%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT252_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 : n009.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 08:27:37 AM UTC 2026
% Result : Theorem 66.64s 17.72s
% Output : Refutation 66.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 116
% Syntax : Number of formulae : 234 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 1909 ( 169 equ; 0 cnn)
% Maximal formula atoms : 116 ( 8 avg)
% Number of connectives : 7594 ( 93 ~; 13 |; 51 &;7092 @)
% ( 35 <=>; 310 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 10 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 13 con; 0-5 aty)
% Number of variables : 484 ( 0 ^; 477 !; 7 ?; 484 :)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(arrow_159774573e_indi_type,type,
arrow_159774573e_indi: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere216010020id_add_decl,type,
ordere216010020id_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(arrow_1958449194le_IIA_decl,type,
arrow_1958449194le_IIA: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ) > $o ).
thf(arrow_1985332922le_Lin_decl,type,
arrow_1985332922le_Lin: bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) ).
thf(arrow_610318064e_Prof_decl,type,
arrow_610318064e_Prof: bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ).
thf(arrow_2069624013nimity_decl,type,
arrow_2069624013nimity: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ) > $o ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(finite_card_decl,type,
finite_card:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > nat ) ).
thf(inj_on_decl,type,
inj_on:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( bool @ ( TB @ fun ) ) > $o ) ).
thf(pi_decl,type,
pi:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ fun ) ) > ( bool @ ( TA @ fun ) @ ( TB @ fun ) ) > ( bool @ ( TA @ ( TB @ fun ) @ fun ) ) ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ fun ) ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( TA @ ( TB @ product_prod ) ) ) ).
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(f_decl,type,
f: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ).
thf(lab_decl,type,
lab: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ).
thf(lba_decl,type,
lba: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ).
thf(a_decl,type,
a: arrow_411405190le_alt ).
thf(b_decl,type,
b: arrow_411405190le_alt ).
thf(h_decl,type,
h: nat @ ( arrow_159774573e_indi @ fun ) ).
thf(114,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(547,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(9,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_le0) ).
thf(150,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,axiom,
nat @ ordere216010020id_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
thf(249,plain,
nat @ ordere216010020id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( A @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_add__less__cancel__right) ).
thf(518,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(40,axiom,
~ ( lba @ ( lab @ ( nat @ zero_zero @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__C1_C) ).
thf(247,plain,
~ ( lba @ ( lab @ ( nat @ zero_zero @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_add_Ocomm__neutral) ).
thf(511,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(45,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096a_A_126_061_Ab_096) ).
thf(269,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(73,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_zero__le__double__add__iff__zero__le__single__add) ).
thf(385,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(115,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_nat__add__left__cancel) ).
thf(550,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(94,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_linorder__neqE__nat) ).
thf(472,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(60,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(340,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(78,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [G: arrow_159774573e_indi] :
( ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
=> ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33__096_B_Bb_H_Ab_Aa_H_Aa_AP_H_AP_O_A_091_124_Aa_A_126_061_Ab_059_Aa_H_A_126_061_Ab_H_059_Aa_A_126_061_Ab_H_059_Ab_A_126_061_Aa_H_059_AP_A_058_AProf_059_AP_H_A_058_AProf_059_AALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_059_Aa_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Aa_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_096) ).
thf(404,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(48,axiom,
arrow_1985332922le_Lin @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( arrow_610318064e_Prof @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ pi ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_assms_I1_J) ).
thf(288,plain,
arrow_1985332922le_Lin @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( arrow_610318064e_Prof @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ pi ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(56,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_le__antisym) ).
thf(320,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_one__reorient) ).
thf(389,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_zero__reorient) ).
thf(125,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)],[4]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_zero__less__double__add__iff__zero__less__single__add) ).
thf(344,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(10,axiom,
~ ( lba @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(152,plain,
~ ( lba @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(49,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(289,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_add__0) ).
thf(448,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(32,axiom,
~ ( lab @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(216,plain,
~ ( lab @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add__strict__increasing2) ).
