%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW522_5 : TPTP v9.3.1. Released v6.0.0.
% 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 : n005.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 : Sun Sep 27 09:10:44 AM UTC 2026
% Result : Theorem 9.33s 4.07s
% Output : Refutation 10.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 102
% Syntax : Number of formulae : 206 ( 121 unt; 0 typ; 0 def)
% Number of atoms : 553 ( 218 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 3999 ( 100 ~; 6 |; 39 &;3702 @)
% ( 13 <=>; 139 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 37 usr; 8 con; 0-10 aty)
% Number of variables : 861 ( 0 ^; 857 !; 4 ?; 861 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(com_type,type,
com: $tType ).
thf(loc_type,type,
loc: $tType ).
thf(pname_type,type,
pname: $tType ).
thf(state_type,type,
state: $tType ).
thf(vname_type,type,
vname: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(wt_decl,type,
wt: com > $o ).
thf(ass_decl,type,
ass: vname > ( nat @ ( state @ fun ) ) > com ).
thf(cond_decl,type,
cond: ( bool @ ( state @ fun ) ) > com > com > com ).
thf(local_decl,type,
local: loc > ( nat @ ( state @ fun ) ) > com > com ).
thf(skip_decl,type,
skip: com ).
thf(semi_decl,type,
semi: com > com > com ).
thf(com_case_decl,type,
com_case:
!>[TA: $tType] : ( TA > ( TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ) ) > ( TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ) ) > ( TA @ ( com @ fun ) @ ( com @ fun ) ) > ( TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ) ) > ( TA @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ) ) > ( TA @ ( pname @ fun ) ) > ( TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ) ) > com > TA ) ).
thf(com_rec_decl,type,
com_rec:
!>[TA: $tType] : ( TA > ( TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ) ) > ( TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ) ) > ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) ) > ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ) ) > ( TA @ ( TA @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ) ) > ( TA @ ( pname @ fun ) ) > ( TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ) ) > com > TA ) ).
thf(com_size_decl,type,
com_size: com > nat ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(hoare_592965047valids_decl,type,
hoare_592965047valids:
!>[TA: $tType] : ( ( bool @ ( TA @ hoare_28830079triple @ fun ) ) > ( bool @ ( TA @ hoare_28830079triple @ fun ) ) > $o ) ).
thf(hoare_1841697145triple_decl,type,
hoare_1841697145triple:
!>[TA: $tType] : ( ( bool @ ( state @ fun ) @ ( TA @ fun ) ) > com > ( bool @ ( state @ fun ) @ ( TA @ fun ) ) > ( TA @ hoare_28830079triple ) ) ).
thf(hoare_376461865e_case_decl,type,
hoare_376461865e_case:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) ) > ( TB @ hoare_28830079triple ) > TA ) ).
thf(hoare_678420151le_rec_decl,type,
hoare_678420151le_rec:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) ) > ( TB @ hoare_28830079triple ) > TA ) ).
thf(hoare_47506394e_size_decl,type,
hoare_47506394e_size:
!>[TA: $tType] : ( ( nat @ ( TA @ fun ) ) > ( TA @ hoare_28830079triple ) > nat ) ).
thf(hoare_1633586161_valid_decl,type,
hoare_1633586161_valid:
!>[TA: $tType] : ( nat > ( TA @ hoare_28830079triple ) > $o ) ).
thf(suc_decl,type,
suc: nat > nat ).
thf(nat_case_decl,type,
nat_case:
!>[TA: $tType] : ( TA > ( TA @ ( nat @ fun ) ) > nat > TA ) ).
thf(nat_rec_decl,type,
nat_rec:
!>[TA: $tType] : ( TA > ( TA @ ( TA @ fun ) @ ( nat @ fun ) ) > nat > TA ) ).
thf(semiri532925092at_aux_decl,type,
semiri532925092at_aux:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) ) > nat > TA > TA ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(evaln_decl,type,
evaln: com > state > nat > state > $o ).
thf(update_decl,type,
update: state > vname > nat > state ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(ga_decl,type,
ga: bool @ ( a @ hoare_28830079triple @ fun ) ).
thf(p_decl,type,
p: a > state > $o ).
thf(n_decl,type,
n: nat ).
thf(60,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(344,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(70,axiom,
! [TA: $tType,A: com,B: com,C: bool @ ( state @ fun ),D: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),E: TA @ ( pname @ fun ),F: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),H: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ),I: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),J: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),K: TA] :
( ( A @ ( B @ ( C @ cond ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) @ ( B @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( C @ ( G @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_com_Orecs_I5_J) ).
thf(398,plain,
! [TA: $tType,A: com,B: com,C: bool @ ( state @ fun ),D: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),E: TA @ ( pname @ fun ),F: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),H: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ),I: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),J: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),K: TA] :
( ( A @ ( B @ ( C @ cond ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) @ ( B @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( C @ ( G @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(85,axiom,
! [A: com,B: state,C: nat,D: com,E: state,F: bool @ ( state @ fun )] :
( ~ ( E @ ( F @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( E @ ( D @ evaln ) ) ) )
=> ( B @ ( C @ ( E @ ( D @ ( A @ ( F @ cond ) ) @ evaln ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_evaln_OIfFalse) ).
thf(464,plain,
! [A: com,B: state,C: nat,D: com,E: state,F: bool @ ( state @ fun )] :
( ~ ( E @ ( F @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( E @ ( D @ evaln ) ) ) )
=> ( B @ ( C @ ( E @ ( D @ ( A @ ( F @ cond ) ) @ evaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(65,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Suc__inject) ).
thf(365,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(92,axiom,
! [A: state,B: nat,C: state,D: com,E: com,F: bool @ ( state @ fun )] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ cond ) ) @ evaln ) ) ) )
=> ( ( ( C @ ( F @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ~ ( A @ ( B @ ( C @ ( E @ evaln ) ) ) ) )
=> ~ ( ~ ( C @ ( F @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ~ ( A @ ( B @ ( C @ ( D @ evaln ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_evaln__elim__cases_I5_J) ).
