%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL755_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 07:52:44 AM UTC 2026
% Result : Theorem 12.55s 5.26s
% Output : Refutation 13.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 113
% Syntax : Number of formulae : 228 ( 96 unt; 0 typ; 0 def)
% Number of atoms : 506 ( 180 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 2599 ( 60 ~; 6 |; 22 &;2275 @)
% ( 18 <=>; 218 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 7 con; 0-5 aty)
% Number of variables : 571 ( 0 ^; 566 !; 5 ?; 571 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[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(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_decl,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
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(it_decl,type,
it: dB > $o ).
thf(abs_decl,type,
abs: dB > dB ).
thf(var_decl,type,
var: nat > dB ).
thf(dB_case_decl,type,
dB_case:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( dB @ fun ) @ ( dB @ fun ) ) > ( TA @ ( dB @ fun ) ) > dB > TA ) ).
thf(dB_rec_decl,type,
dB_rec:
!>[TA: $tType] : ( ( TA @ ( nat @ fun ) ) > ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ) ) > ( TA @ ( TA @ fun ) @ ( dB @ fun ) ) > dB > TA ) ).
thf(lift_decl,type,
lift: dB > nat > dB ).
thf(liftn_decl,type,
liftn: nat > dB > nat > dB ).
thf(subst_decl,type,
subst: dB > dB > nat > dB ).
thf(substn_decl,type,
substn: dB > dB > nat > dB ).
thf(suc_decl,type,
suc: nat > nat ).
thf(nat_case_decl,type,
nat_case:
!>[TA: $tType] : ( TA > ( TA @ ( nat @ fun ) ) > nat > TA ) ).
thf(nat_rec_decl,type,
nat_rec:
!>[TA: $tType] : ( TA > ( TA @ ( TA @ fun ) @ ( nat @ fun ) ) > nat > TA ) ).
thf(semiri532925092at_aux_decl,type,
semiri532925092at_aux:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) ) > nat > TA > TA ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
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(pp_decl,type,
pp: bool > $o ).
thf(ia_decl,type,
ia: nat ).
thf(ja_decl,type,
ja: nat ).
thf(ra_decl,type,
ra: dB ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Suc__less__SucD) ).
thf(500,plain,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__left__imp__eq) ).
thf(118,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)],[4]) ).
thf(43,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_nat__add__left__cancel) ).
thf(214,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)],[43]) ).
thf(9,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_trans__less__add2) ).
thf(138,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(68,axiom,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( nat @ fun ),C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ nat_rec ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ nat_rec ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_nat__rec__Suc) ).
thf(333,plain,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( nat @ fun ),C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ nat_rec ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ nat_rec ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(114,axiom,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ abs @ ( C @ liftn ) ) )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( B @ ( C @ liftn ) ) @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_liftn_Osimps_I3_J) ).
thf(518,plain,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ abs @ ( C @ liftn ) ) )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( B @ ( C @ liftn ) ) @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( ( B @ suc )
!= A )
=> ( A @ ( B @ suc @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Suc__lessI) ).
thf(468,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( ( B @ suc )
!= A )
=> ( A @ ( B @ suc @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(25,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(170,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1,conjecture,
ja @ suc @ ( ia @ suc @ var @ ( ra @ subst ) ) @ abs @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ subst ) ) @ abs @ it ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(115,plain,
~ ( ja @ suc @ ( ia @ suc @ var @ ( ra @ subst ) ) @ abs @ it ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(112,axiom,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_subst__lift) ).
thf(511,plain,
! [A: dB,B: nat,C: dB] :
( ( B @ ( A @ ( B @ ( C @ lift ) @ subst ) ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',fact_76_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(202,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)],[38]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_add__Suc) ).
thf(301,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( A @ suc @ ( B @ ( nat @ ord_less ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_less__antisym) ).
thf(436,plain,
! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( A @ suc @ ( B @ ( nat @ ord_less ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',fact_72_add__right__cancel) ).
thf(125,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)],[6]) ).
thf(18,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_less__add__eq__less) ).
thf(157,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_termination__basic__simps_I2_J) ).
thf(152,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ suc @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_add__Suc__shift) ).
