%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW486_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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:40 AM UTC 2026
% Result : Theorem 12.64s 4.55s
% Output : Refutation 13.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 185
% Syntax : Number of formulae : 372 ( 122 unt; 0 typ; 0 def)
% Number of atoms : 1005 ( 162 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 3681 ( 46 ~; 21 |; 59 &;3094 @)
% ( 31 <=>; 430 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 8 con; 0-4 aty)
% Number of variables : 674 ( 0 ^; 672 !; 2 ?; 674 :)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(real_type,type,
real: $tType ).
thf(cancel1352612707id_add_decl,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(idom_decl,type,
idom:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_decl,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_ring_decl,type,
linordered_ring:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(no_zero_divisors_decl,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_decl,type,
ab_semigroup_mult:
!>[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(ring_n68954251visors_decl,type,
ring_n68954251visors:
!>[TA: $tType] : $o ).
thf(linord581940658strict_decl,type,
linord581940658strict:
!>[TA: $tType] : $o ).
thf(real_normed_vector_decl,type,
real_normed_vector:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere216010020id_add_decl,type,
ordere216010020id_add:
!>[TA: $tType] : $o ).
thf(real_normed_algebra_decl,type,
real_normed_algebra:
!>[TA: $tType] : $o ).
thf(ordere779506340up_add_decl,type,
ordere779506340up_add:
!>[TA: $tType] : $o ).
thf(ab_sem1668676832m_mult_decl,type,
ab_sem1668676832m_mult:
!>[TA: $tType] : $o ).
thf(linord20386208strict_decl,type,
linord20386208strict:
!>[TA: $tType] : $o ).
thf(real_n1866405975lgebra_decl,type,
real_n1866405975lgebra:
!>[TA: $tType] : $o ).
thf(linord893533164strict_decl,type,
linord893533164strict:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : 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(pCons_decl,type,
pCons:
!>[TA: $tType] : ( TA > ( TA @ poly1 ) > ( TA @ poly1 ) ) ).
thf(poly_decl,type,
poly:
!>[TA: $tType] : ( ( TA @ poly1 ) > ( TA @ ( TA @ fun ) ) ) ).
thf(norm_norm_decl,type,
norm_norm:
!>[TA: $tType] : ( TA > real ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(c_decl,type,
c: complex ).
thf(cs_decl,type,
cs: complex @ poly1 ).
thf(m_decl,type,
m: real ).
thf(r_decl,type,
r: real ).
thf(z_decl,type,
z: complex ).
thf(180,axiom,
real @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
thf(645,plain,
real @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(171,axiom,
complex @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocancel__ab__semigroup__add) ).
thf(629,plain,
complex @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_add__le__imp__le__right) ).
thf(365,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_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(121,axiom,
real @ linord581940658strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__ring__strict) ).
thf(479,plain,
real @ linord581940658strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(136,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_order__le__less) ).
thf(518,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( ( ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
thf(352,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(64,axiom,
real @ comm_semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__0) ).
thf(333,plain,
real @ comm_semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(32,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ comm_semiring_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__0) ).
thf(249,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ comm_semiring_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_norm__le__zero__iff) ).
thf(408,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) ) )
& ( ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(247,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(166,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ times_times ) ) @ ( B @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_mult__strict__left__mono__neg) ).
thf(614,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ times_times ) ) @ ( B @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linord219039673up_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Olinordered__ab__group__add) ).
thf(202,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linord219039673up_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere236663937imp_le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(217,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere236663937imp_le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( B @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_mult__pos__neg2) ).
thf(276,plain,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( B @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(102,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_20_add__imp__eq) ).
thf(440,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)],[102]) ).
thf(185,axiom,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) )
!= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_no__zero__divisors) ).
thf(655,plain,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) )
!= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(139,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_linorder__le__less__linear) ).
thf(533,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(130,axiom,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_mult__zero__left) ).
thf(500,plain,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(117,axiom,
real @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(472,plain,
real @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(141,axiom,
real @ linord219039673up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
thf(538,plain,
real @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(96,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_zero__less__double__add__iff__zero__less__single__add) ).