thf(479,plain,
! [A: state,B: nat,C: state,D: com,E: com,F: bool @ ( state @ fun )] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ cond ) ) @ evaln ) ) ) )
=> ( ( ( C @ ( F @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ~ ( A @ ( B @ ( C @ ( E @ evaln ) ) ) ) )
=> ~ ( ~ ( C @ ( F @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ~ ( A @ ( B @ ( C @ ( D @ evaln ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(87,axiom,
! [TA: $tType,A: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),B: TA @ ( pname @ fun ),C: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),E: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ),F: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),G: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),H: TA] :
( ( skip @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) )
= H ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_com_Orecs_I1_J) ).
thf(468,plain,
! [TA: $tType,A: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),B: TA @ ( pname @ fun ),C: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),D: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),E: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ),F: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),G: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),H: TA] :
( ( skip @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) )
= H ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(57,axiom,
! [A: com,B: com,C: bool @ ( state @ fun ),D: com,E: nat @ ( state @ fun ),F: loc] :
( ( D @ ( E @ ( F @ local ) ) )
!= ( A @ ( B @ ( C @ cond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_com_Osimps_I36_J) ).
thf(333,plain,
! [A: com,B: com,C: bool @ ( state @ fun ),D: com,E: nat @ ( state @ fun ),F: loc] :
( ( D @ ( E @ ( F @ local ) ) )
!= ( A @ ( B @ ( C @ cond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(38,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat_Osimps_I3_J) ).
thf(249,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_678420151le_rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_triple_Orecs) ).
thf(170,plain,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_678420151le_rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(46,axiom,
! [TA: $tType,A: com,B: nat @ ( state @ fun ),C: loc,D: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),E: TA @ ( pname @ fun ),F: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),H: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ),I: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),J: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),K: TA] :
( ( A @ ( B @ ( C @ local ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( C @ ( I @ ( TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_com_Orecs_I3_J) ).
thf(276,plain,
! [TA: $tType,A: com,B: nat @ ( state @ fun ),C: loc,D: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),E: TA @ ( pname @ fun ),F: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),H: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ),I: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),J: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),K: TA] :
( ( A @ ( B @ ( C @ local ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( C @ ( I @ ( TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(28,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_nat__induct) ).
thf(202,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(78,axiom,
! [TA: $tType,A: com,B: com,C: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),D: TA @ ( pname @ fun ),E: TA @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),F: TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( com @ fun ) @ ( com @ fun ),H: TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),I: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),J: TA] :
( ( A @ ( B @ semi ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( G @ ( TA @ ( com @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( com @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_com_Osimps_I67_J) ).
thf(440,plain,
! [TA: $tType,A: com,B: com,C: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),D: TA @ ( pname @ fun ),E: TA @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),F: TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( com @ fun ) @ ( com @ fun ),H: TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),I: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),J: TA] :
( ( A @ ( B @ semi ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( G @ ( TA @ ( com @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( com @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(100,axiom,
! [A: state,B: com,C: state,D: nat,E: state,F: com] :
( ( C @ ( D @ ( E @ ( F @ evaln ) ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ evaln ) ) ) )
=> ( A @ ( D @ ( E @ ( B @ ( F @ semi ) @ evaln ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_evaln_OSemi) ).
thf(511,plain,
! [A: state,B: com,C: state,D: nat,E: state,F: com] :
( ( C @ ( D @ ( E @ ( F @ evaln ) ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ evaln ) ) ) )
=> ( A @ ( D @ ( E @ ( B @ ( F @ semi ) @ evaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_ext) ).
thf(174,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(52,axiom,
! [TA: $tType,A: com,B: nat @ ( state @ fun ),C: loc,D: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),E: TA @ ( pname @ fun ),F: TA @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),H: TA @ ( com @ fun ) @ ( com @ fun ),I: TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),J: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),K: TA] :
( ( A @ ( B @ ( C @ local ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( I @ ( TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ aa ) ) ) @ ( TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ aa ) ) ) @ ( TA @ ( com @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_com_Osimps_I66_J) ).
thf(301,plain,
! [TA: $tType,A: com,B: nat @ ( state @ fun ),C: loc,D: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),E: TA @ ( pname @ fun ),F: TA @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),H: TA @ ( com @ fun ) @ ( com @ fun ),I: TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),J: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),K: TA] :
( ( A @ ( B @ ( C @ local ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( I @ ( TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ aa ) ) ) @ ( TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ aa ) ) ) @ ( TA @ ( com @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(40,axiom,
! [A: nat @ ( state @ fun ),B: loc,C: com] :
( ( C @ wt )
=> ( C @ ( A @ ( B @ local ) ) @ wt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_WT_OLocal) ).
thf(257,plain,
! [A: nat @ ( state @ fun ),B: loc,C: com] :
( ( C @ wt )
=> ( C @ ( A @ ( B @ local ) ) @ wt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(24,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_not0__implies__Suc) ).
thf(189,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(11,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Suc__n__not__n) ).
thf(152,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(90,axiom,
skip @ wt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_WT_OSkip) ).
thf(475,plain,
skip @ wt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(79,axiom,
! [A: nat @ ( state @ fun ),B: vname] :
( skip
!= ( A @ ( B @ ass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_com_Osimps_I8_J) ).
thf(443,plain,
! [A: nat @ ( state @ fun ),B: vname] :
( skip
!= ( A @ ( B @ ass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(39,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_nat_Oexhaust) ).
thf(253,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(93,axiom,
! [A: com,B: nat @ ( state @ fun ),C: loc] :
( ( A @ ( B @ ( C @ local ) ) )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_com_Osimps_I11_J) ).
thf(485,plain,
! [A: com,B: nat @ ( state @ fun ),C: loc] :
( ( A @ ( B @ ( C @ local ) ) )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(29,axiom,
! [A: com,B: com,C: com,D: com] :
( ( ( C @ ( D @ semi ) )
= ( A @ ( B @ semi ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_com_Osimps_I3_J) ).
thf(206,plain,
! [A: com,B: com,C: com,D: com] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ semi ) )
= ( A @ ( B @ semi ) ) ) )
& ( ( ( C @ ( D @ semi ) )
= ( A @ ( B @ semi ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_add__left__cancel) ).
thf(116,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,axiom,
! [TA: $tType,A: nat,B: TA @ ( nat @ fun ),C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ nat_case ) ) ) )
= ( A @ ( B @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_nat__case__Suc) ).
