%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM974_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:10:34 AM UTC 2026
% Result : Theorem 7.67s 3.44s
% Output : Refutation 8.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 109
% Syntax : Number of formulae : 220 ( 82 unt; 0 typ; 0 def)
% Number of atoms : 544 ( 167 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2065 ( 59 ~; 5 |; 54 &;1682 @)
% ( 37 <=>; 228 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 3 con; 0-3 aty)
% Number of variables : 310 ( 0 ^; 310 !; 0 ?; 310 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(nat1_decl,type,
nat1: int > nat ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(t_decl,type,
t: int ).
thf(thesis_decl,type,
thesis: $o ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_less__iff__diff__less__0) ).
thf(384,plain,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA] :
( ( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(67,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_gr0I) ).
thf(372,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(8,axiom,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_diff__eq__diff__less__eq) ).
thf(129,plain,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( C @ ( D @ ( TA @ ord_less_eq ) ) ) )
& ( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(38,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(281,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(57,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(336,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(92,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_gr__implies__not0) ).
thf(479,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(62,axiom,
t @ ( int @ one_one @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_t1) ).
thf(352,plain,
t @ ( int @ one_one @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(81,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ minus_minus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_minus__nat_Odiff__0) ).
thf(440,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ minus_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(34,axiom,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_int__0) ).
thf(269,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(18,axiom,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(185,plain,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(77,axiom,
! [A: int] :
( ( ( A @ nat1 )
= ( nat @ zero_zero ) )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_nat__0__iff) ).
thf(417,plain,
! [A: int] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ nat1 )
= ( nat @ zero_zero ) )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(43,axiom,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_int__1) ).
thf(288,plain,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_not__one__less__zero) ).
thf(320,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_of__nat__0__less__iff) ).
thf(436,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(41,axiom,
int @ group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
thf(284,plain,
int @ group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_of__nat__less__iff) ).
thf(152,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [A: int,B: nat] :
( ( B
= ( A @ nat1 ) )
<=> ( ( ~ ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B
= ( nat @ zero_zero ) ) )
& ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A
= ( B @ ( int @ semiring_1_of_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat__eq__iff2) ).
thf(164,plain,
! [A: int,B: nat] :
( ( ( ( ~ ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B
= ( nat @ zero_zero ) ) )
& ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A
= ( B @ ( int @ semiring_1_of_nat ) ) ) ) )
=> ( B
= ( A @ nat1 ) ) )
& ( ( B
= ( A @ nat1 ) )
=> ( ( ~ ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B
= ( nat @ zero_zero ) ) )
& ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A
= ( B @ ( int @ semiring_1_of_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_diff__eq__diff__eq) ).
thf(443,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( ( B = A )
=> ( D = C ) )
& ( ( D = C )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(27,axiom,
! [A: int,B: int,C: int] :
( ( B @ ( C @ ( int @ ord_less ) ) )
=> ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( ( C @ ( A @ ( int @ ord_less_eq ) ) )
| ( A @ ( C @ ( int @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Euler_Oaux2) ).
thf(238,plain,
! [A: int,B: int,C: int] :
( ( B @ ( C @ ( int @ ord_less ) ) )
=> ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( ( C @ ( A @ ( int @ ord_less_eq ) ) )
| ( A @ ( C @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(102,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_less__nat__zero__code) ).
thf(514,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(61,axiom,
! [A: nat,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( B @ nat1 @ ( nat @ ord_less ) ) )
<=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_nat__less__iff) ).
thf(348,plain,
! [A: nat,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( B @ nat1 @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ nat1 @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(63,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(353,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(37,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(280,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(23,axiom,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_transfer__int__nat__numerals_I1_J) ).
thf(221,plain,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(45,axiom,
int @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(293,plain,
int @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(84,axiom,
( ( nat @ one_one )
= ( int @ one_one @ nat1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_transfer__nat__int__numerals_I2_J) ).
thf(453,plain,
( ( nat @ one_one )
= ( int @ one_one @ nat1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(32,axiom,
( ( int @ one_one )
= ( nat @ one_one @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_transfer__int__nat__numerals_I2_J) ).
