TSTP Solution File: LCL748_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL748_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:31:24 EDT 2023
% Result : Theorem 6.40s 2.51s
% Output : Refutation 6.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 145
% Syntax : Number of formulae : 258 ( 124 unt; 34 typ; 0 def)
% Number of atoms : 494 ( 302 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2551 ( 50 ~; 6 |; 43 &;2301 @)
% ( 19 <=>; 132 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 6 con; 0-5 aty)
% Number of variables : 558 ( 0 ^; 538 !; 0 ?; 558 :)
% ( 20 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(zero_neq_one_type,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(it_type,type,
it: dB > $o ).
thf(beta_type,type,
beta: dB > dB > $o ).
thf(abs_type,type,
abs: dB > dB ).
thf(app_type,type,
app: fun @ dB @ ( fun @ dB @ dB ) ).
thf(var_type,type,
var: nat > dB ).
thf(dB_case_type,type,
dB_case:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ dB @ ( fun @ dB @ TA ) ) > ( fun @ dB @ TA ) > dB > TA ) ).
thf(dB_rec_type,type,
dB_rec:
!>[TA: $tType] : ( ( fun @ nat @ TA ) > ( fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) ) > ( fun @ dB @ ( fun @ TA @ TA ) ) > dB > TA ) ).
thf(dB_size_type,type,
dB_size: dB > nat ).
thf(lift_type,type,
lift: dB > nat > dB ).
thf(liftn_type,type,
liftn: nat > dB > nat > dB ).
thf(subst_type,type,
subst: dB > dB > nat > dB ).
thf(substn_type,type,
substn: dB > dB > nat > dB ).
thf(foldl_type,type,
foldl:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TB ) ) > TB > ( list @ TA ) > TB ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(ia_type,type,
ia: nat ).
thf(r_type,type,
r: dB ).
thf(62,axiom,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_dB_Osimps_I5_J) ).
thf(340,plain,
! [A: nat,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(10,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( beta @ D @ C )
=> ( beta @ ( subst @ D @ B @ A ) @ ( subst @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_subst__preserves__beta) ).
thf(138,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( beta @ D @ C )
=> ( beta @ ( subst @ D @ B @ A ) @ ( subst @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(64,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ A )
= ( plus_plus @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(347,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ A )
= ( plus_plus @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Suc__inject) ).
thf(333,plain,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(106,axiom,
! [A: nat] : ( it @ ( lift @ r @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(518,plain,
! [A: nat] : ( it @ ( lift @ r @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(89,axiom,
! [TA: $tType,A: dB,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ dB @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_dB_Osimps_I12_J) ).
thf(449,plain,
! [TA: $tType,A: dB,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ dB @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(70,axiom,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_subst__eq) ).
thf(379,plain,
! [A: dB,B: nat] :
( ( subst @ ( var @ B ) @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(86,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ ( suc @ A ) )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_add__Suc__right) ).
thf(440,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ ( suc @ A ) )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(28,axiom,
! [A: dB,B: list @ dB,C: dB] :
( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_apps__eq__tail__conv) ).
thf(202,plain,
! [A: dB,B: list @ dB,C: dB] :
( ( ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( foldl @ dB @ dB @ app @ C @ B )
= ( foldl @ dB @ dB @ app @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_dB_Osimps_I2_J) ).
thf(174,plain,
! [A: dB,B: dB,C: dB,D: dB] :
( ( ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(57,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Nat_Oadd__0__right) ).
thf(320,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(85,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_Suc__not__Zero) ).
thf(436,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(40,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( one_one @ TA )
!= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_one__neq__zero) ).
thf(257,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( one_one @ TA )
!= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(68,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_add_Ocomm__neutral) ).
thf(372,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(63,axiom,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_dB_Osize_I1_J) ).
thf(344,plain,
! [A: nat] :
( ( dB_size @ ( var @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_add__eq__self__zero) ).
thf(416,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ext) ).
thf(152,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(35,axiom,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_dB_Osimps_I10_J) ).
thf(228,plain,
! [TA: $tType,A: nat,B: fun @ dB @ TA,C: fun @ dB @ ( fun @ dB @ TA ),D: fun @ nat @ TA] :
( ( dB_case @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(32,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_double__eq__0__iff) ).
thf(216,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(96,axiom,
! [A: nat,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( lift @ C @ A ) @ ( lift @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_lift__preserves__beta) ).