thf(243,plain,
! [TA: $tType,A: nat,B: TA @ ( nat @ fun ),C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ nat_case ) ) ) )
= ( A @ ( B @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_zero__reorient) ).
thf(307,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(30,axiom,
! [A: com,B: nat @ ( state @ fun ),C: loc,D: nat @ ( state @ fun ),E: vname] :
( ( D @ ( E @ ass ) )
!= ( A @ ( B @ ( C @ local ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_com_Osimps_I22_J) ).
thf(220,plain,
! [A: com,B: nat @ ( state @ fun ),C: loc,D: nat @ ( state @ fun ),E: vname] :
( ( D @ ( E @ ass ) )
!= ( A @ ( B @ ( C @ local ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(42,axiom,
! [A: com,B: nat @ ( state @ fun ),C: loc,D: com,E: com,F: bool @ ( state @ fun )] :
( ( D @ ( E @ ( F @ cond ) ) )
!= ( A @ ( B @ ( C @ local ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_com_Osimps_I37_J) ).
thf(260,plain,
! [A: com,B: nat @ ( state @ fun ),C: loc,D: com,E: com,F: bool @ ( state @ fun )] :
( ( D @ ( E @ ( F @ cond ) ) )
!= ( A @ ( B @ ( C @ local ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(13,axiom,
! [TA: $tType,A: TA @ hoare_28830079triple,B: nat] :
( ( A @ ( B @ suc @ ( TA @ hoare_1633586161_valid ) ) )
=> ( A @ ( B @ ( TA @ hoare_1633586161_valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_triple__valid__Suc) ).
thf(160,plain,
! [TA: $tType,A: TA @ hoare_28830079triple,B: nat] :
( ( A @ ( B @ suc @ ( TA @ hoare_1633586161_valid ) ) )
=> ( A @ ( B @ ( TA @ hoare_1633586161_valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: TA @ ( TA @ fun )] :
( ( A @ ( nat @ zero_zero @ ( B @ ( TA @ semiri532925092at_aux ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_of__nat__aux_Osimps_I1_J) ).
thf(192,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: TA @ ( TA @ fun )] :
( ( A @ ( nat @ zero_zero @ ( B @ ( TA @ semiri532925092at_aux ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(15,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(165,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(32,axiom,
! [A: com,B: nat @ ( state @ fun ),C: loc] :
( ( A @ ( B @ ( C @ local ) ) @ wt )
=> ( A @ wt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_WTs__elim__cases_I3_J) ).
thf(229,plain,
! [A: com,B: nat @ ( state @ fun ),C: loc] :
( ( A @ ( B @ ( C @ local ) ) @ wt )
=> ( A @ wt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(64,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_n__not__Suc__n) ).
thf(361,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(56,axiom,
! [A: nat @ ( state @ fun ),B: vname,C: com,D: com] :
( ( C @ ( D @ semi ) )
!= ( A @ ( B @ ass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_com_Osimps_I25_J) ).
thf(329,plain,
! [A: nat @ ( state @ fun ),B: vname,C: com,D: com] :
( ( C @ ( D @ semi ) )
!= ( A @ ( B @ ass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(49,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(285,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(31,axiom,
! [A: com,B: com,C: bool @ ( state @ fun )] :
( ( A @ ( B @ ( C @ cond ) ) @ wt )
=> ~ ( ( B @ wt )
=> ~ ( A @ wt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_WTs__elim__cases_I5_J) ).
thf(224,plain,
! [A: com,B: com,C: bool @ ( state @ fun )] :
( ( A @ ( B @ ( C @ cond ) ) @ wt )
=> ~ ( ( B @ wt )
=> ~ ( A @ wt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(12,axiom,
! [TA: $tType,A: nat,B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( C @ ( A @ suc @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( C @ ( A @ ( TA @ hoare_1633586161_valid ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_triples__valid__Suc) ).
thf(156,plain,
! [TA: $tType,A: nat,B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( C @ ( A @ suc @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [C: TA @ hoare_28830079triple] :
( ( B @ ( C @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( C @ ( A @ ( TA @ hoare_1633586161_valid ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(67,axiom,
! [TA: $tType,A: nat @ ( state @ fun ),B: vname,C: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),D: TA @ ( pname @ fun ),E: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),F: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ),H: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),I: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),J: TA] :
( ( A @ ( B @ ass ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( I @ ( TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ aa ) ) ) @ ( TA @ ( nat @ ( state @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_com_Orecs_I2_J) ).
thf(388,plain,
! [TA: $tType,A: nat @ ( state @ fun ),B: vname,C: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),D: TA @ ( pname @ fun ),E: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),F: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ),H: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),I: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),J: TA] :
( ( A @ ( B @ ass ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( I @ ( TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ aa ) ) ) @ ( TA @ ( nat @ ( state @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(9,axiom,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( nat @ fun ),B: TA] :
( ( nat @ zero_zero @ ( A @ ( B @ ( TA @ nat_rec ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_nat__rec__0) ).
thf(141,plain,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( nat @ fun ),B: TA] :
( ( nat @ zero_zero @ ( A @ ( B @ ( TA @ nat_rec ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(97,axiom,
! [A: state,B: nat,C: state,D: com,E: state,F: nat,G: state,H: com] :
( ( E @ ( F @ ( G @ ( H @ evaln ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ evaln ) ) ) )
=> ? [I: nat] :
( ( A @ ( I @ ( C @ ( D @ evaln ) ) ) )
& ( E @ ( I @ ( G @ ( H @ evaln ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_evaln__max2) ).
thf(499,plain,
! [A: state,B: nat,C: state,D: com,E: state,F: nat,G: state,H: com] :
( ( E @ ( F @ ( G @ ( H @ evaln ) ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ evaln ) ) ) )
=> ? [I: nat] :
( ( A @ ( I @ ( C @ ( D @ evaln ) ) ) )
& ( E @ ( I @ ( G @ ( H @ evaln ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(91,axiom,
! [TA: $tType,A: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),B: TA @ ( pname @ fun ),C: TA @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),D: TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),E: TA @ ( com @ fun ) @ ( com @ fun ),F: TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),G: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),H: TA] :
( ( skip @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( TA @ com_case ) ) ) ) ) ) ) ) ) )
= H ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_com_Osimps_I64_J) ).