thf(475,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(99,axiom,
? [A: nat] :
( ( lba @ ( lab @ ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ! [B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ~ ( lba @ ( lab @ ( B @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096EX_Ak_060N_O_A_IALL_Ai_060_061k_O_A_Ia_M_Ab_J_A_126_058_AF_A_I_Fia_O_Aif_Ah_Aia_A_060_Ai_Athen_ALab_Aelse_ALba_J_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Ak_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096) ).
thf(492,plain,
? [A: nat] :
( ( lba @ ( lab @ ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ! [B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ~ ( lba @ ( lab @ ( B @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(105,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_add__eq__self__zero) ).
thf(514,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_nat__add__commute) ).
thf(348,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(65,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_28_nat__add__right__cancel) ).
thf(353,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)],[65]) ).
thf(8,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_78_add__right__imp__eq) ).
thf(147,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add__strict__increasing) ).
thf(397,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(51,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(293,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_nat__le__linear) ).
thf(133,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(82,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(428,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(109,axiom,
bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( h @ ( nat @ ( arrow_159774573e_indi @ inj_on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_injh) ).
thf(527,plain,
bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( h @ ( nat @ ( arrow_159774573e_indi @ inj_on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(29,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_less__eq__nat_Osimps_I1_J) ).
thf(206,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(71,axiom,
lab @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(380,plain,
lab @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(27,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_less__zeroE) ).
thf(201,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__not__refl3) ).
thf(381,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(34,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [G: arrow_159774573e_indi] :
( ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
=> ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_pairwise__neutrality) ).
thf(220,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(13,axiom,
arrow_1985332922le_Lin @ ( lba @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096Lba_A_058_ALin_096) ).
thf(160,plain,
arrow_1985332922le_Lin @ ( lba @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(117,axiom,
arrow_1985332922le_Lin @ ( lab @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096Lab_A_058_ALin_096) ).
thf(561,plain,
arrow_1985332922le_Lin @ ( lab @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(53,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Nat_Oadd__0__right) ).
thf(297,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(17,axiom,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_le__refl) ).
thf(165,plain,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(92,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_less__not__refl) ).
thf(467,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(66,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_nat__add__left__cancel__less) ).
thf(361,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
& ( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__nonneg__pos) ).
thf(522,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_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_79_add__imp__eq) ).
thf(371,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(102,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_26_add__right__cancel) ).
thf(503,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)],[102]) ).
thf(39,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_nat__add__left__commute) ).
thf(244,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(116,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_80_add__left__imp__eq) ).
thf(558,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(83,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_less__not__refl2) ).
thf(430,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(14,axiom,
f @ arrow_2069624013nimity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_u) ).
thf(161,plain,
f @ arrow_2069624013nimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(80,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(423,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if @ ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( bool @ aa ) ) ) @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1,conjecture,
? [A: nat] :
( ( lba @ ( lab @ ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ! [B: nat] :
( ( lba @ ( lab @ ( B @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
& ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: nat] :
( ( lba @ ( lab @ ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ! [B: nat] :
( ( lba @ ( lab @ ( B @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
& ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(118,plain,
~ ? [A: nat] :
( ( lba @ ( lab @ ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ! [B: nat] :
( ( lba @ ( lab @ ( B @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ~ ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
& ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_double__zero__sym) ).
thf(281,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_add__nonpos__neg) ).
thf(204,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(445,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(101,axiom,
~ ! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( A @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(498,plain,
~ ! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( A @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(22,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(181,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(88,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
<=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_add__gr__0) ).
thf(451,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(84,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_less__irrefl__nat) ).
thf(434,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(30,axiom,
nat @ ordere236663937imp_le,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(208,plain,
nat @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(96,axiom,
~ ! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( A @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(477,plain,
~ ! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( A @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_add__nonneg__nonneg) ).
thf(367,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(57,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_less__nat__zero__code) ).
thf(323,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_add__is__0) ).
thf(330,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(90,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_not__less0) ).
thf(462,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( C @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_add__increasing2) ).
thf(240,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( C @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(251,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add__neg__nonpos) ).
thf(399,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(6,axiom,
arrow_1985332922le_Lin @ ( lba @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combk ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__096F_A_I_Fi_O_ALba_J_A_058_ALin_096) ).