thf(475,plain,
! [A: nat,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( lift @ C @ A ) @ ( lift @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(17,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(164,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(87,axiom,
! [A: dB] :
( ( dB_size @ ( abs @ A ) )
= ( plus_plus @ nat @ ( dB_size @ A ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_dB_Osize_I3_J) ).
thf(443,plain,
! [A: dB] :
( ( dB_size @ ( abs @ A ) )
= ( plus_plus @ nat @ ( dB_size @ A ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(66,axiom,
! [A: dB,B: dB] :
( ( substn @ B @ A @ ( zero_zero @ nat ) )
= ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_substn__subst__0) ).
thf(353,plain,
! [A: dB,B: dB] :
( ( substn @ B @ A @ ( zero_zero @ nat ) )
= ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(5,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_add__0__right) ).
thf(121,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(105,axiom,
! [A: dB,B: dB] :
( ( beta @ ( abs @ B ) @ A )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( beta @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_beta__cases_I2_J) ).
thf(514,plain,
! [A: dB,B: dB] :
( ( beta @ ( abs @ B ) @ A )
=> ~ ! [C: dB] :
( ( A
= ( abs @ C ) )
=> ~ ( beta @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(75,axiom,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_appR) ).
thf(397,plain,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ C ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(49,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Zero__not__Suc) ).
thf(293,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(103,axiom,
! [A: nat,B: dB,C: dB] :
( ( substn @ ( abs @ C ) @ B @ A )
= ( abs @ ( substn @ C @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_substn_Osimps_I3_J) ).
thf(507,plain,
! [A: nat,B: dB,C: dB] :
( ( substn @ ( abs @ C ) @ B @ A )
= ( abs @ ( substn @ C @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(109,axiom,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_dB_Osimps_I6_J) ).
thf(527,plain,
! [A: dB,B: nat] :
( ( var @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(54,axiom,
! [A: nat,B: dB] :
( ( liftn @ ( zero_zero @ nat ) @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_liftn__0) ).
thf(312,plain,
! [A: nat,B: dB] :
( ( liftn @ ( zero_zero @ nat ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(90,axiom,
! [A: dB,B: dB,C: dB] :
( ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
=> ( ! [D: dB] :
( ( A
= ( subst @ D @ B @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( beta @ C @ D ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( beta @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_beta__cases_I3_J) ).
thf(452,plain,
! [A: dB,B: dB,C: dB] :
( ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
=> ( ! [D: dB] :
( ( A
= ( subst @ D @ B @ ( zero_zero @ nat ) ) )
=> ( C
!= ( abs @ D ) ) )
=> ( ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ B ) )
=> ~ ( beta @ C @ D ) )
=> ~ ! [D: dB] :
( ( A
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ D ) )
=> ~ ( beta @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(27,axiom,
one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(201,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(111,axiom,
! [A: nat,B: dB,C: nat] :
( ( liftn @ C @ ( abs @ B ) @ A )
= ( abs @ ( liftn @ C @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_liftn_Osimps_I3_J) ).
thf(534,plain,
! [A: nat,B: dB,C: nat] :
( ( liftn @ C @ ( abs @ B ) @ A )
= ( abs @ ( liftn @ C @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(41,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_plus__nat_Oadd__0) ).
thf(260,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( ( suc @ B )
= ( suc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_nat_Oinject) ).
thf(297,plain,
! [A: nat,B: nat] :
( ( ( ( suc @ B )
= ( suc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( suc @ B )
= ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(18,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__imp__eq) ).
thf(165,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(93,axiom,
! [A: dB,B: nat,C: dB] :
( ( subst @ ( lift @ C @ B ) @ A @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_subst__lift) ).
thf(467,plain,
! [A: dB,B: nat,C: dB] :
( ( subst @ ( lift @ C @ B ) @ A @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(25,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(197,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(59,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Suc__neq__Zero) ).
thf(329,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(100,axiom,
! [A: dB,B: dB] :
( ( ( abs @ B )
= ( abs @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_dB_Osimps_I3_J) ).
thf(493,plain,
! [A: dB,B: dB] :
( ( ( ( abs @ B )
= ( abs @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( abs @ B )
= ( abs @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(56,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( substn @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( substn @ D @ B @ A ) ) @ ( substn @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_substn_Osimps_I2_J) ).
thf(317,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( substn @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( substn @ D @ B @ A ) ) @ ( substn @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ B @ A ) )
<=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_one__is__add) ).