thf(476,plain,
! [TA: $tType,A: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),B: TA @ ( pname @ fun ),C: TA @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),D: TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),E: TA @ ( com @ fun ) @ ( com @ fun ),F: TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),G: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),H: TA] :
( ( skip @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( TA @ com_case ) ) ) ) ) ) ) ) ) )
= H ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(94,axiom,
! [A: com,B: state,C: nat,D: com,E: state,F: bool @ ( state @ fun )] :
( ( E @ ( F @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( E @ ( D @ evaln ) ) ) )
=> ( B @ ( C @ ( E @ ( A @ ( D @ ( F @ cond ) ) @ evaln ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_evaln_OIfTrue) ).
thf(489,plain,
! [A: com,B: state,C: nat,D: com,E: state,F: bool @ ( state @ fun )] :
( ( E @ ( F @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ( ( B @ ( C @ ( E @ ( D @ evaln ) ) ) )
=> ( B @ ( C @ ( E @ ( A @ ( D @ ( F @ cond ) ) @ evaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__right__cancel) ).
thf(109,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(88,axiom,
( ( skip @ com_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_com_Osize_I1_J) ).
thf(471,plain,
( ( skip @ com_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(18,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(173,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(98,axiom,
! [A: a @ hoare_28830079triple] :
( ( ga @ ( A @ ( a @ hoare_28830079triple @ member ) ) )
=> ( A @ ( n @ ( a @ hoare_1633586161_valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(503,plain,
! [A: a @ hoare_28830079triple] :
( ( ga @ ( A @ ( a @ hoare_28830079triple @ member ) ) )
=> ( A @ ( n @ ( a @ hoare_1633586161_valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(51,axiom,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( nat @ fun ),B: TA,C: TA @ ( nat @ fun )] :
( ! [D: nat] :
( ( D @ ( C @ ( TA @ ( nat @ aa ) ) ) )
= ( D @ ( A @ ( B @ ( TA @ nat_rec ) ) ) ) )
=> ( ( nat @ zero_zero @ ( C @ ( TA @ ( nat @ aa ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_def__nat__rec__0) ).
thf(298,plain,
! [TA: $tType,A: TA @ ( TA @ fun ) @ ( nat @ fun ),B: TA,C: TA @ ( nat @ fun )] :
( ! [D: nat] :
( ( D @ ( C @ ( TA @ ( nat @ aa ) ) ) )
= ( D @ ( A @ ( B @ ( TA @ nat_rec ) ) ) ) )
=> ( ( nat @ zero_zero @ ( C @ ( TA @ ( nat @ aa ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(16,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_mem__def) ).
thf(166,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(43,axiom,
! [A: nat @ ( state @ fun ),B: vname,C: com,D: com,E: bool @ ( state @ fun )] :
( ( C @ ( D @ ( E @ cond ) ) )
!= ( A @ ( B @ ass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_com_Osimps_I27_J) ).
thf(264,plain,
! [A: nat @ ( state @ fun ),B: vname,C: com,D: com,E: bool @ ( state @ fun )] :
( ( C @ ( D @ ( E @ cond ) ) )
!= ( A @ ( B @ ass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(47,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat_Osimps_I2_J) ).
thf(279,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(21,axiom,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( nat @ fun ),C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ nat_rec ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ nat_rec ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_nat__rec__Suc) ).
thf(180,plain,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( nat @ fun ),C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ nat_rec ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ nat_rec ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(101,axiom,
! [A: state,B: nat,C: state] :
( ( A @ ( B @ ( C @ ( skip @ evaln ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_evaln__elim__cases_I1_J) ).
thf(513,plain,
! [A: state,B: nat,C: state] :
( ( A @ ( B @ ( C @ ( skip @ evaln ) ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(75,axiom,
! [A: com,B: com] :
( ( A @ ( B @ semi ) @ wt )
=> ~ ( ( B @ wt )
=> ~ ( A @ wt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_WTs__elim__cases_I4_J) ).
thf(430,plain,
! [A: com,B: com] :
( ( A @ ( B @ semi ) @ wt )
=> ~ ( ( B @ wt )
=> ~ ( A @ wt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(73,axiom,
! [A: nat @ ( state @ fun ),B: vname] :
( ( A @ ( B @ ass ) @ com_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_com_Osize_I2_J) ).
thf(423,plain,
! [A: nat @ ( state @ fun ),B: vname] :
( ( A @ ( B @ ass ) @ com_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(41,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(259,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(68,axiom,
! [A: com,B: com] :
( ( A @ ( B @ semi ) @ com_size )
= ( nat @ zero_zero @ suc @ ( A @ com_size @ ( B @ com_size @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_com_Osize_I4_J) ).
thf(391,plain,
! [A: com,B: com] :
( ( A @ ( B @ semi ) @ com_size )
= ( nat @ zero_zero @ suc @ ( A @ com_size @ ( B @ com_size @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(10,axiom,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( A @ ( B @ ( TA @ hoare_592965047valids ) ) )
<=> ! [C: nat] :
( ! [D: TA @ hoare_28830079triple] :
( ( B @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [D: TA @ hoare_28830079triple] :
( ( A @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_hoare__valids__def) ).
thf(144,plain,
! [TA: $tType,A: bool @ ( TA @ hoare_28830079triple @ fun ),B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ( ! [C: nat] :
( ! [D: TA @ hoare_28830079triple] :
( ( B @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [D: TA @ hoare_28830079triple] :
( ( A @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) ) )
=> ( A @ ( B @ ( TA @ hoare_592965047valids ) ) ) )
& ( ( A @ ( B @ ( TA @ hoare_592965047valids ) ) )
=> ! [C: nat] :
( ! [D: TA @ hoare_28830079triple] :
( ( B @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) )
=> ! [D: TA @ hoare_28830079triple] :
( ( A @ ( D @ ( TA @ hoare_28830079triple @ member ) ) )
=> ( D @ ( C @ ( TA @ hoare_1633586161_valid ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(86,axiom,
! [A: state,B: nat,C: state,D: com] :
( ( A @ ( B @ ( C @ ( D @ evaln ) ) ) )
=> ( A @ ( B @ suc @ ( C @ ( D @ evaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_evaln__Suc) ).