thf(135,plain,
arrow_1985332922le_Lin @ ( lba @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combk ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_add__le__cancel__left) ).
thf(167,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(81,axiom,
! [A: nat] : ( arrow_610318064e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PiProf) ).
thf(426,plain,
! [A: nat] : ( arrow_610318064e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(15,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(162,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(70,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( B != A )
=> ( ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_notin__Lin__iff) ).
thf(374,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( B != A )
=> ( ( ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(31,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_27_add__left__cancel) ).
thf(209,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)],[31]) ).
thf(25,axiom,
arrow_1985332922le_Lin @ ( lab @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combk ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__096F_A_I_Fi_O_ALab_J_A_058_ALin_096) ).
thf(194,plain,
arrow_1985332922le_Lin @ ( lab @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combk ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(93,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_le__trans) ).
thf(470,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(113,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_gr0I) ).
thf(544,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(21,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_73_mem__def) ).
thf(177,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)],[21]) ).
thf(23,axiom,
lba @ ( lab @ ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__C2_C) ).
thf(182,plain,
lba @ ( lab @ ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_add__le__cancel__right) ).
thf(154,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Lin__irrefl) ).
thf(175,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(100,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(497,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_add__less__cancel__left) ).
thf(539,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_double__add__less__zero__iff__single__add__less__zero) ).
thf(482,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(108,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_add__0__left) ).
thf(524,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(33,axiom,
! [A: nat] : ( arrow_1985332922le_Lin @ ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15__C0_C) ).
thf(218,plain,
! [A: nat] : ( arrow_1985332922le_Lin @ ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(42,axiom,
f @ arrow_1958449194le_IIA,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).
thf(250,plain,
f @ arrow_1958449194le_IIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_add__neg__neg) ).
thf(465,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(77,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_nat__add__assoc) ).
thf(401,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_eq__imp__le) ).
thf(171,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_610318064e_Prof @ ( A @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combk ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_const__Lin__Prof) ).
thf(158,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_610318064e_Prof @ ( A @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combk ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(64,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_add__pos__nonneg) ).
thf(351,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_add__0__right) ).
thf(290,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_double__add__le__zero__iff__single__add__le__zero) ).
thf(235,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(103,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(510,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_add__nonneg__eq__0__iff) ).
thf(272,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(54,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [F: arrow_159774573e_indi] :
( ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( F @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
=> ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32__C4_C) ).
thf(300,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [F: arrow_159774573e_indi] :
( ( ( F @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( F @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_gr__implies__not0) ).
thf(315,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(24,axiom,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_nat__less__cases) ).
thf(183,plain,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(58,axiom,
( ? [A: arrow_159774573e_indi] :
~ ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( lba = lab ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__096_I_Fi_O_Aif_Ah_Ai_A_060_AN_Athen_ALab_Aelse_ALba_J_A_061_A_I_Fp_O_ALab_J_096) ).
thf(326,plain,
( ? [A: arrow_159774573e_indi] :
~ ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( arrow_159774573e_indi @ finite_card ) @ ( A @ ( h @ ( nat @ ( arrow_159774573e_indi @ aa ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( lba = lab ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(341,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(26,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_nat__add__left__cancel__le) ).
thf(195,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(85,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_neq0__conv) ).
thf(437,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(79,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_le__0__eq) ).
thf(415,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) ) )
& ( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(36,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(239,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(38,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_add__pos__pos) ).
thf(242,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(52,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_plus__nat_Oadd__0) ).
thf(294,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
| ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_nat__neq__iff) ).
thf(136,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
| ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp )
| ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(110,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [G: arrow_159774573e_indi] :
( ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
=> ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34__096_B_Bb_H_Ab_Aa_H_Aa_AP_H_AP_O_A_091_124_Aa_A_126_061_Ab_059_Aa_H_A_126_061_Ab_H_059_Aa_A_126_061_Ab_H_059_Ab_A_126_061_Aa_H_059_AP_A_058_AProf_059_AP_H_A_058_AProf_059_AALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_A_124_093_A_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096) ).
thf(528,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( G @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( G @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( F @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(459,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_add__nonpos__nonpos) ).