thf(289,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ plus_plus ) ) )
= ( A @ suc @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: nat,B: nat,C: TA @ ( nat @ fun )] :
( ! [D: nat] : ( D @ suc @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( D @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_lift__Suc__mono__less__iff) ).
thf(448,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: nat,B: nat,C: TA @ ( nat @ fun )] :
( ! [D: nat] : ( D @ suc @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( D @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(106,axiom,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_dB_Orecs_I1_J) ).
thf(492,plain,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_nat__add__right__cancel) ).
thf(179,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)],[29]) ).
thf(42,axiom,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_not__add__less2) ).
thf(211,plain,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(104,axiom,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_dB_Osimps_I7_J) ).
thf(485,plain,
! [A: nat,B: dB] :
( ( B @ abs )
!= ( A @ var ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(72,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ suc @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_less__trans__Suc) ).
thf(353,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ suc @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(5,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 ) ) )
<=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_add__less__cancel__left) ).
thf(121,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(113,axiom,
! [A: nat] :
( A
!= ( A @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_n__not__Suc__n) ).
thf(514,plain,
! [A: nat] :
( A
!= ( A @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA] : ( TA @ one_one @ ( A @ ( TA @ plus_plus ) ) @ ( A @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_less__add__one) ).
thf(147,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA] : ( TA @ one_one @ ( A @ ( TA @ plus_plus ) ) @ ( A @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__strict__right__mono) ).
thf(132,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(83,axiom,
! [A: nat,B: nat] : ( B @ ( A @ var @ ( ra @ subst ) ) @ it ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(396,plain,
! [A: nat,B: nat] : ( B @ ( A @ var @ ( ra @ subst ) ) @ it ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(3,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 ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__less__imp__less__right) ).
thf(116,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(61,axiom,
! [A: nat] : ( A @ suc @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_lessI) ).
thf(312,plain,
! [A: nat] : ( A @ suc @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(56,axiom,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ ( C @ suc @ liftn ) ) )
= ( A @ ( A @ ( B @ ( C @ liftn ) ) @ lift ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_liftn__lift) ).
thf(292,plain,
! [A: nat,B: dB,C: nat] :
( ( A @ ( B @ ( C @ suc @ liftn ) ) )
= ( A @ ( A @ ( B @ ( C @ liftn ) ) @ lift ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(95,axiom,
! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( A @ suc @ ( B @ ( nat @ ord_less ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_not__less__less__Suc__eq) ).
thf(452,plain,
! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( ( B = A )
=> ( A @ suc @ ( B @ ( nat @ ord_less ) ) ) )
& ( ( A @ suc @ ( B @ ( nat @ ord_less ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_linorder__neqE__nat) ).
thf(248,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(91,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ suc @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_less__SucI) ).
thf(439,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ suc @ ( B @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: nat,B: nat,C: TA @ ( nat @ fun )] :
( ! [D: nat] : ( D @ suc @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( D @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_lift__Suc__mono__less) ).
thf(366,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: nat,B: nat,C: TA @ ( nat @ fun )] :
( ! [D: nat] : ( D @ suc @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( D @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(19,axiom,
nat @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(160,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(33,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_add__lessD1) ).
thf(192,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(103,axiom,
ra @ it,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(484,plain,
ra @ it,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(35,axiom,
bool @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(197,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: nat,C: TA @ ( TA @ fun )] :
( ( A @ ( B @ suc @ ( C @ ( TA @ semiri532925092at_aux ) ) ) )
= ( A @ ( C @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ semiri532925092at_aux ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_of__nat__aux_Osimps_I2_J) ).
thf(361,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA,B: nat,C: TA @ ( TA @ fun )] :
( ( A @ ( B @ suc @ ( C @ ( TA @ semiri532925092at_aux ) ) ) )
= ( A @ ( C @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ semiri532925092at_aux ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(65,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ abs @ subst ) ) )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( B @ lift ) @ ( C @ subst ) ) @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_subst__Abs) ).
thf(324,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ abs @ subst ) ) )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( B @ lift ) @ ( C @ subst ) ) @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(17,axiom,
nat @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(156,plain,
nat @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(31,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_add__strict__mono) ).