thf(356,plain,
! [A: nat,B: nat] :
( ( ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ B @ A ) )
=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) )
& ( ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) )
=> ( ( suc @ ( zero_zero @ nat ) )
= ( plus_plus @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(82,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(420,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(30,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(212,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(6,axiom,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ ( fun @ TA @ TA ),D: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),E: fun @ nat @ TA] :
( ( dB_rec @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) @ D @ B ) @ A ) @ ( dB_rec @ TA @ E @ D @ C @ B ) ) @ ( dB_rec @ TA @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_dB_Orecs_I2_J) ).
thf(124,plain,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ ( fun @ TA @ TA ),D: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),E: fun @ nat @ TA] :
( ( dB_rec @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( aa @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) @ ( aa @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ) @ D @ B ) @ A ) @ ( dB_rec @ TA @ E @ D @ C @ B ) ) @ ( dB_rec @ TA @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(225,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(24,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Zero__neq__Suc) ).
thf(193,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(112,axiom,
! [A: dB,B: dB] : ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) @ ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_beta) ).
thf(537,plain,
! [A: dB,B: dB] : ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ B ) ) @ A ) @ ( subst @ B @ A @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(73,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(393,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(102,axiom,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_dB_Osimps_I7_J) ).
thf(503,plain,
! [A: nat,B: dB] :
( ( abs @ B )
!= ( var @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(43,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(266,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(8,axiom,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_dB_Osimps_I11_J) ).
thf(128,plain,
! [TA: $tType,A: dB,B: dB,C: fun @ dB @ TA,D: fun @ dB @ ( fun @ dB @ TA ),E: fun @ nat @ TA] :
( ( dB_case @ TA @ E @ D @ C @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( aa @ dB @ TA @ ( aa @ dB @ ( fun @ dB @ TA ) @ D @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
<=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_add__is__0) ).
thf(237,plain,
! [A: nat,B: nat] :
( ( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) )
=> ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_nat__add__commute) ).
thf(412,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(84,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_add__right__cancel) ).
thf(430,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(16,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_zero__neq__one) ).
thf(161,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(69,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_n__not__Suc__n) ).
thf(375,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(83,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_zero__reorient) ).
thf(423,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(77,axiom,
! [A: dB,B: nat] :
~ ( beta @ ( var @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_beta__cases_I1_J) ).
thf(402,plain,
! [A: dB,B: nat] :
~ ( beta @ ( var @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(4,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_nat__add__assoc) ).
thf(118,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(71,axiom,
! [A: nat,B: nat] :
( ( ( var @ B )
= ( var @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_dB_Osimps_I1_J) ).
thf(382,plain,
! [A: nat,B: nat] :
( ( ( ( var @ B )
= ( var @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( var @ B )
= ( var @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(65,axiom,
! [A: nat,B: dB,C: dB,D: nat] :
( ( liftn @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( liftn @ D @ C @ A ) ) @ ( liftn @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_liftn_Osimps_I2_J) ).
thf(350,plain,
! [A: nat,B: dB,C: dB,D: nat] :
( ( liftn @ D @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( liftn @ D @ C @ A ) ) @ ( liftn @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(22,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__0) ).
thf(187,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1,conjecture,
it @ ( lift @ ( abs @ r ) @ ia ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ( it @ ( lift @ ( abs @ r ) @ ia ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,plain,
~ ( it @ ( lift @ ( abs @ r ) @ ia ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) )
<=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_add__is__1) ).
thf(274,plain,
! [A: nat,B: nat] :
( ( ( ( plus_plus @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) )
=> ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) ) )
& ( ( ( ( B
= ( suc @ ( zero_zero @ nat ) ) )
& ( A
= ( zero_zero @ nat ) ) )
| ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( suc @ ( zero_zero @ nat ) ) ) ) )
=> ( ( plus_plus @ nat @ B @ A )
= ( suc @ ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(46,axiom,
! [A: dB,B: dB] :
( ( dB_size @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( dB_size @ B ) @ ( dB_size @ A ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_dB_Osize_I2_J) ).
thf(271,plain,
! [A: dB,B: dB] :
( ( dB_size @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) )
= ( plus_plus @ nat @ ( plus_plus @ nat @ ( dB_size @ B ) @ ( dB_size @ A ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(97,axiom,
! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Abs__apps__eq__Abs__apps__conv) ).