thf(466,plain,
! [A: state,B: nat,C: state,D: com] :
( ( A @ ( B @ ( C @ ( D @ evaln ) ) ) )
=> ( A @ ( B @ suc @ ( C @ ( D @ evaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(81,axiom,
! [A: state,B: nat,C: state,D: nat @ ( state @ fun ),E: vname] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ass ) @ evaln ) ) ) )
=> ( A
= ( C @ ( D @ ( nat @ ( state @ aa ) ) ) @ ( E @ ( C @ update ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_evaln__elim__cases_I2_J) ).
thf(451,plain,
! [A: state,B: nat,C: state,D: nat @ ( state @ fun ),E: vname] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ass ) @ evaln ) ) ) )
=> ( A
= ( C @ ( D @ ( nat @ ( state @ aa ) ) ) @ ( E @ ( C @ update ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_376461865e_case ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_triple_Osimps_I2_J) ).
thf(434,plain,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_376461865e_case ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(61,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_nat_Oinject) ).
thf(345,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ suc )
= ( A @ suc ) ) )
& ( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(103,axiom,
! [A: com,B: com,C: bool @ ( state @ fun )] :
( ( A @ ( B @ ( C @ cond ) ) )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_com_Osimps_I15_J) ).
thf(520,plain,
! [A: com,B: com,C: bool @ ( state @ fun )] :
( ( A @ ( B @ ( C @ cond ) ) )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(27,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Zero__not__Suc) ).
thf(198,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(84,axiom,
! [A: nat,B: state] : ( B @ ( A @ ( B @ ( skip @ evaln ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_evaln_OSkip) ).
thf(462,plain,
! [A: nat,B: state] : ( B @ ( A @ ( B @ ( skip @ evaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(69,axiom,
! [A: com,B: com,C: com,D: com,E: bool @ ( state @ fun )] :
( ( C @ ( D @ ( E @ cond ) ) )
!= ( A @ ( B @ semi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_com_Osimps_I45_J) ).
thf(394,plain,
! [A: com,B: com,C: com,D: com,E: bool @ ( state @ fun )] :
( ( C @ ( D @ ( E @ cond ) ) )
!= ( A @ ( B @ semi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(7,axiom,
! [A: nat @ ( state @ fun ),B: vname,C: com,D: nat @ ( state @ fun ),E: loc] :
( ( C @ ( D @ ( E @ local ) ) )
!= ( A @ ( B @ ass ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_com_Osimps_I23_J) ).
thf(135,plain,
! [A: nat @ ( state @ fun ),B: vname,C: com,D: nat @ ( state @ fun ),E: loc] :
( ( C @ ( D @ ( E @ local ) ) )
!= ( A @ ( B @ ass ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(99,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: nat] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TA @ hoare_1633586161_valid ) ) )
<=> ! [E: TA,F: state] :
( ( F @ ( E @ ( C @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ! [G: state] :
( ( G @ ( D @ ( F @ ( B @ evaln ) ) ) )
=> ( G @ ( E @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_triple__valid__def2) ).
thf(505,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: nat] :
( ( ! [E: TA,F: state] :
( ( F @ ( E @ ( C @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ! [G: state] :
( ( G @ ( D @ ( F @ ( B @ evaln ) ) ) )
=> ( G @ ( E @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) ) )
=> ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TA @ hoare_1633586161_valid ) ) ) )
& ( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TA @ hoare_1633586161_valid ) ) )
=> ! [E: TA,F: state] :
( ( F @ ( E @ ( C @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp )
=> ! [G: state] :
( ( G @ ( D @ ( F @ ( B @ evaln ) ) ) )
=> ( G @ ( E @ ( A @ ( bool @ ( state @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( state @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(89,axiom,
! [A: nat,B: state,C: nat @ ( state @ fun ),D: vname] : ( B @ ( C @ ( nat @ ( state @ aa ) ) ) @ ( D @ ( B @ update ) ) @ ( A @ ( B @ ( C @ ( D @ ass ) @ evaln ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_evaln_OAssign) ).
thf(473,plain,
! [A: nat,B: state,C: nat @ ( state @ fun ),D: vname] : ( B @ ( C @ ( nat @ ( state @ aa ) ) ) @ ( D @ ( B @ update ) ) @ ( A @ ( B @ ( C @ ( D @ ass ) @ evaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(74,axiom,
! [A: com,B: nat @ ( state @ fun ),C: loc,D: com,E: com] :
( ( D @ ( E @ semi ) )
!= ( A @ ( B @ ( C @ local ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_com_Osimps_I35_J) ).
thf(426,plain,
! [A: com,B: nat @ ( state @ fun ),C: loc,D: com,E: com] :
( ( D @ ( E @ semi ) )
!= ( A @ ( B @ ( C @ local ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(14,axiom,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( nat @ fun ),C: TA,D: TA @ ( nat @ fun )] :
( ! [E: nat] :
( ( E @ ( D @ ( TA @ ( nat @ aa ) ) ) )
= ( E @ ( B @ ( C @ ( TA @ nat_rec ) ) ) ) )
=> ( ( A @ suc @ ( D @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_def__nat__rec__Suc) ).
thf(162,plain,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( nat @ fun ),C: TA,D: TA @ ( nat @ fun )] :
( ! [E: nat] :
( ( E @ ( D @ ( TA @ ( nat @ aa ) ) ) )
= ( E @ ( B @ ( C @ ( TA @ nat_rec ) ) ) ) )
=> ( ( A @ suc @ ( D @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(102,axiom,
! [A: state,B: nat,C: state,D: com,E: com] :
( ( A @ ( B @ ( C @ ( D @ ( E @ semi ) @ evaln ) ) ) )
=> ~ ! [F: state] :
( ( F @ ( B @ ( C @ ( E @ evaln ) ) ) )
=> ~ ( A @ ( B @ ( F @ ( D @ evaln ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_evaln__elim__cases_I4_J) ).