thf(265,plain,
( ( int @ one_one )
= ( nat @ one_one @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(106,axiom,
t @ ( int @ one_one @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_tpos) ).
thf(527,plain,
t @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(29,axiom,
! [A: int] :
( ( ~ ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( int @ semiring_1_of_nat ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_int__nat__eq) ).
thf(248,plain,
! [A: int] :
( ( ~ ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( int @ semiring_1_of_nat ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(69,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_not__less0) ).
thf(381,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(56,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zero__less__one) ).
thf(334,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_of__nat__le__iff) ).
thf(160,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(75,axiom,
! [A: int,B: int] :
( ( A @ nat1 @ ( B @ nat1 @ ( nat @ ord_less ) ) )
<=> ( ( A @ ( B @ ( int @ ord_less ) ) )
& ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zless__nat__conj) ).
thf(407,plain,
! [A: int,B: int] :
( ( ( ( A @ ( B @ ( int @ ord_less ) ) )
& ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
=> ( A @ nat1 @ ( B @ nat1 @ ( nat @ ord_less ) ) ) )
& ( ( A @ nat1 @ ( B @ nat1 @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( int @ ord_less ) ) )
& ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_eq__iff__diff__eq__0) ).
thf(429,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(10,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( B @ nat1 )
= ( A @ nat1 ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_transfer__nat__int__relations_I1_J) ).
thf(137,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( B = A )
=> ( ( B @ nat1 )
= ( A @ nat1 ) ) )
& ( ( ( B @ nat1 )
= ( A @ nat1 ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( C @ ( D @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_diff__eq__diff__less) ).
thf(484,plain,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( C @ ( D @ ( TA @ ord_less ) ) ) )
& ( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_nat__neq__iff) ).
thf(361,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)],[66]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_of__nat__0) ).
thf(461,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(95,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( int @ minus_minus ) ) @ nat1 )
= ( B @ nat1 @ ( A @ nat1 @ ( nat @ minus_minus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_nat__diff__distrib) ).
thf(493,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( int @ minus_minus ) ) @ nat1 )
= ( B @ nat1 @ ( A @ nat1 @ ( nat @ minus_minus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(42,axiom,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ nat1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_nat__int) ).
thf(285,plain,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ nat1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(25,axiom,
! [A: int,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= A )
<=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
& ( B
= ( A @ nat1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_int__eq__iff) ).
thf(224,plain,
! [A: int,B: nat] :
( ( ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
& ( B
= ( A @ nat1 ) ) )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= A ) )
& ( ( ( B @ ( int @ semiring_1_of_nat ) )
= A )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
& ( B
= ( A @ nat1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(52,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_of__nat__1) ).
thf(317,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_not__one__le__zero) ).
thf(156,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_one__neq__zero) ).
thf(388,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(97,axiom,
! [A: int] :
( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_int__one__le__iff__zero__less) ).
thf(499,plain,
! [A: int] :
( ( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(91,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_less__not__refl) ).
thf(476,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(55,axiom,
! [A: int,B: int] :
( ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_zle__diff1__eq) ).
thf(328,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) )
& ( ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_zero__neq__one) ).
thf(471,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(30,axiom,
! [A: nat] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_int__eq__0__conv) ).
thf(256,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(7,axiom,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(128,plain,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(99,axiom,
( ( int @ zero_zero @ nat1 )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_nat__0) ).
thf(508,plain,
( ( int @ zero_zero @ nat1 )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_less__not__refl3) ).
thf(425,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(101,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(513,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(31,axiom,
int @ ordered_ab_group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add) ).
thf(264,plain,
int @ ordered_ab_group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(47,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( ( B @ nat1 @ ( A @ nat1 @ ( nat @ ord_less ) ) )
<=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_nat__mono__iff) ).
thf(296,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ nat1 @ ( A @ nat1 @ ( nat @ ord_less ) ) ) )
& ( ( B @ nat1 @ ( A @ nat1 @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(68,axiom,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_zero__less__int__conv) ).
thf(375,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(72,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_neq0__conv) ).