thf(477,plain,
! [A: list @ dB,B: dB,C: list @ dB,D: dB] :
( ( ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( foldl @ dB @ dB @ app @ ( abs @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(58,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_double__zero__sym) ).
thf(323,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(11,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add__right__imp__eq) ).
thf(140,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(31,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(213,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(107,axiom,
! [A: dB,B: dB,C: dB] :
( ( abs @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_dB_Osimps_I9_J) ).
thf(520,plain,
! [A: dB,B: dB,C: dB] :
( ( abs @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(14,axiom,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_subst__App) ).
thf(155,plain,
! [A: nat,B: dB,C: dB,D: dB] :
( ( subst @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ D ) @ C ) @ B @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( subst @ D @ B @ A ) ) @ ( subst @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( plus_plus @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__Suc__shift) ).
thf(399,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( plus_plus @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(44,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(267,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(74,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_add__0__left) ).
thf(394,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(52,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_nat_Osimps_I2_J) ).
thf(306,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(95,axiom,
! [A: list @ dB,B: dB,C: dB] :
( ( it @ ( foldl @ dB @ dB @ app @ ( subst @ C @ B @ ( zero_zero @ nat ) ) @ A ) )
=> ( ( it @ B )
=> ( it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Beta) ).
thf(473,plain,
! [A: list @ dB,B: dB,C: dB] :
( ( it @ ( foldl @ dB @ dB @ app @ ( subst @ C @ B @ ( zero_zero @ nat ) ) @ A ) )
=> ( ( it @ B )
=> ( it @ ( foldl @ dB @ dB @ app @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( abs @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(99,axiom,
! [A: nat,B: dB,C: dB] :
( ( subst @ ( abs @ C ) @ B @ A )
= ( abs @ ( subst @ C @ ( lift @ B @ ( zero_zero @ nat ) ) @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_subst__Abs) ).
thf(490,plain,
! [A: nat,B: dB,C: dB] :
( ( subst @ ( abs @ C ) @ B @ A )
= ( abs @ ( subst @ C @ ( lift @ B @ ( zero_zero @ nat ) ) @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(110,axiom,
! [A: nat,B: dB,C: nat] :
( ( liftn @ ( suc @ C ) @ B @ A )
= ( lift @ ( liftn @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_liftn__lift) ).
thf(531,plain,
! [A: nat,B: dB,C: nat] :
( ( liftn @ ( suc @ C ) @ B @ A )
= ( lift @ ( liftn @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(29,axiom,
! [TA: $tType,A: nat,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_dB_Orecs_I1_J) ).
thf(209,plain,
! [TA: $tType,A: nat,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( var @ A ) )
= ( aa @ nat @ TA @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(42,axiom,
! [A: nat,B: dB,C: dB] :
( ( substn @ C @ B @ A )
= ( subst @ C @ ( liftn @ A @ B @ ( zero_zero @ nat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_substn__subst__n) ).
thf(263,plain,
! [A: nat,B: dB,C: dB] :
( ( substn @ C @ B @ A )
= ( subst @ C @ ( liftn @ A @ B @ ( zero_zero @ nat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(53,axiom,
( ( one_one @ nat )
= ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_One__nat__def) ).
thf(310,plain,
( ( one_one @ nat )
= ( suc @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(7,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(127,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(94,axiom,
! [TA: $tType,A: dB,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ TA @ TA @ ( aa @ dB @ ( fun @ TA @ TA ) @ B @ A ) @ ( dB_rec @ TA @ D @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_dB_Orecs_I3_J) ).
thf(470,plain,
! [TA: $tType,A: dB,B: fun @ dB @ ( fun @ TA @ TA ),C: fun @ dB @ ( fun @ dB @ ( fun @ TA @ ( fun @ TA @ TA ) ) ),D: fun @ nat @ TA] :
( ( dB_rec @ TA @ D @ C @ B @ ( abs @ A ) )
= ( aa @ TA @ TA @ ( aa @ dB @ ( fun @ TA @ TA ) @ B @ A ) @ ( dB_rec @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(88,axiom,
! [A: nat,B: dB] :
( ( lift @ ( abs @ B ) @ A )
= ( abs @ ( lift @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_lift_Osimps_I3_J) ).
thf(446,plain,
! [A: nat,B: dB] :
( ( lift @ ( abs @ B ) @ A )
= ( abs @ ( lift @ B @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(12,axiom,
! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Var__apps__eq__Var__apps__conv) ).