thf(516,plain,
! [A: state,B: nat,C: state,D: com,E: com] :
( ( A @ ( B @ ( C @ ( D @ ( E @ semi ) @ evaln ) ) ) )
=> ~ ! [F: state] :
( ( F @ ( B @ ( C @ ( E @ evaln ) ) ) )
=> ~ ( A @ ( B @ ( F @ ( D @ evaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(5,axiom,
! [A: com,B: com,C: bool @ ( state @ fun ),D: com,E: com] :
( ( D @ ( E @ semi ) )
!= ( A @ ( B @ ( C @ cond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_com_Osimps_I44_J) ).
thf(123,plain,
! [A: com,B: com,C: bool @ ( state @ fun ),D: com,E: com] :
( ( D @ ( E @ semi ) )
!= ( A @ ( B @ ( C @ cond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(62,axiom,
! [A: com,B: com,C: bool @ ( state @ fun ),D: nat @ ( state @ fun ),E: vname] :
( ( D @ ( E @ ass ) )
!= ( A @ ( B @ ( C @ cond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_com_Osimps_I26_J) ).
thf(355,plain,
! [A: com,B: com,C: bool @ ( state @ fun ),D: nat @ ( state @ fun ),E: vname] :
( ( D @ ( E @ ass ) )
!= ( A @ ( B @ ( C @ cond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(83,axiom,
! [A: nat @ ( state @ fun ),B: vname] :
( ( A @ ( B @ ass ) )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_com_Osimps_I9_J) ).
thf(458,plain,
! [A: nat @ ( state @ fun ),B: vname] :
( ( A @ ( B @ ass ) )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(20,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: nat,C: TA @ ( TA @ fun )] :
( ( A @ ( B @ suc @ ( C @ ( TA @ semiri532925092at_aux ) ) ) )
= ( A @ ( C @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ semiri532925092at_aux ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_of__nat__aux_Osimps_I2_J) ).
thf(177,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: nat,C: TA @ ( TA @ fun )] :
( ( A @ ( B @ suc @ ( C @ ( TA @ semiri532925092at_aux ) ) ) )
= ( A @ ( C @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ semiri532925092at_aux ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(66,axiom,
! [A: com,B: nat @ ( state @ fun ),C: loc,D: com,E: nat @ ( state @ fun ),F: loc] :
( ( ( D @ ( E @ ( F @ local ) ) )
= ( A @ ( B @ ( C @ local ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_com_Osimps_I2_J) ).
thf(370,plain,
! [A: com,B: nat @ ( state @ fun ),C: loc,D: com,E: nat @ ( state @ fun ),F: loc] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ local ) ) )
= ( A @ ( B @ ( C @ local ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ local ) ) )
= ( A @ ( B @ ( C @ local ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_nat__add__right__cancel) ).
thf(127,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(63,axiom,
! [A: com,B: com] :
( ( B @ wt )
=> ( ( A @ wt )
=> ( A @ ( B @ semi ) @ wt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_WT_OSemi) ).
thf(359,plain,
! [A: com,B: com] :
( ( B @ wt )
=> ( ( A @ wt )
=> ( A @ ( B @ semi ) @ wt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(96,axiom,
! [A: com,B: com] :
( skip
!= ( A @ ( B @ semi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_com_Osimps_I12_J) ).
thf(495,plain,
! [A: com,B: com] :
( skip
!= ( A @ ( B @ semi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(1,conjecture,
! [A: a,B: state] :
( ! [C: state] :
( ( C @ ( A @ p ) )
| ~ ( C @ ( n @ ( B @ ( skip @ evaln ) ) ) ) )
| ~ ( B @ ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ! [A: a,B: state] :
( ! [C: state] :
( ( C @ ( A @ p ) )
| ~ ( C @ ( n @ ( B @ ( skip @ evaln ) ) ) ) )
| ~ ( B @ ( A @ p ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(104,plain,
~ ! [A: a,B: state] :
( ! [C: state] :
( ( C @ ( A @ p ) )
| ~ ( C @ ( n @ ( B @ ( skip @ evaln ) ) ) ) )
| ~ ( B @ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(53,axiom,
! [TA: $tType,A: nat @ ( state @ fun ),B: vname,C: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),D: TA @ ( pname @ fun ),E: TA @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),F: TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( com @ fun ) @ ( com @ fun ),H: TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),I: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),J: TA] :
( ( A @ ( B @ ass ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( I @ ( TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ aa ) ) ) @ ( TA @ ( nat @ ( state @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_com_Osimps_I65_J) ).
thf(304,plain,
! [TA: $tType,A: nat @ ( state @ fun ),B: vname,C: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),D: TA @ ( pname @ fun ),E: TA @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),F: TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( com @ fun ) @ ( com @ fun ),H: TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),I: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),J: TA] :
( ( A @ ( B @ ass ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( I @ ( TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ aa ) ) ) @ ( TA @ ( nat @ ( state @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(23,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: nat @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TA @ hoare_47506394e_size ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_triple_Osize_I1_J) ).
thf(186,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: nat @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TA @ hoare_47506394e_size ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(71,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Suc__not__Zero) ).
thf(401,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(8,axiom,
! [A: nat @ ( state @ fun ),B: vname] : ( A @ ( B @ ass ) @ wt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_WT_OAssign) ).
thf(139,plain,
! [A: nat @ ( state @ fun ),B: vname] : ( A @ ( B @ ass ) @ wt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(45,axiom,
! [A: com,B: com,C: nat @ ( state @ fun ),D: vname] :
( ( C @ ( D @ ass ) )
!= ( A @ ( B @ semi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_com_Osimps_I24_J) ).
thf(272,plain,
! [A: com,B: com,C: nat @ ( state @ fun ),D: vname] :
( ( C @ ( D @ ass ) )
!= ( A @ ( B @ semi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(50,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: bool @ ( state @ fun ) @ ( TA @ fun ),E: com,F: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ( ( D @ ( E @ ( F @ ( TA @ hoare_1841697145triple ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_triple_Oinject) ).
thf(287,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: bool @ ( state @ fun ) @ ( TA @ fun ),E: com,F: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ ( TA @ hoare_1841697145triple ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ ( TA @ hoare_1841697145triple ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(34,axiom,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Suc__neq__Zero) ).