thf(417,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(48,axiom,
z @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( z @ ( complex @ times_times ) ) @ ( complex @ norm_norm ) @ ( c @ ( complex @ norm_norm ) @ ( real @ plus_plus ) ) @ ( z @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( z @ ( complex @ times_times ) ) @ ( c @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096cmod_A_Ic_A_L_Az_A_K_Apoly_Acs_Az_J_A_060_061_Acmod_Ac_A_L_Acmod_A_Iz_A_K_Apoly_Acs_Az_J_096) ).
thf(288,plain,
z @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( z @ ( complex @ times_times ) ) @ ( complex @ norm_norm ) @ ( c @ ( complex @ norm_norm ) @ ( real @ plus_plus ) ) @ ( z @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( z @ ( complex @ times_times ) ) @ ( c @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(52,axiom,
real @ real_n1866405975lgebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__div__algebra) ).
thf(301,plain,
real @ real_n1866405975lgebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_mult__neg__neg) ).
thf(320,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(184,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_42_add__less__cancel__right) ).
thf(651,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)],[184]) ).
thf(36,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ring_char_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Int_Oring__char__0) ).
thf(257,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ring_char_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(77,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_leD) ).
thf(372,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ~ ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(155,axiom,
real @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring) ).
thf(587,plain,
real @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(146,axiom,
! [A: complex,B: complex] : ( A @ ( complex @ norm_norm ) @ ( A @ ( B @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ plus_plus ) ) @ ( B @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_complex__mod__triangle__sub) ).
thf(559,plain,
! [A: complex,B: complex] : ( A @ ( complex @ norm_norm ) @ ( A @ ( B @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ plus_plus ) ) @ ( B @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(178,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( ~ ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_less__le__not__le) ).
thf(638,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( ( ~ ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ~ ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( TA @ zero_zero @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) )
<=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_mult__less__cancel__left__neg) ).
thf(421,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( TA @ zero_zero @ ( C @ ( TA @ ord_less ) ) )
=> ( ( ( B @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(163,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_order__less__imp__le) ).
thf(606,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(284,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(95,axiom,
real @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__semigroup__add) ).
thf(416,plain,
real @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_linorder__antisym__conv2) ).
thf(325,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly1 @ ab_semigroup_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oab__semigroup__add) ).
thf(228,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly1 @ ab_semigroup_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(49,axiom,
complex @ ring_n68954251visors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors) ).
thf(289,plain,
complex @ ring_n68954251visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ times_times ) ) @ ( C @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_mult__strict__left__mono) ).
thf(448,plain,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ times_times ) ) @ ( C @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(38,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_16_add__right__cancel) ).
thf(261,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)],[38]) ).
thf(158,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_43_add__less__cancel__left) ).
thf(591,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)],[158]) ).
thf(103,axiom,
real @ linord20386208strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semiring__strict) ).
thf(443,plain,
real @ linord20386208strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_order__le__less__trans) ).
thf(376,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(124,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_mult__less__cancel__left__pos) ).
thf(485,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(134,axiom,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_divisors__zero) ).
thf(514,plain,
! [TA: $tType] :
( ( TA @ no_zero_divisors )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(150,axiom,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_add__mono) ).
thf(574,plain,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(122,axiom,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_mult__strict__right__mono) ).
thf(480,plain,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel_semigroup_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__semigroup__add) ).
thf(211,plain,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel_semigroup_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(181,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ( ( TA @ poly1 @ zero_zero @ ( TA @ zero_zero @ ( TA @ pCons ) ) )
= ( TA @ poly1 @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_pCons__0__0) ).
thf(646,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ( ( TA @ poly1 @ zero_zero @ ( TA @ zero_zero @ ( TA @ pCons ) ) )
= ( TA @ poly1 @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oidom) ).
thf(253,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(86,axiom,
real @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
thf(397,plain,
real @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(43,axiom,
real @ ordere779506340up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add) ).
thf(280,plain,
real @ ordere779506340up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(17,axiom,
bool @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(221,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_double__add__less__zero__iff__single__add__less__zero) ).
thf(453,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere216010020id_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oordered__comm__monoid__add) ).
thf(243,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere216010020id_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(9,axiom,
bool @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(206,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ linord893533164strict )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ times_times ) ) @ ( C @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_comm__mult__strict__left__mono) ).