thf(143,plain,
! [A: list @ dB,B: nat,C: list @ dB,D: nat] :
( ( ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
= ( foldl @ dB @ dB @ app @ ( var @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(108,axiom,
! [A: nat,B: dB,C: dB] :
( ( lift @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( lift @ C @ A ) ) @ ( lift @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_lift_Osimps_I2_J) ).
thf(524,plain,
! [A: nat,B: dB,C: dB] :
( ( lift @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B ) @ A )
= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ ( lift @ C @ A ) ) @ ( lift @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(39,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_nat__add__left__cancel) ).
thf(250,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(92,axiom,
! [A: dB,B: dB] :
( ( beta @ B @ A )
=> ( beta @ ( abs @ B ) @ ( abs @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_abs) ).
thf(465,plain,
! [A: dB,B: dB] :
( ( beta @ B @ A )
=> ( beta @ ( abs @ B ) @ ( abs @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(36,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( B
= ( plus_plus @ TA @ B @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_add__0__iff) ).
thf(231,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( ( B
= ( plus_plus @ TA @ B @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( B
= ( plus_plus @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(15,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_add__Suc) ).
thf(158,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ ( suc @ B ) @ A )
= ( suc @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(72,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(390,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(3,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_nat_Osimps_I3_J) ).
thf(114,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(48,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat__add__left__commute) ).
thf(290,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(38,axiom,
! [A: nat] :
( ( suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Suc__n__not__n) ).
thf(246,plain,
! [A: nat] :
( ( suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(104,axiom,
! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
!= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Var__apps__neq__Abs__apps) ).
thf(510,plain,
! [A: list @ dB,B: dB,C: list @ dB,D: nat] :
( ( foldl @ dB @ dB @ app @ ( var @ D ) @ C )
!= ( foldl @ dB @ dB @ app @ ( abs @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(55,axiom,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_appL) ).
thf(315,plain,
! [A: dB,B: dB,C: dB] :
( ( beta @ C @ B )
=> ( beta @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ A ) @ ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(19,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add__left__cancel) ).
thf(168,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(78,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_one__reorient) ).
thf(405,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(23,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(190,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,axiom,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_dB_Osimps_I4_J) ).
thf(183,plain,
! [A: dB,B: dB,C: nat] :
( ( var @ C )
!= ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(51,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(305,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(45,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(268,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(80,axiom,
semiri456707255roduct @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(415,plain,
semiri456707255roduct @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(91,axiom,
it @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(464,plain,
it @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(9,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_nat__add__right__cancel) ).
thf(131,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(200,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(101,axiom,
! [A: dB] :
( ( it @ A )
=> ( it @ ( abs @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Lambda) ).
thf(501,plain,
! [A: dB] :
( ( it @ A )
=> ( it @ ( abs @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(98,axiom,
! [A: dB,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( abs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_dB_Osimps_I8_J) ).
thf(486,plain,
! [A: dB,B: dB,C: dB] :
( ( aa @ dB @ dB @ ( aa @ dB @ ( fun @ dB @ dB ) @ app @ C ) @ B )
!= ( abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(61,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add__left__imp__eq) ).
thf(337,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(33,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(222,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(541,plain,
$false,
inference(e,[status(thm)],[340,138,347,333,518,449,379,440,202,174,320,436,257,372,344,416,152,228,216,475,164,443,353,121,514,397,293,507,527,312,452,201,534,260,297,165,467,197,329,493,317,356,420,212,124,225,193,537,393,503,266,128,237,412,430,161,375,423,402,118,382,350,187,113,274,271,477,323,140,213,520,155,399,267,394,306,473,490,531,209,263,310,127,470,446,143,524,250,465,231,158,390,114,290,246,510,315,168,405,190,183,305,268,415,464,131,200,501,486,337,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL748_5 : TPTP v8.1.2. Released v6.0.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n018.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 16:03:28 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.94/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.56/1.03 % [INFO] Parsing done (182ms).
% 1.56/1.04 % [INFO] Running in sequential loop mode.
% 1.97/1.23 % [INFO] eprover registered as external prover.
% 1.97/1.23 % [INFO] cvc4 registered as external prover.
% 1.97/1.24 % [INFO] Scanning for conjecture ...
% 2.19/1.32 % [INFO] Found a conjecture and 112 axioms. Running axiom selection ...
