fun___Orderings_Oord, fact_17_residual__perm__empty, fact_133_name__fresh, tcon_fun___Agent_Ocp__name__name, tcon_Agent_Oname___Agent_Ofs__name_19, fact_207__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_Aa_091x_093_A_092_060prec_062_AP_H_092_060close_062, fact_101_false__eqvt, fact_70_map__tailrec__rev_Oinduct, fact_49_prod__induct5, fact_214_residual_Odistinct_I1_J, fact_79_min__list_Oinduct, fact_206_simCasesCont, fact_53_prod__cases6, fact_93__092_060open_062y_A_092_060sharp_062_AP_092_060close_062, tcon_Product__Type_Oprod___Agent_Ofs__name_24, fact_38_swap__simps_I2_J, fact_247_inputIneqTrans, fact_11_Late__Semantics_Osubject_Oinject_I2_J, fact_3__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062, tcon_HOL_Obool___Orderings_Olinorder, tcon_Late__Semantics_OfreeRes__Rep___Agent_Opt__name_35, fact_5_perm__swap_I1_J, fact_174_Collect__mono, fact_67_eq__eqvt, fact_60_not__Cons__self2, fact_198_sumIdempRight, fact_143_le__fun__def, tcon_HOL_Obool___Orderings_Oord_11, fact_107_disj__eqvt, fact_185_freshBoundDerivative_I1_J, fact_199_sumAssocRight, fact_218_resCasesF_H, tcon_Late__Semantics_Oresidual__Rep___Agent_Ocp__name__name_38, fact_254_Late__Semantics_Osubject_Odistinct_I1_J, fact_126_derivativeMonotonic, fact_134_pi_Ofresh_I7_J, fact_233_IdD, fact_14_list_Oinject, fact_246_inputBoundOutputTrans, fact_146_ord__eq__le__subst, fact_122_fresh__prodD_I2_J, fact_65_perm__app, fact_192_sumCases, fact_109_perm__boolI, fact_46_Collect__mem__eq, fact_241_resTrans_I2_J, tcon_Late__Semantics_OfreeRes___Agent_Opt__name_26, fact_35_shuffles_Ocases, fact_26_fresh__perm__app, fact_158_ord__le__eq__trans, fact_32_arg__min__list_Ocases, fact_97_old_Oprod_Orec, fact_66_in__eqvt, fact_173_subset__refl, fact_131_subsetI, fact_28_fresh__eqvt, tcon_Late__Semantics_OfreeRes__Rep___Agent_Ocp__name__name_34, fact_24_Bound_Ohyps_I4_J, fact_34_sorted__wrt_Ocases, fact_116_pt__bij3, fact_177_Collect__mono__iff, fact_235_shift__def, help_If_1_1_T, fact_88_list_Odistinct_I1_J, fact_63_perm__compose, fact_195_transitions_OResB, fact_231_simCases, fact_236_perm__residual__Rep_Osimps_I2_J, fact_82_splice_Oinduct, fact_52_prod__cases7, fact_221_freshFreeDerivative_I1_J, tcon_Agent_Opi__Rep___Agent_Opt__name_21, fact_83_list__induct2_H, fact_200_sumIdempLeft, tcon_Product__Type_Oprod___Agent_Opt__name_23, fact_222_Open, fact_250_name__calc_I1_J, fact_227_resCases_H, fact_121_fresh__prodD_I1_J, fact_170_equalityD1, fact_44_prod__induct6, fact_225_simE_I2_J, fact_245_resInputFreeTrans, fact_242_pi_Odistinct_I53_J, fact_13__092_060open_062y_A_092_060sharp_062_AP_H_092_060close_062, fact_129_Bound_Ohyps_I2_J, fact_40_fresh__aux, fact_178_alphaRes, fact_169_subset__eq, fact_7_name__swap, fact_23_name__fresh__fresh, fact_208_Late__Semantics1_OfreeRes_Oinject, fact_58_prod__cases, fact_209_Late__Semantics_OfreeRes_Oinject, fact_45_mem__Collect__eq, fact_57_Pair__inject, fact_132_order__refl, fact_90_pair__in__Id__conv, fact_167_subsetD, fact_239_product__lists_Osimps_I1_J, fact_117_abs__fun__if, fact_237_residual__Rep_Oinject_I2_J, fact_204_alphaBoundResidual, tcon_fun___Agent_Opt__name, fact_75_sorted__wrt_Oinduct, fact_85_list_Oinducts, tcon_Late__Semantics_Osubject___Agent_Ofs__name_30, fact_111_perm__bool__def, fact_92_fresh__prod, fact_95_derivativeEqvtI, fact_216_residual_Oinject_I2_J, fact_87_list_OdiscI, fact_187_freshBoundDerivative_I2_J, fact_203_eqvtI, tcon_HOL_Obool___Agent_Ofs__name_13, fact_108_perm__boolE, fact_81_induct__list012, fact_37_swap__simps_I1_J, fact_212_residual_Operm_I2_J, fact_251_Late__Semantics1_Osubject_Oinject_I1_J, tcon_Late__Semantics_OfreeRes___Agent_Ocp__name__name_25, fact_154_le__cases3, fact_226_resCasesB_H, fact_69_strict__sorted_Ocases, fact_47_Collect__cong, fact_29_fresh__bij, fact_98_eqvtRelI, tcon_Agent_Opi___Agent_Ocp__name__name_6, fact_115_if__eqvt, help_If_2_1_T, fact_64_perm__bij, fact_4_Eqvt, fact_194_eqvt, fact_71_list__nonempty__induct, fact_210_freeRes_Operm_I1_J, fact_230_simulation__def, fact_184_residual_Operm_I1_J, help_If_3_1_T, tcon_Late__Semantics_Oresidual__Rep___Agent_Opt__name_39, tcon_Late__Semantics_Oresidual___Agent_Opt__name_32, fact_25_subseteq__eqvt, tcon_List_Olist___Agent_Ofs__name_16, fact_141_le__funE, fact_36_splice_Ocases, fact_182_sumResLeft, fact_76_remdups__adj_Ocases, fact_10_perm__swap_I2_J, fact_213_residual_Ofresh_I2_J, fact_166_in__mono, fact_8_name__swap__bij, fact_130_subset__antisym, fact_147_ord__le__eq__subst, fact_43_prod__induct7, fact_33_successively_Ocases, fact_125_IdE, fact_16_old_Oprod_Oinject, fact_220_freshFreeDerivative_I2_J, fact_27_name__exists__fresh, fact_172_subset__iff, fact_1_cOpen_Ohyps_I2_J, fact_186_Late__Semantics_OResB, tcon_List_Olist___Agent_Opt__name_15, tcon_HOL_Obool___Agent_Opt__name_12, tcon_Agent_Opi___Agent_Opt__name_7, fact_102_subject_Ofresh_I2_J, fact_171_equalityD2, fact_80_min__list_Ocases, tcon_Late__Semantics_Osubject__Rep___Agent_Ocp__name__name_36, tcon_fun___Orderings_Opreorder, fact_137_pi_Odistinct_I81_J, tcon_Set_Oset___Agent_Opt__name_5, fact_191_sumCases_H, fact_223_residual_Ostrong__inducts, fact_176_set__eq__subset, fact_89__092_060open_062y_A_092_060sharp_062_AQ_092_060close_062, tcon_Agent_Opi__Rep___Agent_Ocp__name__name_20, fact_68_strict__sorted_Oinduct, fact_62_name__perm__compose, fact_150_linear, fact_6_name__id, fact_229_resSimCases, fact_15_prod_Oinject, fact_151_eq__refl, fact_12_Late__Semantics1_Osubject_Oinject_I2_J, tcon_Late__Semantics_Osubject__Rep___Agent_Opt__name_37, fact_232_supports__def, fact_112_nil__eqvt, fact_86_list_Oexhaust, fact_20_pi__perm__empty, tcon_Late__Semantics_Oresidual___Agent_Ocp__name__name_31, fact_142_le__funI, fact_55_prod__cases4, fact_74_remdups__adj_Oinduct, fact_160_order__trans, fact_124_subrelI, tcon_Agent_Oname___Agent_Opt__name_18, fact_249_inputCases, fact_180_Bound_Ohyps_I1_J, fact_197_Strong__Late__Sim_Oreflexive, fact_127_eqvtRelE, fact_41_old_Oprod_Oinducts, tcon_HOL_Obool___Orderings_Opreorder_8, fact_228_resCasesB, fact_31_name__calc_I2_J, fact_39_swap__simps_I3_J, fact_152_le__cases, fact_0_Id, fact_135_pi_Operm_I7_J, fact_211_freeRes_Ofresh_I1_J, fact_2_cOpen_Ohyps_I3_J, fact_248_resInputBoundOutputTrans, fact_96_derivativeEqvtI2, fact_78_shuffles_Oinduct, fact_113_fresh__list__nil, fact_157_ord__eq__le__trans, fact_73_arg__min__list_Oinduct, fact_119_perm__prod_Osimps, fact_51_prod__induct3, fact_224_residual_Ostrong__induct, fact_189_Sum2, fact_193_freshResidual, tcon_HOL_Obool___Agent_Ocp__name__name_9, fact_50_prod__induct4, fact_215_residual_Oinducts, fact_94_derivativeReflexive, fact_77_transpose_Ocases, fact_72_successively_Oinduct, fact_162_linorder__wlog, fact_104_imp__eqvt, fact_118_eqvt__def, fact_253_subject_Operm_I1_J, fact_84_neq__Nil__conv, fact_219_resCasesF, fact_100_true__eqvt, fact_139_freshRes, tcon_Product__Type_Oprod___Agent_Ocp__name__name_22, fact_123_fresh__list__cons, fact_110_pt__set__bij3, tcon_Set_Oset___Orderings_Oord_4, fact_18_subject__perm__empty, fact_103_name__bij, fact_179_calculation, fact_54_prod__cases5, fact_136_pi_Operm_I9_J, fact_138_pi_Oinject_I6_J, tcon_Set_Oset___Orderings_Opreorder_1, fact_106_conj__eqvt, fact_19_freeRes__perm__empty, fact_234_supports__subset
% 78.49/53.61 % No. of inferences in proof: 580
% 78.49/53.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 53322 ms resp. 52803 ms w/o parsing
% 79.94/53.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 79.94/53.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------