thf(235,plain,
! [A: nat] :
( ( A @ suc )
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(37,axiom,
! [TA: $tType,A: TA @ ( nat @ fun ),B: TA] :
( ( nat @ zero_zero @ ( A @ ( B @ ( TA @ nat_case ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_nat__case__0) ).
thf(246,plain,
! [TA: $tType,A: TA @ ( nat @ fun ),B: TA] :
( ( nat @ zero_zero @ ( A @ ( B @ ( TA @ nat_case ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(80,axiom,
! [A: com,B: com] :
( ( A @ ( B @ semi ) )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_com_Osimps_I13_J) ).
thf(447,plain,
! [A: com,B: com] :
( ( A @ ( B @ semi ) )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(55,axiom,
! [A: nat @ ( state @ fun ),B: vname,C: nat @ ( state @ fun ),D: vname] :
( ( ( C @ ( D @ ass ) )
= ( A @ ( B @ ass ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_com_Osimps_I1_J) ).
thf(315,plain,
! [A: nat @ ( state @ fun ),B: vname,C: nat @ ( state @ fun ),D: vname] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ass ) )
= ( A @ ( B @ ass ) ) ) )
& ( ( ( C @ ( D @ ass ) )
= ( A @ ( B @ ass ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(72,axiom,
! [A: com,B: com,C: bool @ ( state @ fun ),D: com,E: com,F: bool @ ( state @ fun )] :
( ( ( D @ ( E @ ( F @ cond ) ) )
= ( A @ ( B @ ( C @ cond ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_com_Osimps_I4_J) ).
thf(405,plain,
! [A: com,B: com,C: bool @ ( state @ fun ),D: com,E: com,F: bool @ ( state @ fun )] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ cond ) ) )
= ( A @ ( B @ ( C @ cond ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ cond ) ) )
= ( A @ ( B @ ( C @ cond ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(22,axiom,
! [A: com,B: nat @ ( state @ fun ),C: loc] :
( ( A @ ( B @ ( C @ local ) ) @ com_size )
= ( nat @ zero_zero @ suc @ ( A @ com_size @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_com_Osize_I3_J) ).
thf(183,plain,
! [A: com,B: nat @ ( state @ fun ),C: loc] :
( ( A @ ( B @ ( C @ local ) ) @ com_size )
= ( nat @ zero_zero @ suc @ ( A @ com_size @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(35,axiom,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Zero__neq__Suc) ).
thf(239,plain,
! [A: nat] :
( ( nat @ zero_zero )
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(59,axiom,
! [TA: $tType,A: TA @ hoare_28830079triple] :
~ ! [B: bool @ ( state @ fun ) @ ( TA @ fun ),C: com,D: bool @ ( state @ fun ) @ ( TA @ fun )] :
( A
!= ( D @ ( C @ ( B @ ( TA @ hoare_1841697145triple ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_triple_Oexhaust) ).
thf(341,plain,
! [TA: $tType,A: TA @ hoare_28830079triple] :
~ ! [B: bool @ ( state @ fun ) @ ( TA @ fun ),C: com,D: bool @ ( state @ fun ) @ ( TA @ fun )] :
( A
!= ( D @ ( C @ ( B @ ( TA @ hoare_1841697145triple ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(44,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zero__induct) ).
thf(268,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ suc @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(26,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_triple_Osize_I2_J) ).
thf(195,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(77,axiom,
! [TA: $tType,A: com,B: com,C: bool @ ( state @ fun ),D: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),E: TA @ ( pname @ fun ),F: TA @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),H: TA @ ( com @ fun ) @ ( com @ fun ),I: TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),J: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),K: TA] :
( ( A @ ( B @ ( C @ cond ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( G @ ( TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ aa ) ) ) @ ( TA @ ( com @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( com @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_com_Osimps_I68_J) ).
thf(437,plain,
! [TA: $tType,A: com,B: com,C: bool @ ( state @ fun ),D: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),E: TA @ ( pname @ fun ),F: TA @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),H: TA @ ( com @ fun ) @ ( com @ fun ),I: TA @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),J: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),K: TA] :
( ( A @ ( B @ ( C @ cond ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( TA @ com_case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( G @ ( TA @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ aa ) ) ) @ ( TA @ ( com @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( com @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(48,axiom,
! [A: bool @ ( state @ fun ),B: com,C: com] :
( ( C @ wt )
=> ( ( B @ wt )
=> ( B @ ( C @ ( A @ cond ) ) @ wt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_WT_OIf) ).
thf(283,plain,
! [A: bool @ ( state @ fun ),B: com,C: com] :
( ( C @ wt )
=> ( ( B @ wt )
=> ( B @ ( C @ ( A @ cond ) ) @ wt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(58,axiom,
! [A: com,B: com,C: com,D: nat @ ( state @ fun ),E: loc] :
( ( C @ ( D @ ( E @ local ) ) )
!= ( A @ ( B @ semi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_com_Osimps_I34_J) ).
thf(337,plain,
! [A: com,B: com,C: com,D: nat @ ( state @ fun ),E: loc] :
( ( C @ ( D @ ( E @ local ) ) )
!= ( A @ ( B @ semi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(95,axiom,
! [A: com,B: com,C: bool @ ( state @ fun )] :
( skip
!= ( A @ ( B @ ( C @ cond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_com_Osimps_I14_J) ).
thf(491,plain,
! [A: com,B: com,C: bool @ ( state @ fun )] :
( skip
!= ( A @ ( B @ ( C @ cond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(82,axiom,
! [A: com,B: nat @ ( state @ fun ),C: loc] :
( skip
!= ( A @ ( B @ ( C @ local ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_com_Osimps_I10_J) ).
thf(454,plain,
! [A: com,B: nat @ ( state @ fun ),C: loc] :
( skip
!= ( A @ ( B @ ( C @ local ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(33,axiom,
! [TA: $tType,A: com,B: com,C: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),D: TA @ ( pname @ fun ),E: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),F: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ),H: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),I: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),J: TA] :
( ( A @ ( B @ semi ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( G @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_com_Orecs_I4_J) ).