thf(391,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(11,axiom,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_of__nat__eq__iff) ).
thf(144,plain,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(26,axiom,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_zero__zle__int) ).
thf(236,plain,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(110,axiom,
! [A: nat] :
( ( A
= ( nat @ one_one @ ( t @ nat1 @ ( nat @ minus_minus ) ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> thesis ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(540,plain,
! [A: nat] :
( ( A
= ( nat @ one_one @ ( t @ nat1 @ ( nat @ minus_minus ) ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> thesis ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_zero__le__one) ).
thf(219,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( A @ ( nat @ minus_minus ) ) @ ( B @ ( A @ ( nat @ minus_minus ) ) @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_diff__less__mono2) ).
thf(451,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( A @ ( nat @ minus_minus ) ) @ ( B @ ( A @ ( nat @ minus_minus ) ) @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_zero__le__imp__of__nat) ).
thf(271,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) )
=> ( ( ( B @ ( A @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_diffs0__imp__equal) ).
thf(345,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) )
=> ( ( ( B @ ( A @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(21,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_zless__int) ).
thf(213,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(28,axiom,
! [A: nat] :
( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_int__le__0__conv) ).
thf(240,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) ) )
& ( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(104,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_linorder__neqE__nat) ).
thf(521,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)],[104]) ).
thf(73,axiom,
! [A: int,B: nat] :
( ( A @ nat1 @ ( B @ ( nat @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zless__nat__eq__int__zless) ).
thf(399,plain,
! [A: int,B: nat] :
( ( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
=> ( A @ nat1 @ ( B @ ( nat @ ord_less ) ) ) )
& ( ( A @ nat1 @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(85,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( ( B
!= ( int @ one_one @ ( A @ ( int @ minus_minus ) ) ) )
=> ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Euler_Oaux1) ).
thf(455,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( ( B
!= ( int @ one_one @ ( A @ ( int @ minus_minus ) ) ) )
=> ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(24,axiom,
int @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(223,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',fact_13_linorder__neqE__linordered__idom) ).
thf(306,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)],[50]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_of__nat__0__le__iff) ).
thf(135,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(33,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
~ ( TA @ zero_zero @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_of__nat__less__0__iff) ).
thf(267,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
~ ( TA @ zero_zero @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(98,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_less__zeroE) ).
thf(505,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(94,axiom,
! [A: int] :
( ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 )
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_nat__le__0) ).
thf(490,plain,
! [A: int] :
( ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 )
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(108,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_one__reorient) ).
thf(531,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)],[108]) ).
thf(3,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_less__int__def) ).
thf(112,plain,
! [A: int,B: int] :
( ( ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: nat] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_int__less__0__conv) ).
thf(123,plain,
! [A: nat] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(65,axiom,
! [A: int] :
( ( A @ nat1 @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_zero__less__nat__eq) ).
thf(355,plain,
! [A: int] :
( ( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ nat1 @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ nat1 @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_diff__self) ).
thf(458,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(39,axiom,
int @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(282,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(76,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ minus_minus ) ) )
= ( B @ ( A @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ minus_minus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_diff__commute) ).
thf(414,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ minus_minus ) ) )
= ( B @ ( A @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(109,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(539,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(105,axiom,
! [A: nat] :
( ( A @ ( A @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_diff__self__eq__0) ).
thf(524,plain,
! [A: nat] :
( ( A @ ( A @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(103,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( B @ nat1 @ ( nat @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_transfer__nat__int__relations_I2_J) ).
thf(517,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ nat1 @ ( B @ nat1 @ ( nat @ ord_less ) ) ) )
& ( ( A @ nat1 @ ( B @ nat1 @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(49,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_less__imp__diff__less) ).
thf(304,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(15,axiom,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(158,plain,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [A: nat,B: int] :
( ( ( B @ nat1 )
= A )
<=> ( ( ~ ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) )
& ( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B
= ( A @ ( int @ semiring_1_of_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nat__eq__iff) ).
