TSTP Solution File: SWW485_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW485_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:24:52 EDT 2023
% Result : Theorem 5.30s 2.23s
% Output : Refutation 5.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 68
% Syntax : Number of formulae : 117 ( 30 unt; 21 typ; 0 def)
% Number of atoms : 290 ( 49 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 913 ( 10 ~; 3 |; 22 &; 749 @)
% ( 9 <=>; 120 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 6 con; 0-4 aty)
% Number of variables : 198 ( 0 ^; 179 !; 4 ?; 198 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(idom_type,type,
idom:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_type,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(dense_linorder_type,type,
dense_linorder:
!>[TA: $tType] : $o ).
thf(real_normed_vector_type,type,
real_normed_vector:
!>[TA: $tType] : $o ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(poly_type,type,
poly:
!>[TA: $tType] : ( ( poly1 @ TA ) > ( fun @ TA @ TA ) ) ).
thf(norm_norm_type,type,
norm_norm:
!>[TA: $tType] : ( TA > real ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(cs_type,type,
cs: poly1 @ complex ).
thf(r_type,type,
r: real ).
thf(thesis_type,type,
thesis: $o ).
thf(22,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ C @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ A ) ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_dense__le__bounded) ).
thf(115,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ C @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ A ) ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(36,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(152,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(31,axiom,
real_normed_vector @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__vector) ).
thf(147,plain,
real_normed_vector @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(17,axiom,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( idom @ TA ) )
=> ! [A: poly1 @ TA,B: poly1 @ TA] :
( ( ( poly @ TA @ B )
= ( poly @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_poly__eq__iff) ).
thf(92,plain,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( idom @ TA ) )
=> ! [A: poly1 @ TA,B: poly1 @ TA] :
( ( ( ( poly @ TA @ B )
= ( poly @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( poly @ TA @ B )
= ( poly @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_dense__le) ).
thf(73,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( ord_less @ ( fun @ TA @ TB ) @ B @ A )
<=> ( ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A )
& ~ ( ord_less_eq @ ( fun @ TA @ TB ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_less__fun__def) ).
thf(80,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( ( ord_less @ ( fun @ TA @ TB ) @ B @ A )
=> ( ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A )
& ~ ( ord_less_eq @ ( fun @ TA @ TB ) @ A @ B ) ) )
& ( ( ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A )
& ~ ( ord_less_eq @ ( fun @ TA @ TB ) @ A @ B ) )
=> ( ord_less @ ( fun @ TA @ TB ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(34,axiom,
idom @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oidom) ).
thf(150,plain,
idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(3,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Orderings_Oord) ).
thf(50,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ord @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(46,axiom,
? [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
& ! [B: complex] :
( ( ord_less_eq @ real @ ( norm_norm @ complex @ B ) @ r )
=> ( ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_pCons) ).
thf(175,plain,
? [A: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
& ! [B: complex] :
( ( ord_less_eq @ real @ ( norm_norm @ complex @ B ) @ r )
=> ( ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(16,axiom,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] :
~ ( ord_less @ real @ ( norm_norm @ TA @ A ) @ ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_norm__not__less__zero) ).
thf(90,plain,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] :
~ ( ord_less @ real @ ( norm_norm @ TA @ A ) @ ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__idom) ).
thf(56,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,axiom,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ( ( norm_norm @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_norm__zero) ).
thf(142,plain,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ( ( norm_norm @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A )
<=> ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_le__fun__def) ).
thf(153,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ( ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A )
=> ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) )
& ( ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) )
=> ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(4,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ozero) ).
thf(52,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,axiom,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ real @ ( norm_norm @ TA @ A ) @ ( zero_zero @ real ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_norm__le__zero__iff) ).
thf(125,plain,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] :
( ( ( ord_less_eq @ real @ ( norm_norm @ TA @ A ) @ ( zero_zero @ real ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ord_less_eq @ real @ ( norm_norm @ TA @ A ) @ ( zero_zero @ real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( ord_less_eq @ ( fun @ TA @ TB ) @ C @ B )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_le__funD) ).