thf(188,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(11,axiom,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_not__add__less1) ).
thf(141,plain,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(100,axiom,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_dB_Osimps_I10_J) ).
thf(471,plain,
! [TA: $tType,A: nat,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ var @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(70,axiom,
! [A: bool @ ( nat @ fun ),B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ! [D: nat] :
( ( B
= ( D @ suc ) )
=> ( D @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ! [D: nat] :
( ( B @ ( D @ ( nat @ ord_less ) ) )
=> ( ( D @ suc @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) )
=> ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_strict__inc__induct) ).
thf(339,plain,
! [A: bool @ ( nat @ fun ),B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ! [D: nat] :
( ( B
= ( D @ suc ) )
=> ( D @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ! [D: nat] :
( ( B @ ( D @ ( nat @ ord_less ) ) )
=> ( ( D @ suc @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) )
=> ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(105,axiom,
! [A: dB,B: nat,C: nat] :
( ( nat @ one_one @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ suc @ ( C @ ( A @ lift ) @ lift ) )
= ( C @ ( B @ ( A @ lift ) @ lift ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_lift__lift) ).
thf(489,plain,
! [A: dB,B: nat,C: nat] :
( ( nat @ one_one @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ suc @ ( C @ ( A @ lift ) @ lift ) )
= ( C @ ( B @ ( A @ lift ) @ lift ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(82,axiom,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ abs @ substn ) ) )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( B @ ( C @ substn ) ) @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_substn_Osimps_I3_J) ).
thf(393,plain,
! [A: nat,B: dB,C: dB] :
( ( A @ ( B @ ( C @ abs @ substn ) ) )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( B @ ( C @ substn ) ) @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(27,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_add__less__mono) ).
thf(173,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(78,axiom,
! [TA: $tType,A: nat,B: TA @ ( nat @ fun ),C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ nat_case ) ) ) )
= ( A @ ( B @ ( TA @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_nat__case__Suc) ).
thf(371,plain,
! [TA: $tType,A: nat,B: TA @ ( nat @ fun ),C: TA] :
( ( A @ suc @ ( B @ ( C @ ( TA @ nat_case ) ) ) )
= ( A @ ( B @ ( TA @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__not__refl3) ).
thf(134,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_nat__neq__iff) ).
thf(237,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',fact_53_nat__add__assoc) ).
thf(205,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)],[39]) ).
thf(111,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ? [C: nat] :
( A
= ( C @ ( B @ ( nat @ plus_plus ) ) @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_less__imp__Suc__add) ).
thf(508,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ? [C: nat] :
( A
= ( C @ ( B @ ( nat @ plus_plus ) ) @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(84,axiom,
! [A: dB] :
( ( A @ it )
=> ( A @ abs @ it ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Lambda) ).
thf(398,plain,
! [A: dB] :
( ( A @ it )
=> ( A @ abs @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(58,axiom,
! [A: nat,B: dB] :
( ( A @ ( B @ abs @ lift ) )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( B @ lift ) @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_lift_Osimps_I3_J) ).
thf(298,plain,
! [A: nat,B: dB] :
( ( A @ ( B @ abs @ lift ) )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) @ ( B @ lift ) @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(22,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(166,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(50,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_less__irrefl__nat) ).
thf(264,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(20,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 ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__less__imp__less__left) ).
thf(161,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( ( B @ var )
= ( A @ var ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_dB_Osimps_I1_J) ).
thf(279,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ var )
= ( A @ var ) ) )
& ( ( ( B @ var )
= ( A @ var ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(93,axiom,
! [A: nat] :
( ( A @ suc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Suc__n__not__n) ).
thf(444,plain,
! [A: nat] :
( ( A @ suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(14,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_nat__add__commute) ).
thf(149,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',fact_73_add__right__imp__eq) ).
thf(144,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)],[12]) ).
thf(108,axiom,
! [A: nat,B: nat] : ( B @ ( A @ ( nat @ plus_plus ) ) @ suc @ ( B @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__add__Suc2) ).
thf(498,plain,
! [A: nat,B: nat] : ( B @ ( A @ ( nat @ plus_plus ) ) @ suc @ ( B @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(71,axiom,
! [A: nat] :
( ( A @ suc )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Suc__eq__plus1) ).