thf(163,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_add__increasing) ).
thf(369,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(44,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( D != C )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [E: arrow_159774573e_indi] :
( ( E @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( E @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
=> ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30__C3_C) ).
thf(254,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( D != C )
=> ( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( arrow_610318064e_Prof @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ! [E: arrow_159774573e_indi] :
( ( ( E @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( E @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( E @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( E @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(98,axiom,
! [A: nat] :
( ~ ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__096_B_Bn_O_A_I_Ia_M_Ab_J_A_126_058_AF_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_J_A_061_A_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096) ).
thf(486,plain,
! [A: nat] :
( ( ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ~ ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( lba @ ( lab @ ( A @ ( h @ ( nat @ ord_less @ ( arrow_159774573e_indi @ ( bool @ ( nat @ fun ) @ ( nat @ combb ) ) ) ) @ ( bool @ ( nat @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ combc ) ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(122,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(112,axiom,
lba @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(543,plain,
lba @ ( a @ ( b @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(5357,plain,
$false,
inference(e,[status(thm)],[547,150,249,518,247,511,269,385,550,472,340,404,288,320,389,125,344,152,289,448,216,475,492,514,348,353,147,397,293,133,428,527,206,380,201,381,220,160,561,297,165,467,361,522,371,503,244,558,430,161,423,118,281,204,445,498,181,451,434,208,477,367,323,330,462,240,251,399,135,167,426,162,374,209,194,470,544,177,182,154,175,497,539,482,524,218,250,465,401,171,158,351,290,235,510,272,300,315,183,326,341,195,437,415,239,242,294,136,528,459,163,369,254,486,122,543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT252_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % 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
% 0.15/0.42 % Computer : n009.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 06:46:02 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.92/1.33 % [INFO] Parsing done (329ms).
% 1.92/1.34 % [INFO] Running in sequential loop mode.
% 2.80/1.73 % [INFO] eprover registered as external prover.
% 2.80/1.74 % [INFO] Scanning for conjecture ...
% 3.30/1.97 % [INFO] Found a conjecture (or negated_conjecture) and 115 axioms. Running axiom selection ...
% 3.71/2.13 % [INFO] Axiom selection finished. Selected 115 axioms (removed 0 axioms).
% 4.80/2.34 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.80/2.37 % [INFO] Type checking passed.
% 4.80/2.38 % [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 ...
% 6.17/2.69 % [INFO] [Domain constraints] Detected constraint on bool
% 6.17/2.69 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 66.64/17.71 % External prover 'e' found a proof!
% 66.64/17.71 % [INFO] Killing All external provers ...
% 66.64/17.71 % Time passed: 17153ms (effective reasoning time: 16365ms)
% 66.64/17.71 % 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)>