% 2.37/1.39 % [INFO] Axiom selection finished. Selected 110 axioms (removed 2 axioms).
% 2.81/1.50 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.81/1.52 % [INFO] Type checking passed.
% 2.81/1.53 % [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 ...
% 6.40/2.50 % External prover 'e' found a proof!
% 6.40/2.50 % [INFO] Killing All external provers ...
% 6.40/2.51 % Time passed: 1981ms (effective reasoning time: 1464ms)
% 6.40/2.51 % 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)>
% 6.40/2.51 % Axioms used in derivation (110): fact_41_liftn__0, fact_88_Suc__neq__Zero, fact_75_dB_Osize_I3_J, fact_37_add__is__0, fact_74_Beta, fact_58_nat__add__commute, fact_21_dB_Orecs_I1_J, fact_45_add__0, fact_12_dB_Osimps_I2_J, fact_82_one__is__add, fact_52_add__imp__eq, fact_22_dB_Osimps_I10_J, fact_86_n__not__Suc__n, fact_63_one__neq__zero, fact_38_liftn_Osimps_I2_J, fact_40_substn__subst__n, fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_27_dB_Osimps_I9_J, fact_46_add__0__left, fact_56_nat__add__assoc, fact_0_Lambda, fact_81_liftn__lift, fact_90_nat_Osimps_I3_J, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_43_add_Ocomm__neutral, fact_96_apps__eq__tail__conv, fact_50_substn__subst__0, fact_64_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_83_add__is__1, fact_29_nat__add__left__cancel, fact_24_dB_Orecs_I2_J, fact_76_dB_Osize_I2_J, fact_44_add__0__right, fact_34_subst__Abs, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_48_Nat_Oadd__0__right, fact_62_zero__neq__one, fact_5_abs, fact_42_zero__reorient, fact_35_beta, fact_2_dB_Osimps_I12_J, fact_73_ext, fact_14_appL, fact_79_add__Suc__right, fact_85_Suc__n__not__n, fact_28_substn_Osimps_I3_J, fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_47_add__eq__self__zero, fact_10_dB_Osimps_I6_J, fact_54_ab__semigroup__add__class_Oadd__ac_I1_J, fact_15_appR, fact_13_dB_Osimps_I1_J, fact_20_subst__eq, fact_4_lift_Osimps_I3_J, fact_33_liftn_Osimps_I3_J, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_3_dB_Orecs_I3_J, arity_Nat_Onat___Groups_Ozero, fact_97_Var__apps__neq__Abs__apps, fact_91_Suc__not__Zero, fact_23_dB_Osimps_I11_J, fact_95_Abs__apps__eq__Abs__apps__conv, fact_51_add__right__imp__eq, fact_57_nat__add__left__commute, fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_26_dB_Osimps_I8_J, fact_8_lift__preserves__beta, fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, conj_1, fact_19_dB_Osimps_I5_J, fact_11_beta__cases_I2_J, fact_78_add__Suc, fact_55_one__reorient, arity_Nat_Onat___Groups_Oone, fact_31_add__left__cancel, fact_7_lift_Osimps_I2_J, fact_39_substn_Osimps_I2_J, fact_18_dB_Osimps_I4_J, fact_92_nat_Osimps_I2_J, fact_16_subst__App, fact_36_double__zero__sym, fact_6_subst__lift, fact_53_add__left__imp__eq, fact_93_Zero__not__Suc, fact_30_nat__add__right__cancel, fact_84_Suc__inject, fact_59_double__eq__0__iff, fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, arity_Nat_Onat___Groups_Omonoid__add, fact_77_nat_Oinject, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_80_One__nat__def, fact_65_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_60_beta__cases_I3_J, fact_61_dB_Osize_I1_J, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, conj_0, fact_25_subst__preserves__beta, fact_66_add__0__iff, fact_87_add__Suc__shift, fact_1_dB_Osimps_I3_J, fact_49_plus__nat_Oadd__0, fact_9_dB_Osimps_I7_J, arity_Nat_Onat___Rings_Ozero__neq__one, fact_89_Zero__neq__Suc, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_94_Var__apps__eq__Var__apps__conv, fact_32_add__right__cancel, fact_17_beta__cases_I1_J
% 6.40/2.51 % No. of inferences in proof: 224
% 6.40/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1981 ms resp. 1464 ms w/o parsing
% 6.52/2.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.52/2.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------