thf(307,plain,
! [TA: $tType] :
( ( TA @ linord893533164strict )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ times_times ) ) @ ( C @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly1,B: TA,C: TA @ poly1,D: TA] :
( ( ( C @ ( D @ ( TA @ pCons ) ) )
= ( A @ ( B @ ( TA @ pCons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_pCons__eq__iff) ).
thf(292,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly1,B: TA,C: TA @ poly1,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ pCons ) ) )
= ( A @ ( B @ ( TA @ pCons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ pCons ) ) )
= ( A @ ( B @ ( TA @ pCons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ order ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Orderings_Oorder) ).
thf(233,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(143,axiom,
real @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
thf(546,plain,
real @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) )
<=> ( ( ( C @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( A @ ( C @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_mult__less__cancel__right__disj) ).
thf(334,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( ( C @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( A @ ( C @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) )
=> ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) )
=> ( ( ( C @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( A @ ( C @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly1,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ pCons ) ) @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( TA @ times_times ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_poly__pCons) ).
thf(302,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly1,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ pCons ) ) @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( TA @ times_times ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(160,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_order__less__le__trans) ).
thf(598,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(147,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_norm__eq__zero) ).
thf(561,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) )
& ( ( ( A @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_zero__reorient) ).
thf(192,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)],[5]) ).
thf(92,axiom,
real @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) ).
thf(407,plain,
real @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(172,axiom,
complex @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(630,plain,
complex @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(115,axiom,
! [A: complex] :
( ( r @ ( A @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( m @ ( A @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_m) ).
thf(467,plain,
! [A: complex] :
( ( r @ ( A @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( m @ ( A @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(169,axiom,
r @ ( z @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_H) ).
thf(625,plain,
r @ ( z @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(154,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_add__le__cancel__left) ).
thf(583,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(126,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_add__neg__neg) ).
thf(493,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linord581940658strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__ring__strict) ).
thf(224,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linord581940658strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(183,axiom,
real @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(650,plain,
real @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ linordered_ring )
=> ! [A: TA] :
~ ( TA @ zero_zero @ ( A @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_not__square__less__zero) ).
thf(403,plain,
! [TA: $tType] :
( ( TA @ linordered_ring )
=> ! [A: TA] :
~ ( TA @ zero_zero @ ( A @ ( A @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linord20386208strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__semiring__strict) ).
thf(188,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linord20386208strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly1,B: TA] :
( ( ( A @ ( B @ ( TA @ pCons ) ) )
= ( TA @ poly1 @ zero_zero ) )
<=> ( ( A
= ( TA @ poly1 @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_pCons__eq__0__iff) ).
thf(388,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA @ poly1,B: TA] :
( ( ( ( A
= ( TA @ poly1 @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ pCons ) ) )
= ( TA @ poly1 @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ pCons ) ) )
= ( TA @ poly1 @ zero_zero ) )
=> ( ( A
= ( TA @ poly1 @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_double__add__le__zero__iff__single__add__le__zero) ).
thf(356,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(129,axiom,
complex @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(499,plain,
complex @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(119,axiom,
complex @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocomm__monoid__add) ).
thf(476,plain,
complex @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(137,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_linorder__not__less) ).
thf(526,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ~ ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(177,axiom,
real @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(637,plain,
real @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(125,axiom,
? [A: real] :
( ! [B: complex] :
( ( r @ ( B @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( A @ ( B @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ) )
& ( A @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_pCons) ).
thf(489,plain,
? [A: real] :
( ! [B: complex] :
( ( r @ ( B @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( A @ ( B @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ) )
& ( A @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(157,axiom,
real @ real_normed_algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__algebra) ).
thf(590,plain,
real @ real_normed_algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(144,axiom,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zero__less__mult__pos) ).
thf(547,plain,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(111,axiom,
complex @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Omult__zero) ).
thf(457,plain,
complex @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(131,axiom,
! [TA: $tType] :
( ( TA @ real_n1866405975lgebra )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ norm_norm ) )
= ( A @ ( TA @ norm_norm ) @ ( B @ ( TA @ norm_norm ) @ ( real @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_norm__mult) ).
thf(503,plain,
! [TA: $tType] :
( ( TA @ real_n1866405975lgebra )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ norm_norm ) )
= ( A @ ( TA @ norm_norm ) @ ( B @ ( TA @ norm_norm ) @ ( real @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly1 @ comm_semiring_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__1) ).