% 66.64/17.72 % Axioms used in derivation (115): fact_2__096a_A_126_061_Ab_096, fact_97_le__refl, fact_49_assms_I1_J, fact_59_add__eq__self__zero, fact_15__C0_C, fact_40_le__0__eq, fact_77_add__pos__nonneg, fact_74_add__strict__increasing2, fact_80_add__left__imp__eq, fact_45_double__add__less__zero__iff__single__add__less__zero, fact_50_zero__reorient, fact_84_less__not__refl3, fact_66_add__nonneg__nonneg, fact_65_add__nonneg__eq__0__iff, fact_11__096EX_Ak_060N_O_A_IALL_Ai_060_061k_O_A_Ia_M_Ab_J_A_126_058_AF_A_I_Fia_O_Aif_Ah_Aia_A_060_Ai_Athen_ALab_Aelse_ALba_J_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Ak_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096, fact_39_add__is__0, fact_35_double__zero__sym, fact_69_Lin__irrefl, fact_0_assms_I3_J, fact_29_nat__add__left__cancel, fact_7__096_B_Bn_O_A_I_Ia_M_Ab_J_A_126_058_AF_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_J_A_061_A_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096, fact_34__096_B_Bb_H_Ab_Aa_H_Aa_AP_H_AP_O_A_091_124_Aa_A_126_061_Ab_059_Aa_H_A_126_061_Ab_H_059_Aa_A_126_061_Ab_H_059_Ab_A_126_061_Aa_H_059_AP_A_058_AProf_059_AP_H_A_058_AProf_059_AALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_A_124_093_A_061_061_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_J_096, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_3__096Lab_A_058_ALin_096, fact_44_zero__le__double__add__iff__zero__le__single__add, fact_85_less__not__refl2, fact_52_add_Ocomm__neutral, fact_48_add__gr__0, fact_73_mem__def, fact_87_linorder__neqE__nat, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_13_injh, fact_19_nat__add__left__cancel__le, fact_88_nat__neq__iff, fact_83_nat__less__cases, fact_5__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, fact_20_nat__add__left__cancel__less, fact_36_less__zeroE, fact_89_less__not__refl, help_COMBB_1_1_U, help_If_1_1_T, fact_26_add__right__cancel, fact_76_add__nonneg__pos, fact_8__C2_C, fact_82_one__reorient, fact_16__C1_C, fact_70_notin__Lin__iff, fact_94_le__trans, fact_41_less__eq__nat_Osimps_I1_J, fact_54_add__0, fact_23_add__le__cancel__right, fact_37_less__nat__zero__code, fact_25__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_56_gr0I, fact_60_Nat_Oadd__0__right, fact_46_zero__less__double__add__iff__zero__less__single__add, fact_72_add__neg__nonpos, fact_18__096F_A_I_Fi_O_ALab_J_A_058_ALin_096, fact_27_add__left__cancel, fact_42_le0, fact_32__C4_C, fact_71_add__nonpos__neg, fact_53_add__0__right, arity_Nat_Onat___Groups_Ozero, arity_Nat_Onat___Groups_Oordered__comm__monoid__add, fact_38_neq0__conv, fact_12__096_I_Fi_O_Aif_Ah_Ai_A_060_AN_Athen_ALab_Aelse_ALba_J_A_061_A_I_Fp_O_ALab_J_096, fact_68_add__pos__pos, help_If_3_1_T, fact_81_ab__semigroup__add__class_Oadd__ac_I1_J, fact_31_pairwise__neutrality, help_If_2_1_T, help_COMBK_1_1_U, fact_6__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, fact_17__096F_A_I_Fi_O_ALba_J_A_058_ALin_096, fact_22_add__less__cancel__left, fact_28_nat__add__right__cancel, fact_91_nat__add__left__commute, help_COMBC_1_1_U, fact_14_PiProf, fact_21_add__less__cancel__right, fact_1_u, fact_90_nat__add__assoc, fact_47__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_63_add__increasing2, fact_51_const__Lin__Prof, arity_Nat_Onat___Groups_Oone, fact_43_double__add__le__zero__iff__single__add__le__zero, fact_95_eq__imp__le, fact_62_add__nonpos__nonpos, fact_30__C3_C, fact_58_not__less0, fact_57_gr__implies__not0, fact_96_nat__le__linear, help_pp_1_1_U, fact_79_add__imp__eq, arity_Nat_Onat___Groups_Omonoid__add, fact_86_less__irrefl__nat, fact_67_add__neg__neg, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_61_plus__nat_Oadd__0, fact_33__096_B_Bb_H_Ab_Aa_H_Aa_AP_H_AP_O_A_091_124_Aa_A_126_061_Ab_059_Aa_H_A_126_061_Ab_H_059_Aa_A_126_061_Ab_H_059_Ab_A_126_061_Aa_H_059_AP_A_058_AProf_059_AP_H_A_058_AProf_059_AALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_059_Aa_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Aa_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_096, fact_10__096_Ia_M_Ab_J_A_126_058_ALba_096, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_4__096Lba_A_058_ALin_096, fact_75_add__strict__increasing, help_pp_2_1_U, fact_92_nat__add__commute, fact_64_add__increasing, fact_24_add__le__cancel__left, fact_93_le__antisym, fact_9__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_55_add__0__left, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_78_add__right__imp__eq
% 66.64/17.72 % No. of inferences in proof: 234
% 66.64/17.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 17153 ms resp. 16365 ms w/o parsing
% 66.64/17.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 66.64/17.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------