thf(232,plain,
! [TA: $tType,A: com,B: com,C: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( pname @ fun ) @ ( vname @ fun ),D: TA @ ( pname @ fun ),E: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),F: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ fun ),G: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ fun ),H: TA @ ( TA @ fun ) @ ( com @ fun ) @ ( nat @ ( state @ fun ) @ fun ) @ ( loc @ fun ),I: TA @ ( nat @ ( state @ fun ) @ fun ) @ ( vname @ fun ),J: TA] :
( ( A @ ( B @ semi ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( TA @ com_rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( G @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( com @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(524,plain,
$false,
inference(e,[status(thm)],[344,398,464,365,479,468,333,249,170,276,202,440,511,174,301,257,189,152,475,443,253,485,206,116,243,307,220,260,160,192,165,229,361,329,285,224,156,388,141,499,476,489,109,471,173,503,298,166,264,279,180,513,430,423,259,391,144,466,451,434,345,520,198,462,394,135,505,473,426,162,516,123,355,458,177,370,127,359,495,104,304,186,401,139,272,287,235,246,447,315,405,183,239,341,268,195,437,283,337,491,454,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW522_5 : TPTP v9.3.1. Released v6.0.0.
% 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
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 16:10:46 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.40/1.29 % [INFO] Parsing done (302ms).
% 1.86/1.30 % [INFO] Running in sequential loop mode.
% 2.60/1.70 % [INFO] eprover registered as external prover.
% 2.88/1.70 % [INFO] Scanning for conjecture ...
% 3.16/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 101 axioms. Running axiom selection ...
% 3.36/1.99 % [INFO] Axiom selection finished. Selected 101 axioms (removed 0 axioms).
% 4.03/2.22 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.03/2.26 % [INFO] Type checking passed.
% 4.03/2.26 % [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 ...
% 9.33/4.06 % External prover 'e' found a proof!
% 9.33/4.06 % [INFO] Killing All external provers ...
% 9.33/4.06 % Time passed: 3524ms (effective reasoning time: 2755ms)
% 9.33/4.06 % 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)>
% 9.33/4.06 % Axioms used in derivation (101): fact_20_com_Osimps_I68_J, fact_34_triple_Oexhaust, fact_55_com_Osimps_I1_J, fact_25_WT_OSkip, fact_92_add__right__cancel, fact_2_triple__valid__def2, fact_3_evaln__max2, fact_73_nat__rec__0, fact_37_Suc__inject, arity_Nat_Onat___Rings_Osemiring__1, fact_82_def__nat__rec__0, fact_60_com_Osimps_I24_J, fact_31_nat_Oinject, fact_38_of__nat__aux_Osimps_I2_J, fact_90_com_Osize_I3_J, fact_52_com_Osimps_I66_J, fact_39_nat__case__Suc, fact_42_WTs__elim__cases_I3_J, fact_28_com_Osimps_I13_J, fact_18_com_Osimps_I67_J, fact_59_com_Osimps_I25_J, fact_50_com_Osimps_I10_J, fact_61_com_Osimps_I22_J, fact_13_com_Osimps_I3_J, fact_70_nat__case__0, fact_33_triple_Osimps_I2_J, fact_53_def__nat__rec__Suc, fact_58_com_Osimps_I26_J, fact_43_com_Osimps_I2_J, fact_64_com_Osimps_I9_J, fact_14_WTs__elim__cases_I5_J, fact_19_com_Orecs_I4_J, fact_65_com_Orecs_I2_J, fact_80_triple_Osize_I1_J, fact_51_com_Orecs_I3_J, fact_29_com_Osimps_I12_J, fact_89_com_Osize_I2_J, fact_83_zero__reorient, fact_47_com_Osimps_I35_J, fact_15_WTs__elim__cases_I4_J, fact_30_evaln__elim__cases_I4_J, fact_84_not0__implies__Suc, fact_7_com_Orecs_I1_J, fact_68_evaln_OAssign, fact_72_mem__def, fact_44_WT_OLocal, fact_78_nat_Osimps_I2_J, fact_12_com_Osimps_I4_J, fact_62_com_Osimps_I23_J, fact_45_com_Osimps_I37_J, fact_88_com_Osize_I1_J, fact_66_com_Osimps_I65_J, fact_16_com_Osimps_I44_J, fact_56_WT_OAssign, fact_85_nat__induct, fact_36_Suc__n__not__n, fact_35_n__not__Suc__n, fact_40_triples__valid__Suc, fact_6_evaln_OSemi, fact_0_evaln_OSkip, fact_93_add__left__cancel, arity_Nat_Onat___Groups_Ozero, fact_94_nat__add__right__cancel, fact_74_Suc__neq__Zero, fact_10_evaln__elim__cases_I5_J, fact_79_Zero__not__Suc, fact_69_of__nat__aux_Osimps_I1_J, fact_48_com_Osimps_I34_J, fact_49_com_Osimps_I11_J, fact_24_evaln__Suc, fact_91_com_Osize_I4_J, fact_86_nat_Oexhaust, fact_87_zero__induct, fact_76_nat_Osimps_I3_J, fact_8_evaln_OIfFalse, fact_26_com_Osimps_I15_J, fact_46_com_Osimps_I36_J, fact_71_ext, fact_63_com_Osimps_I8_J, fact_77_Suc__not__Zero, fact_23_WT_OIf, fact_75_Zero__neq__Suc, fact_81_triple_Osize_I2_J, fact_17_com_Osimps_I45_J, fact_21_com_Orecs_I5_J, help_pp_1_1_U, fact_4_triple__valid__Suc, fact_22_WT_OSemi, fact_32_triple_Orecs, fact_57_com_Osimps_I27_J, fact_54_hoare__valids__def, fact_1_evaln__elim__cases_I1_J, fact_11_triple_Oinject, conj_0, help_pp_2_1_U, fact_5_com_Osimps_I64_J, fact_67_evaln__elim__cases_I2_J, fact_9_evaln_OIfTrue, fact_41_nat__rec__Suc, fact_27_com_Osimps_I14_J, arity_Nat_Onat___Groups_Ocancel__semigroup__add
% 9.33/4.06 % No. of inferences in proof: 206
% 9.33/4.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3524 ms resp. 2755 ms w/o parsing
% 10.03/4.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.03/4.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------