thf(157,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( ord_less_eq @ ( fun @ TA @ TB ) @ C @ B )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( ord_less_eq @ ( fun @ TA @ TB ) @ C @ B )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_le__funE) ).
thf(164,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( ord_less_eq @ ( fun @ TA @ TB ) @ C @ B )
=> ( ord_less_eq @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(48,axiom,
! [A: real] :
( ! [B: complex] :
( ( ord_less_eq @ real @ ( norm_norm @ complex @ B ) @ r )
=> ( ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ B ) ) @ A ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(179,plain,
! [A: real] :
( ! [B: complex] :
( ( ord_less_eq @ real @ ( norm_norm @ complex @ B ) @ r )
=> ( ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ B ) ) @ A ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(84,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_char_0 @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Int_Oring__char__0) ).
thf(60,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_char_0 @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( idom @ TA ) )
=> ! [A: poly1 @ TA] :
( ( ( poly @ TA @ A )
= ( poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) )
<=> ( A
= ( zero_zero @ ( poly1 @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_poly__zero) ).
thf(102,plain,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( idom @ TA ) )
=> ! [A: poly1 @ TA] :
( ( ( ( poly @ TA @ A )
= ( poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) )
=> ( A
= ( zero_zero @ ( poly1 @ TA ) ) ) )
& ( ( A
= ( zero_zero @ ( poly1 @ TA ) ) )
=> ( ( poly @ TA @ A )
= ( poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(38,axiom,
ord @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oord) ).
thf(156,plain,
ord @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(27,axiom,
dense_linorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Odense__linorder) ).
thf(141,plain,
dense_linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(44,axiom,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] :
( ( ( norm_norm @ TA @ A )
= ( zero_zero @ real ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_norm__eq__zero) ).
thf(166,plain,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] :
( ( ( ( norm_norm @ TA @ A )
= ( zero_zero @ real ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( norm_norm @ TA @ A )
= ( zero_zero @ real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(32,axiom,
comm_semiring_0 @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__0) ).
thf(148,plain,
comm_semiring_0 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(41,axiom,
zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
thf(161,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(33,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(149,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(5,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__0) ).
thf(54,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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(49,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ord_less @ real @ C @ B )
& ( ord_less @ real @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_real__lbound__gt__zero) ).
thf(86,plain,
! [A: real,B: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ord_less @ real @ C @ B )
& ( ord_less @ real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) )
=> ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_le__funI) ).
thf(159,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) )
=> ( ord_less_eq @ ( fun @ TA @ TB ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(172,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(12,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( B = A )
=> ( ord_less @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_ord__less__eq__trans) ).
thf(76,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ( B = A )
=> ( ord_less @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_ord__eq__le__trans) ).
thf(98,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
ring_char_0 @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Oring__char__0) ).
thf(140,plain,
ring_char_0 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_zero__reorient) ).
thf(66,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ( B = A )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_ord__le__eq__trans) ).
thf(108,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ C @ B )
=> ( ( B = A )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(42,axiom,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( norm_norm @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_norm__ge__zero) ).
thf(162,plain,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] : ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( norm_norm @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(21,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_poly__0) ).
thf(112,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
real_normed_vector @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__vector) ).
thf(145,plain,
real_normed_vector @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(23,axiom,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( norm_norm @ TA @ A ) )
<=> ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_zero__less__norm__iff) ).
thf(119,plain,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ ( norm_norm @ TA @ A ) )
=> ( A
!= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ real @ ( zero_zero @ real ) @ ( norm_norm @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oidom) ).
thf(58,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(35,axiom,
comm_semiring_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__0) ).
thf(151,plain,
comm_semiring_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(30,axiom,
idom @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oidom) ).
thf(146,plain,
idom @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(25,axiom,
! [A: real,B: real] :
( ( ord_less_eq @ real @ B @ A )
<=> ( ( ord_less @ real @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_less__eq__real__def) ).