thf(237,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ( TA @ poly1 @ comm_semiring_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ times_times ) ) @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mult__strict__right__mono__neg) ).
thf(311,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ times_times ) ) @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_add__pos__pos) ).
thf(398,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(138,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(530,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(174,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_not__leE) ).
thf(633,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly1,B: TA,C: TA @ poly1,D: TA] :
( ( A @ ( B @ ( TA @ pCons ) ) @ ( C @ ( D @ ( TA @ pCons ) ) @ ( TA @ poly1 @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ poly1 @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ pCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_add__pCons) ).
thf(360,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ poly1,B: TA,C: TA @ poly1,D: TA] :
( ( A @ ( B @ ( TA @ pCons ) ) @ ( C @ ( D @ ( TA @ pCons ) ) @ ( TA @ poly1 @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ poly1 @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ pCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(98,axiom,
real @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oorder) ).
thf(425,plain,
real @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(42,axiom,
complex @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring) ).
thf(279,plain,
complex @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(104,axiom,
complex @ cancel1352612707id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocancel__comm__monoid__add) ).
thf(444,plain,
complex @ cancel1352612707id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(79,axiom,
real @ ring_n68954251visors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__no__zero__divisors) ).
thf(375,plain,
real @ ring_n68954251visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(133,axiom,
complex @ real_normed_vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__vector) ).
thf(513,plain,
complex @ real_normed_vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
<=> ( ( C = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_crossproduct__eq) ).
thf(430,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( C = A )
| ( D = B ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
=> ( ( C = A )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(89,axiom,
r @ ( real @ zero_zero @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_rp) ).
thf(402,plain,
r @ ( real @ zero_zero @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(152,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_mult__left__idem) ).
thf(577,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(259,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(44,axiom,
real @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(281,plain,
real @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(8,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ( TA @ poly1 @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ozero) ).
thf(204,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ( TA @ poly1 @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(105,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA,B: TA] : ( A @ ( TA @ norm_norm ) @ ( B @ ( TA @ norm_norm ) @ ( real @ plus_plus ) ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_norm__triangle__ineq) ).
thf(445,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA,B: TA] : ( A @ ( TA @ norm_norm ) @ ( B @ ( TA @ norm_norm ) @ ( real @ plus_plus ) ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(82,axiom,
complex @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ono__zero__divisors) ).
thf(382,plain,
complex @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly1,B: TA @ poly1] :
( ( ( B @ ( TA @ poly ) )
= ( A @ ( TA @ poly ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_poly__eq__iff) ).
thf(313,plain,
! [TA: $tType] :
( ( ( TA @ idom )
& ( TA @ ring_char_0 ) )
=> ! [A: TA @ poly1,B: TA @ poly1] :
( ( ( B = A )
=> ( ( B @ ( TA @ poly ) )
= ( A @ ( TA @ poly ) ) ) )
& ( ( ( B @ ( TA @ poly ) )
= ( A @ ( TA @ poly ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(114,axiom,
real @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(466,plain,
real @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(1,conjecture,
z @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( z @ ( complex @ times_times ) ) @ ( complex @ norm_norm ) @ ( c @ ( complex @ norm_norm ) @ ( real @ plus_plus ) ) @ ( z @ ( cs @ ( c @ ( complex @ pCons ) ) @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( z @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( z @ ( complex @ times_times ) ) @ ( complex @ norm_norm ) @ ( c @ ( complex @ norm_norm ) @ ( real @ plus_plus ) ) @ ( z @ ( cs @ ( c @ ( complex @ pCons ) ) @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(187,plain,
~ ( z @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( z @ ( complex @ times_times ) ) @ ( complex @ norm_norm ) @ ( c @ ( complex @ norm_norm ) @ ( real @ plus_plus ) ) @ ( z @ ( cs @ ( c @ ( complex @ pCons ) ) @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linord893533164strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__comm__semiring__strict) ).
thf(219,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linord893533164strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22,axiom,
bool @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(230,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__pos__pos) ).
thf(451,plain,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly1 @ comm_monoid_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocomm__monoid__add) ).
thf(245,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ( TA @ poly1 @ comm_monoid_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(182,axiom,
complex @ comm_semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__0) ).
thf(649,plain,
complex @ comm_semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(167,axiom,
real @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__add) ).
thf(616,plain,
real @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(120,axiom,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_add__left__mono) ).