thf(186,plain,
! [A: nat,B: int] :
( ( ( ( ~ ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) )
& ( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B
= ( A @ ( int @ semiring_1_of_nat ) ) ) ) )
=> ( ( B @ nat1 )
= A ) )
& ( ( ( B @ nat1 )
= A )
=> ( ( ~ ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) )
& ( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B
= ( A @ ( int @ semiring_1_of_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(44,axiom,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( int @ semiring_1_of_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_nat__0__le) ).
thf(290,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( int @ semiring_1_of_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ minus_minus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_diff__0__right) ).
thf(510,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ minus_minus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(20,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
thf(207,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(151,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
<=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_le__iff__diff__le__0) ).
thf(300,plain,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA] :
( ( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(74,axiom,
( ( nat @ zero_zero )
= ( int @ zero_zero @ nat1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_transfer__nat__int__numerals_I1_J) ).
thf(405,plain,
( ( nat @ zero_zero )
= ( int @ zero_zero @ nat1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(36,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( B @ nat1 )
= ( A @ nat1 ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_eq__nat__nat__iff) ).
thf(273,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( B = A )
=> ( ( B @ nat1 )
= ( A @ nat1 ) ) )
& ( ( ( B @ nat1 )
= ( A @ nat1 ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_less__not__refl2) ).
thf(341,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( A @ ( nat @ minus_minus ) ) @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_diff__less) ).
thf(474,plain,
! [A: nat,B: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( A @ ( nat @ minus_minus ) ) @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(40,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(283,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_less__imp__of__nat__less) ).
thf(294,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(6,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_of__nat__less__imp__less) ).
thf(126,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_right__minus__eq) ).
thf(464,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(107,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_less__irrefl__nat) ).
thf(528,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(111,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ minus_minus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( B @ ( A @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_zero__less__diff) ).
thf(322,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ minus_minus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ minus_minus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(64,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(354,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_zero__reorient) ).
thf(309,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(96,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_diff__0__eq__0) ).
thf(496,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(58,axiom,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ nat1 @ ( B @ nat1 @ ( nat @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_nat__less__eq__zless) ).
thf(337,plain,
! [A: int,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ nat1 @ ( B @ nat1 @ ( nat @ ord_less ) ) ) )
& ( ( A @ nat1 @ ( B @ nat1 @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(4,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(122,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(547,plain,
$false,
inference(e,[status(thm)],[384,372,129,281,336,479,352,440,269,185,417,288,320,436,284,152,164,443,238,514,348,353,280,221,293,453,265,527,248,381,334,160,407,429,137,484,361,461,493,285,224,317,156,388,499,476,328,471,256,128,508,425,513,264,296,375,391,144,236,540,219,451,271,345,213,240,521,399,455,223,306,135,267,505,490,531,112,123,355,458,282,414,539,524,517,304,158,186,290,510,207,151,300,405,273,341,474,283,294,126,464,528,111,322,354,309,496,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM974_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n006.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 04:23:40 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.40/1.26 % [INFO] Parsing done (263ms).
% 1.40/1.27 % [INFO] Running in sequential loop mode.
% 2.40/1.65 % [INFO] eprover registered as external prover.
% 2.40/1.66 % [INFO] Scanning for conjecture ...
% 2.60/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 116 axioms. Running axiom selection ...
% 2.79/1.89 % [INFO] Axiom selection finished. Selected 108 axioms (removed 8 axioms).
% 3.39/2.05 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.39/2.06 % [INFO] Type checking passed.
% 3.39/2.07 % [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 ...
% 7.67/3.44 % External prover 'e' found a proof!
% 7.67/3.44 % [INFO] Killing All external provers ...