thf(131,plain,
! [A: real,B: real] :
( ( ( ord_less_eq @ real @ B @ A )
=> ( ( ord_less @ real @ B @ A )
| ( B = A ) ) )
& ( ( ( ord_less @ real @ B @ A )
| ( B = A ) )
=> ( ord_less_eq @ real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_ord__eq__less__trans) ).
thf(62,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(47,axiom,
zero @ complex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(178,plain,
zero @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(183,plain,
$false,
inference(e,[status(thm)],[115,152,147,92,73,80,150,50,175,90,56,142,153,52,125,157,164,179,84,60,102,156,141,166,148,161,149,54,49,86,159,172,76,98,140,66,108,162,112,145,119,58,151,146,131,62,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW485_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.13 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n001.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu May 18 22:52:21 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.93/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.58/1.07 % [INFO] Parsing done (202ms).
% 1.58/1.07 % [INFO] Running in sequential loop mode.
% 2.02/1.27 % [INFO] eprover registered as external prover.
% 2.02/1.27 % [INFO] cvc4 registered as external prover.
% 2.02/1.27 % [INFO] Scanning for conjecture ...
% 2.21/1.35 % [INFO] Found a conjecture and 140 axioms. Running axiom selection ...
% 2.28/1.41 % [INFO] Axiom selection finished. Selected 46 axioms (removed 94 axioms).
% 2.62/1.48 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.62/1.49 % [INFO] Type checking passed.
% 2.62/1.49 % [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 ...
% 5.30/2.23 % External prover 'e' found a proof!
% 5.30/2.23 % [INFO] Killing All external provers ...
% 5.30/2.23 % Time passed: 1748ms (effective reasoning time: 1154ms)
% 5.30/2.23 % 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)>
% 5.30/2.23 % Axioms used in derivation (46): fact_67_zero__reorient, fact_68_real__lbound__gt__zero, arity_Polynomial_Opoly___Rings_Olinordered__idom, arity_RealDef_Oreal___Rings_Oidom, arity_RealDef_Oreal___Int_Oring__char__0, arity_RealDef_Oreal___Rings_Ocomm__semiring__0, fact_30_ord__eq__less__trans, fact_66_less__fun__def, fact_3_norm__ge__zero, conj_0, fact_58_le__funI, arity_Complex_Ocomplex___Rings_Ocomm__semiring__0, arity_fun___Orderings_Oord, arity_RealDef_Oreal___Groups_Ozero, fact_63_dense__le__bounded, fact_13_poly__0, fact_35_poly__zero, fact_2_poly__eq__iff, fact_12_ord__le__eq__trans, fact_5_le__fun__def, arity_Complex_Ocomplex___Rings_Oidom, arity_Complex_Ocomplex___Int_Oring__char__0, fact_64_dense__le, fact_0_pCons, fact_65_less__eq__real__def, arity_Polynomial_Opoly___Rings_Oidom, fact_74_ext, arity_RealDef_Oreal___Orderings_Oord, fact_9_le__funD, arity_Polynomial_Opoly___Groups_Ozero, fact_36_norm__not__less__zero, arity_Polynomial_Opoly___Orderings_Oord, arity_Polynomial_Opoly___Int_Oring__char__0, arity_RealDef_Oreal___Orderings_Odense__linorder, fact_14_norm__eq__zero, fact_15_norm__zero, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_11_ord__eq__le__trans, arity_RealDef_Oreal___RealVector_Oreal__normed__vector, fact_4_norm__le__zero__iff, fact_31_ord__less__eq__trans, arity_Polynomial_Opoly___Rings_Ocomm__semiring__0, arity_Complex_Ocomplex___Groups_Ozero, arity_Complex_Ocomplex___RealVector_Oreal__normed__vector, fact_55_le__funE, fact_16_zero__less__norm__iff
% 5.30/2.23 % No. of inferences in proof: 96
% 5.30/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1748 ms resp. 1154 ms w/o parsing
% 5.72/2.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.72/2.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------