thf(477,plain,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(84,axiom,
complex @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) ).
thf(387,plain,
complex @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(173,axiom,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mult__pos__neg) ).
thf(631,plain,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(140,axiom,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_mult__zero__right) ).
thf(535,plain,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ mult_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Omult__zero) ).
thf(213,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ mult_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(33,axiom,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel1352612707id_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__comm__monoid__add) ).
thf(251,plain,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel1352612707id_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(626,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_double__zero__sym) ).
thf(345,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add__right__mono) ).
thf(367,plain,
! [TA: $tType] :
( ( TA @ ordere779506340up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(176,axiom,
complex @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oab__semigroup__add) ).
thf(636,plain,
complex @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(41,axiom,
m @ ( z @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_th) ).
thf(278,plain,
m @ ( z @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(164,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zero__le__double__add__iff__zero__le__single__add) ).
thf(608,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(20,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ no_zero_divisors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ono__zero__divisors) ).
thf(226,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ no_zero_divisors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Orderings_Olinorder) ).
thf(241,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(186,axiom,
~ ! [A: real] :
~ ! [B: complex] :
( ( r @ ( B @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( A @ ( B @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(658,plain,
~ ! [A: real] :
~ ! [B: complex] :
( ( r @ ( B @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) )
=> ( A @ ( B @ ( cs @ ( complex @ poly ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(473,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(99,axiom,
real @ real_normed_vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__vector) ).
thf(426,plain,
real @ real_normed_vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(78,axiom,
complex @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Oring__char__0) ).
thf(374,plain,
complex @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere779506340up_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oordered__ab__semigroup__add) ).
thf(255,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ ordere779506340up_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__idom) ).
thf(209,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(168,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) )
<=> ( ( ( B @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( C @ ( TA @ ord_less ) ) ) )
| ( ( A @ ( B @ ( TA @ ord_less ) ) )
& ( C @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_mult__less__cancel__left__disj) ).
thf(617,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( ( B @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( C @ ( TA @ ord_less ) ) ) )
| ( ( A @ ( B @ ( TA @ ord_less ) ) )
& ( C @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) )
=> ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) )
=> ( ( ( B @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( C @ ( TA @ ord_less ) ) ) )
| ( ( A @ ( B @ ( TA @ ord_less ) ) )
& ( C @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(66,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(342,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(69,axiom,
real @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(355,plain,
real @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(112,axiom,
complex @ ab_semigroup_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oab__semigroup__mult) ).
thf(458,plain,
complex @ ab_semigroup_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(153,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly1,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ poly1 @ plus_plus ) ) @ ( TA @ poly1 @ times_times ) ) )
= ( A @ ( B @ ( TA @ poly1 @ times_times ) ) @ ( A @ ( C @ ( TA @ poly1 @ times_times ) ) @ ( TA @ poly1 @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_mult__poly__add__left) ).
thf(580,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA @ poly1,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ poly1 @ plus_plus ) ) @ ( TA @ poly1 @ times_times ) ) )
= ( A @ ( B @ ( TA @ poly1 @ times_times ) ) @ ( A @ ( C @ ( TA @ poly1 @ times_times ) ) @ ( TA @ poly1 @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(45,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_pos__add__strict) ).
thf(282,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(57,axiom,
complex @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocancel__semigroup__add) ).
thf(310,plain,
complex @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(151,axiom,
real @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Opreorder) ).
thf(576,plain,
real @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(179,axiom,
! [TA: $tType] :
( ( TA @ real_normed_algebra )
=> ! [A: TA,B: TA] : ( A @ ( TA @ norm_norm ) @ ( B @ ( TA @ norm_norm ) @ ( real @ times_times ) ) @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_norm__mult__ineq) ).
thf(643,plain,
! [TA: $tType] :
( ( TA @ real_normed_algebra )
=> ! [A: TA,B: TA] : ( A @ ( TA @ norm_norm ) @ ( B @ ( TA @ norm_norm ) @ ( real @ times_times ) ) @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ norm_norm ) @ ( real @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(161,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ poly1 @ plus_plus ) ) @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_poly__add) ).
thf(600,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ poly1 @ plus_plus ) ) @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(149,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_19_add__right__imp__eq) ).
thf(571,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)],[149]) ).