thf(350,plain,
! [A: nat] :
( ( A @ suc )
= ( nat @ one_one @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(30,axiom,
nat @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(187,plain,
nat @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(80,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ ord_less ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_less__Suc__eq) ).
thf(377,plain,
! [A: nat,B: nat] :
( ( ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( A @ suc @ ( B @ ( nat @ ord_less ) ) ) )
& ( ( A @ suc @ ( B @ ( nat @ ord_less ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_one__reorient) ).
thf(271,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)],[53]) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_add__less__mono1) ).
thf(208,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
<=> ( B @ suc @ ( A @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_not__less__eq) ).
thf(387,plain,
! [A: nat,B: nat] :
( ( ( B @ suc @ ( A @ ( nat @ ord_less ) ) )
=> ~ ( A @ ( B @ ( nat @ ord_less ) ) ) )
& ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ suc @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(10,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(140,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',fact_71_add__left__cancel) ).
thf(251,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)],[48]) ).
thf(36,axiom,
nat @ ordere223160158up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(198,plain,
nat @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(67,axiom,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_subst__eq) ).
thf(330,plain,
! [A: dB,B: nat] :
( ( B @ ( A @ ( B @ var @ subst ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(97,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( nat @ plus_plus ) ) @ suc @ ( B @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__add__Suc1) ).
thf(462,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( nat @ plus_plus ) ) @ suc @ ( B @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(45,axiom,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( 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 ) ) )
=> ( 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/sandbox2/benchmark/theBenchmark.p',fact_31_nat__less__cases) ).
thf(226,plain,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( 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 ) ) )
=> ( 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)],[45]) ).
thf(51,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(267,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(23,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(167,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(89,axiom,
! [A: dB,B: dB] :
( ( ( B @ abs )
= ( A @ abs ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_dB_Osimps_I3_J) ).
thf(426,plain,
! [A: dB,B: dB] :
( ( ( B = A )
=> ( ( B @ abs )
= ( A @ abs ) ) )
& ( ( ( B @ abs )
= ( A @ abs ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(79,axiom,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( nat @ fun ),C: TA,D: TA @ ( nat @ fun )] :
( ! [E: nat] :
( ( E @ ( D @ ( TA @ ( nat @ aa ) ) ) )
= ( E @ ( B @ ( C @ ( TA @ nat_rec ) ) ) ) )
=> ( ( A @ suc @ ( D @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_def__nat__rec__Suc) ).
thf(374,plain,
! [TA: $tType,A: nat,B: TA @ ( TA @ fun ) @ ( nat @ fun ),C: TA,D: TA @ ( nat @ fun )] :
( ! [E: nat] :
( ( E @ ( D @ ( TA @ ( nat @ aa ) ) ) )
= ( E @ ( B @ ( C @ ( TA @ nat_rec ) ) ) ) )
=> ( ( A @ suc @ ( D @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( D @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( A
!= ( B @ suc ) )
=> ~ ! [C: nat] :
( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( C @ suc ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_lessE) ).
thf(355,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( A
!= ( B @ suc ) )
=> ~ ! [C: nat] :
( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( C @ suc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',fact_74_add__imp__eq) ).
thf(194,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)],[34]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add__Suc__right) ).
thf(295,plain,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(66,axiom,
! [A: dB,B: dB,C: nat,D: nat] :
( ( nat @ one_one @ ( C @ ( nat @ plus_plus ) ) @ ( D @ ( nat @ ord_less ) ) )
=> ( ( D @ ( C @ ( A @ ( B @ subst ) ) @ lift ) )
= ( nat @ one_one @ ( C @ ( nat @ plus_plus ) ) @ ( D @ ( A @ lift ) @ ( D @ ( B @ lift ) @ subst ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_lift__subst__lt) ).
thf(327,plain,
! [A: dB,B: dB,C: nat,D: nat] :
( ( nat @ one_one @ ( C @ ( nat @ plus_plus ) ) @ ( D @ ( nat @ ord_less ) ) )
=> ( ( D @ ( C @ ( A @ ( B @ subst ) ) @ lift ) )
= ( nat @ one_one @ ( C @ ( nat @ plus_plus ) ) @ ( D @ ( A @ lift ) @ ( D @ ( B @ lift ) @ subst ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',fact_54_nat__add__left__commute) ).