% 7.67/3.44 % Time passed: 2889ms (effective reasoning time: 2160ms)
% 7.67/3.44 % 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)>
% 7.67/3.44 % Axioms used in derivation (108): fact_54_int__less__0__conv, fact_64_int__eq__0__conv, fact_41_nat__mono__iff, fact_92_not__one__le__zero, fact_48_of__nat__0, fact_70_less__int__def, fact_31_gr__implies__not0, fact_20_linorder__neqE__nat, fact_68_nat__int, fact_61_int__0, fact_12_zero__reorient, fact_37_zero__less__nat__eq, fact_58_of__nat__0__le__iff, arity_Int_Oint___Groups_Oone, fact_76_nat__eq__iff2, fact_24_zero__neq__one, fact_10_not__one__less__zero, fact_36_less__imp__diff__less, fact_2_diff__0__eq__0, arity_Int_Oint___Rings_Olinordered__idom, fact_51_int__nat__eq, fact_28_diff__0__right, arity_Nat_Onat___Rings_Osemiring__1, fact_82_transfer__int__nat__numerals_I2_J, fact_5_less__nat__zero__code, fact_39_nat__0, fact_66_int__eq__iff, fact_65_int__le__0__conv, fact_69_Euler_Oaux2, fact_18_less__not__refl2, fact_29_diff__eq__diff__less, fact_3_diff__self__eq__0, fact_77_nat__eq__iff, fact_56_transfer__int__nat__numerals_I1_J, fact_60_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, fact_83_int__1, fact_97_transfer__nat__int__relations_I2_J, fact_79_diff__eq__diff__less__eq, fact_49_of__nat__less__iff, fact_96_nat__less__eq__zless, fact_90_zero__less__int__conv, fact_26_right__minus__eq, fact_21_nat__neq__iff, fact_59_zero__zle__int, fact_71_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_1_zero__less__diff, fact_50_of__nat__1, arity_Int_Oint___Rings_Osemiring__1, fact_85_nat__le__0, fact_32_not__less0, fact_17_less__not__refl3, fact_25_one__neq__zero, fact_19_less__irrefl__nat, fact_55_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_53_zle__diff1__eq, fact_23_diff__commute, fact_52_nat__0__iff, fact_8_diff__less, fact_34_minus__nat_Odiff__0, fact_44_Euler_Oaux1, fact_81_Nat__Transfer_Otransfer__int__nat__relations_I2_J, arity_Nat_Onat___Rings_Olinordered__semidom, fact_67_nat__0__le, arity_Nat_Onat___Groups_Ozero, fact_11_zero__less__one, fact_78_nat__less__iff, arity_Int_Oint___Groups_Ogroup__add, fact_93_zero__le__one, fact_7_diff__self, fact_80_zless__int, fact_88_less__imp__of__nat__less, fact_73_transfer__nat__int__relations_I1_J, fact_35_diff__less__mono2, fact_40_transfer__nat__int__numerals_I2_J, fact_30_gr0I, fact_0_t1, fact_43_transfer__nat__int__numerals_I1_J, arity_Nat_Onat___Nat_Osemiring__char__0, fact_9_less__iff__diff__less__0, fact_84_int__one__le__iff__zero__less, fact_45_of__nat__0__less__iff, arity_Int_Oint___Rings_Ozero__neq__one, fact_22_less__not__refl, arity_Nat_Onat___Groups_Oone, fact_86_nat__diff__distrib, arity_Int_Oint___Groups_Oordered__ab__group__add, fact_4_neq0__conv, fact_72_eq__nat__nat__iff, fact_27_eq__iff__diff__eq__0, fact_87_of__nat__less__0__iff, fact_15_diff__eq__diff__eq, fact_14_one__reorient, fact_13_linorder__neqE__linordered__idom, fact_89_of__nat__less__imp__less, fact_46_of__nat__eq__iff, fact_94_zless__nat__eq__int__zless, fact_95_le__iff__diff__le__0, arity_Int_Oint___Groups_Ozero, fact_42_tpos, conj_0, arity_Int_Oint___Nat_Osemiring__char__0, arity_Int_Oint___Rings_Olinordered__semidom, fact_47_of__nat__le__iff, fact_57_zero__le__imp__of__nat, arity_Nat_Onat___Rings_Ozero__neq__one, fact_6_less__zeroE, fact_33_diffs0__imp__equal, fact_38_zless__nat__conj
% 7.67/3.44 % No. of inferences in proof: 220
% 7.67/3.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2889 ms resp. 2160 ms w/o parsing
% 8.02/3.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.02/3.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------