thf(159,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_21_add__left__imp__eq) ).
thf(595,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)],[159]) ).
thf(165,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_order__refl) ).
thf(612,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ ring_n68954251visors ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oring__no__zero__divisors) ).
thf(231,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ ring_n68954251visors ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(108,axiom,
real @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
thf(450,plain,
real @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(72,axiom,
complex @ real_normed_algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra) ).
thf(363,plain,
complex @ real_normed_algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(142,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_linorder__antisym__conv1) ).
thf(539,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_order__neq__le__trans) ).
thf(482,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(127,axiom,
complex @ idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oidom) ).
thf(495,plain,
complex @ idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(156,axiom,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_zero__less__mult__pos2) ).
thf(588,plain,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(135,axiom,
real @ linordered_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__ring) ).
thf(517,plain,
real @ linordered_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(148,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_norm__zero) ).
thf(568,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(25,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ ab_semigroup_mult ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oab__semigroup__mult) ).
thf(235,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ ab_semigroup_mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ semiri456707255roduct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(207,plain,
! [TA: $tType] :
( ( TA @ idom )
=> ( TA @ poly1 @ semiri456707255roduct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_add__le__cancel__right) ).
thf(383,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(145,axiom,
! [TA: $tType] :
( ( TA @ ring_n68954251visors )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_mult__eq__0__iff) ).
thf(549,plain,
! [TA: $tType] :
( ( TA @ ring_n68954251visors )
=> ! [A: TA,B: TA] :
( ( ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(47,axiom,
real @ idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oidom) ).
thf(287,plain,
real @ idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
~ ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_norm__not__less__zero) ).
thf(290,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
~ ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_linorder__not__le) ).
thf(378,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( ( B @ ( A @ ( TA @ ord_less ) ) )
=> ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
& ( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(106,axiom,
real @ cancel1352612707id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__comm__monoid__add) ).
thf(447,plain,
real @ cancel1352612707id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_mult__neg__pos) ).
thf(405,plain,
! [TA: $tType] :
( ( TA @ linord20386208strict )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ times_times ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_ring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__ring) ).
thf(190,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_ring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(162,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_order__le__neq__trans) ).
thf(603,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_leI) ).
thf(305,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(27,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Osemiring) ).
thf(239,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ( TA @ poly1 @ semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_add__le__imp__le__left) ).
thf(400,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_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(175,axiom,
complex @ real_n1866405975lgebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__div__algebra) ).
thf(635,plain,
complex @ real_n1866405975lgebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(94,axiom,
real @ linord893533164strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__comm__semiring__strict) ).
thf(415,plain,
real @ linord893533164strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(132,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
<=> ( A
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_zero__less__norm__iff) ).
thf(506,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A
!= ( TA @ zero_zero ) )
=> ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) ) )
& ( ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
=> ( A
!= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_order__less__le) ).
thf(268,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( ( ( B != A )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(63,axiom,
real @ ordere216010020id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) ).
thf(332,plain,
real @ ordere216010020id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_order__le__imp__less__or__eq) ).
thf(427,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(113,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_15_add__left__cancel) ).
thf(459,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)],[113]) ).
thf(6,axiom,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel146912293up_add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__ab__semigroup__add) ).
thf(200,plain,
! [TA: $tType] :
( ( TA @ cancel1352612707id_add )
=> ( TA @ poly1 @ cancel146912293up_add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_combine__common__factor) ).
thf(369,plain,
! [TA: $tType] :
( ( TA @ semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(61,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_22_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(322,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)],[61]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_poly__0) ).
thf(469,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA] :
( ( A @ ( TA @ poly1 @ zero_zero @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(56,axiom,
real @ ab_semigroup_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__semigroup__mult) ).
thf(309,plain,
real @ ab_semigroup_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ preorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Orderings_Opreorder) ).
thf(215,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_semidom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__semidom) ).
thf(222,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ( TA @ poly1 @ linordered_semidom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(128,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ poly1 @ times_times ) ) @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_poly__mult) ).
thf(496,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_0 )
=> ! [A: TA,B: TA @ poly1,C: TA @ poly1] :
( ( A @ ( B @ ( C @ ( TA @ poly1 @ times_times ) ) @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ poly ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(73,axiom,
real @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) ).