thf(199,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)],[37]) ).
thf(92,axiom,
! [TA: $tType,A: dB,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_dB_Orecs_I3_J) ).
thf(441,plain,
! [TA: $tType,A: dB,B: TA @ ( TA @ fun ) @ ( dB @ fun ),C: TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ dB_rec ) ) ) ) @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( dB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_Suc__less__eq) ).
thf(502,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) ) )
& ( ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(69,axiom,
! [A: dB,B: dB,C: nat,D: nat] :
( ( nat @ one_one @ ( C @ ( nat @ plus_plus ) ) @ ( D @ ( nat @ ord_less ) ) )
=> ( ( C @ ( D @ ( A @ ( B @ subst ) ) @ lift ) )
= ( D @ ( C @ ( A @ lift ) @ ( nat @ one_one @ ( C @ ( nat @ plus_plus ) ) @ ( B @ lift ) @ subst ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_lift__subst) ).
thf(336,plain,
! [A: dB,B: dB,C: nat,D: nat] :
( ( nat @ one_one @ ( C @ ( nat @ plus_plus ) ) @ ( D @ ( nat @ ord_less ) ) )
=> ( ( C @ ( D @ ( A @ ( B @ subst ) ) @ lift ) )
= ( D @ ( C @ ( A @ lift ) @ ( nat @ one_one @ ( C @ ( nat @ plus_plus ) ) @ ( B @ lift ) @ subst ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(16,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_termination__basic__simps_I1_J) ).
thf(154,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,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 ) ) )
<=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_add__less__cancel__right) ).
thf(175,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(62,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less ) ) )
=> ~ ! [C: nat] :
( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( C @ suc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Suc__lessE) ).
thf(314,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less ) ) )
=> ~ ! [C: nat] :
( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( C @ suc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Suc__mono) ).
thf(482,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ suc @ ( B @ suc @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(107,axiom,
! [A: nat] :
( ( A @ suc )
= ( A @ ( nat @ one_one @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Suc__eq__plus1__left) ).
thf(495,plain,
! [A: nat] :
( ( A @ suc )
= ( A @ ( nat @ one_one @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(77,axiom,
! [A: dB,B: dB,C: dB,D: nat,E: nat] :
( ( nat @ one_one @ ( D @ ( nat @ plus_plus ) ) @ ( E @ ( nat @ ord_less ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ subst ) ) @ ( D @ suc @ ( E @ ( B @ lift ) @ ( C @ subst ) ) @ subst ) ) )
= ( D @ ( B @ ( E @ ( A @ ( C @ subst ) ) @ subst ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_subst__subst) ).
thf(368,plain,
! [A: dB,B: dB,C: dB,D: nat,E: nat] :
( ( nat @ one_one @ ( D @ ( nat @ plus_plus ) ) @ ( E @ ( nat @ ord_less ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ subst ) ) @ ( D @ suc @ ( E @ ( B @ lift ) @ ( C @ subst ) ) @ subst ) ) )
= ( D @ ( B @ ( E @ ( A @ ( C @ subst ) ) @ subst ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(63,axiom,
! [A: dB,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( A @ ( C @ var @ subst ) ) )
= ( C @ var ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_subst__lt) ).
thf(319,plain,
! [A: dB,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( A @ ( C @ var @ subst ) ) )
= ( C @ var ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ var @ lift ) )
= ( nat @ one_one @ ( B @ ( nat @ plus_plus ) ) @ var ) ) )
& ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ var @ lift ) )
= ( B @ var ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_lift_Osimps_I1_J) ).
thf(304,plain,
! [A: nat,B: nat] :
( ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ var @ lift ) )
= ( nat @ one_one @ ( B @ ( nat @ plus_plus ) ) @ var ) ) )
& ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ var @ lift ) )
= ( B @ var ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(49,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_nat__add__left__cancel__less) ).
thf(258,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_add__strict__left__mono) ).
thf(171,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(88,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
<=> ? [C: nat] :
( A
= ( C @ ( B @ ( nat @ plus_plus ) ) @ suc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__iff__Suc__add) ).
thf(418,plain,
! [A: nat,B: nat] :
( ( ? [C: nat] :
( A
= ( C @ ( B @ ( nat @ plus_plus ) ) @ suc ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ? [C: nat] :
( A
= ( C @ ( B @ ( nat @ plus_plus ) ) @ suc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(24,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_trans__less__add1) ).
thf(168,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(86,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nat_Oinject) ).
thf(405,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ suc )
= ( A @ suc ) ) )
& ( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(32,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(190,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(41,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(210,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(52,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_linorder__neqE__linordered__idom) ).
thf(268,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat] :
( ( ~ ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( C @ var @ ( A @ liftn ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ var ) ) )
& ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( C @ var @ ( A @ liftn ) ) )
= ( C @ var ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_liftn_Osimps_I1_J) ).
thf(474,plain,
! [A: nat,B: nat,C: nat] :
( ( ~ ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( C @ var @ ( A @ liftn ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ var ) ) )
& ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( B @ ( C @ var @ ( A @ liftn ) ) )
= ( C @ var ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Suc__inject) ).
thf(400,plain,
! [A: nat,B: nat] :
( ( ( B @ suc )
= ( A @ suc ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(87,axiom,
! [TA: $tType,A: dB,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( TA @ ( dB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_dB_Osimps_I12_J) ).
thf(415,plain,
! [TA: $tType,A: dB,B: TA @ ( dB @ fun ),C: TA @ ( dB @ fun ) @ ( dB @ fun ),D: TA @ ( nat @ fun )] :
( ( A @ abs @ ( B @ ( C @ ( D @ ( TA @ dB_case ) ) ) ) )
= ( A @ ( B @ ( TA @ ( dB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(98,axiom,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_dB_Osimps_I6_J) ).
thf(464,plain,
! [A: dB,B: nat] :
( ( B @ var )
!= ( A @ abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ ord_less ) ) )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_less__SucE) ).
thf(459,plain,
! [A: nat,B: nat] :
( ( A @ suc @ ( B @ ( nat @ ord_less ) ) )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(21,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_less__not__refl) ).
thf(163,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(64,axiom,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ ( B @ lift ) @ it ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_lift__IT) ).
thf(322,plain,
! [A: nat,B: dB] :
( ( B @ it )
=> ( A @ ( B @ lift ) @ it ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_less__not__refl2) ).
thf(222,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(75,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Suc__lessD) ).
thf(364,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ suc @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(524,plain,
$false,
inference(e,[status(thm)],[500,118,214,138,333,518,468,170,115,511,202,301,436,125,157,152,289,448,492,179,211,485,353,121,514,147,132,396,116,312,292,452,248,439,366,160,192,484,197,361,324,156,188,141,471,339,489,393,173,371,134,237,205,508,398,298,166,264,161,279,444,149,144,498,350,187,377,271,208,387,140,251,198,330,462,226,267,167,426,374,355,194,295,327,199,441,502,336,154,175,314,482,495,368,319,304,258,171,418,168,405,190,210,268,474,400,415,464,459,163,322,222,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL755_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n002.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 23:32:35 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.08/1.14 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.09/1.56 % [INFO] Parsing done (422ms).
% 2.09/1.59 % [INFO] Running in sequential loop mode.
% 4.05/2.17 % [INFO] eprover registered as external prover.
% 4.05/2.18 % [INFO] Scanning for conjecture ...
% 4.33/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 112 axioms. Running axiom selection ...
% 4.71/2.55 % [INFO] Axiom selection finished. Selected 112 axioms (removed 0 axioms).
% 5.47/2.84 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.47/2.88 % [INFO] Type checking passed.
% 5.47/2.88 % [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 ...
% 12.55/5.26 % External prover 'e' found a proof!
% 12.55/5.26 % [INFO] Killing All external provers ...
% 12.55/5.26 % Time passed: 4668ms (effective reasoning time: 3662ms)
% 12.55/5.26 % 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)>
% 12.55/5.26 % Axioms used in derivation (112): arity_Nat_Onat___Rings_Osemiring__1, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_30_less__not__refl3, fact_79_add__strict__mono, fact_51_add__Suc__right, fact_48_nat__add__right__cancel, fact_33_not__less__less__Suc__eq, fact_75_add__left__imp__eq, arity_HOL_Obool___Orderings_Oorder, fact_50_add__Suc, fact_85_lift_Osimps_I1_J, fact_59_add__less__mono, fact_15_dB_Osimps_I12_J, fact_20_nat__rec__Suc, fact_17_dB_Orecs_I1_J, fact_87_liftn_Osimps_I3_J, fact_72_add__right__cancel, fact_47_strict__inc__induct, fact_0_Lambda, fact_44_lessE, fact_26_nat__neq__iff, fact_45_Suc__lessE, fact_66_less__add__Suc2, fact_42_lift__Suc__mono__less, fact_35_less__SucI, fact_91_lift__lift, fact_93_lift__subst__lt, fact_71_add__left__cancel, fact_9_Suc__inject, fact_54_nat__add__left__commute, fact_18_nat__case__Suc, fact_49_nat__add__left__cancel, fact_86_lift_Osimps_I3_J, fact_74_add__imp__eq, fact_39_Suc__lessD, fact_76_ab__semigroup__add__class_Oadd__ac_I1_J, fact_55_nat__add__commute, fact_38_less__SucE, fact_89_Suc__eq__plus1__left, fact_13_of__nat__aux_Osimps_I2_J, fact_81_add__less__imp__less__left, fact_7_n__not__Suc__n, fact_6_dB_Osimps_I6_J, fact_88_Suc__eq__plus1, fact_73_add__right__imp__eq, fact_94_less__add__one, fact_67_less__add__Suc1, fact_58_less__add__eq__less, fact_69_add__less__cancel__right, fact_80_add__less__imp__less__right, fact_41_lift__Suc__mono__less__iff, fact_52_nat__add__left__cancel__less, fact_70_less__imp__Suc__add, fact_11_subst__lift, fact_25_less__not__refl, fact_90_one__reorient, arity_Nat_Onat___Rings_Olinordered__semidom, fact_56_add__Suc__shift, fact_24_Suc__mono, fact_34_less__antisym, fact_22_not__less__eq, fact_31_nat__less__cases, fact_32_less__Suc__eq, fact_36_Suc__lessI, fact_64_not__add__less1, fact_40_Suc__less__SucD, fact_62_trans__less__add1, fact_37_less__trans__Suc, fact_97_subst__Abs, fact_5_dB_Osimps_I7_J, fact_21_lessI, fact_14_dB_Osimps_I10_J, fact_43_def__nat__rec__Suc, fact_46_liftn_Osimps_I1_J, fact_63_not__add__less2, fact_68_add__less__cancel__left, fact_96_linorder__neqE__linordered__idom, fact_82_termination__basic__simps_I1_J, fact_3_nat_Oinject, conj_1, fact_12_liftn__lift, fact_92_lift__subst, fact_23_Suc__less__eq, arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, arity_Nat_Onat___Groups_Oone, fact_8_Suc__n__not__n, fact_16_dB_Orecs_I3_J, fact_10_lift__IT, fact_60_add__less__mono1, arity_Nat_Onat___Orderings_Oorder, fact_84_subst__subst, fact_65_less__iff__Suc__add, fact_77_add__strict__right__mono, help_pp_1_1_U, fact_27_linorder__neqE__nat, fact_28_less__irrefl__nat, fact_95_substn_Osimps_I3_J, fact_2_dB_Osimps_I1_J, fact_4_subst__eq, fact_19_subst__lt, fact_83_termination__basic__simps_I2_J, fact_57_add__lessD1, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_61_trans__less__add2, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, conj_0, help_pp_2_1_U, fact_1_dB_Osimps_I3_J, fact_29_less__not__refl2, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_53_nat__add__assoc, fact_78_add__strict__left__mono
% 12.55/5.26 % No. of inferences in proof: 228
% 12.55/5.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4668 ms resp. 3662 ms w/o parsing
% 13.18/5.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.18/5.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------