thf(364,plain,
real @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(665,plain,
$false,
inference(e,[status(thm)],[645,629,365,479,518,352,333,249,408,247,614,202,217,276,440,655,533,500,472,538,417,288,301,320,651,257,372,587,559,638,421,606,284,416,325,228,289,448,261,591,443,376,485,514,574,480,211,646,253,397,280,221,453,243,206,307,292,233,546,334,302,598,561,192,407,630,467,625,583,493,224,650,403,188,388,356,499,476,526,637,489,590,547,457,503,237,311,398,530,633,360,425,279,444,375,513,430,402,577,259,281,204,445,382,313,466,187,219,230,451,245,649,616,477,387,631,535,213,251,626,345,367,636,278,608,226,241,658,473,426,374,255,209,617,342,355,458,580,282,310,576,643,600,571,595,612,231,450,363,539,482,495,588,517,568,235,207,383,549,287,290,378,447,405,190,603,305,239,400,635,415,506,268,332,427,459,200,369,322,469,309,215,222,496,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW486_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
% 0.13/0.38 % Computer : n009.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 16:08:59 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.87/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.29 % [INFO] Parsing done (324ms).
% 2.04/1.30 % [INFO] Running in sequential loop mode.
% 2.80/1.72 % [INFO] eprover registered as external prover.
% 2.80/1.73 % [INFO] Scanning for conjecture ...
% 3.18/1.90 % [INFO] Found a conjecture (or negated_conjecture) and 186 axioms. Running axiom selection ...
% 3.18/2.02 % [INFO] Axiom selection finished. Selected 184 axioms (removed 2 axioms).
% 3.94/2.27 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.16/2.31 % [INFO] Type checking passed.
% 4.16/2.31 % [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 ...
% 12.64/4.54 % External prover 'e' found a proof!
% 12.64/4.54 % [INFO] Killing All external provers ...
% 12.64/4.54 % Time passed: 4008ms (effective reasoning time: 3230ms)
% 12.64/4.54 % 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)>
% 12.64/4.54 % Axioms used in derivation (184): arity_RealDef_Oreal___RealVector_Oreal__normed__div__algebra, arity_Polynomial_Opoly___Groups_Oordered__ab__semigroup__add, arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add, arity_HOL_Obool___Orderings_Oorder, arity_Polynomial_Opoly___Rings_Oring__no__zero__divisors, arity_Complex_Ocomplex___Rings_Ocomm__semiring__0, fact_49_zero__less__double__add__iff__zero__less__single__add, fact_41_double__zero__sym, fact_88_leI, arity_HOL_Obool___Orderings_Opreorder, arity_Complex_Ocomplex___Groups_Oab__semigroup__add, fact_80_order__le__neq__trans, fact_9_add__le__cancel__left, arity_RealDef_Oreal___Rings_Olinordered__ring__strict, arity_Complex_Ocomplex___RealVector_Oreal__normed__div__algebra, fact_58_mult__less__cancel__right__disj, fact_71_add__neg__neg, fact_28_add__right__mono, fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, arity_Complex_Ocomplex___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_19_add__right__imp__eq, arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add, fact_64_mult__pos__neg2, arity_Polynomial_Opoly___Rings_Ono__zero__divisors, fact_54_zero__less__norm__iff, fact_12_norm__mult__ineq, arity_RealDef_Oreal___Groups_Ozero, arity_Complex_Ocomplex___Rings_Ocomm__semiring__1, arity_Polynomial_Opoly___Groups_Oordered__comm__monoid__add, fact_46_poly__0, arity_Complex_Ocomplex___Groups_Ocancel__semigroup__add, fact_14_pCons__eq__iff, fact_45_pCons__0__0, arity_Complex_Ocomplex___Rings_Oidom, fact_39_mult__zero__right, arity_Complex_Ocomplex___Int_Oring__char__0, arity_Polynomial_Opoly___Groups_Olinordered__ab__group__add, fact_30_rp, fact_38_mult__zero__left, arity_RealDef_Oreal___Rings_Oring__no__zero__divisors, arity_Complex_Ocomplex___Rings_Ono__zero__divisors, arity_RealDef_Oreal___Rings_Olinordered__comm__semiring__strict, arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra, fact_69_mult__neg__pos, fact_81_order__le__imp__less__or__eq, arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add, fact_68_mult__less__cancel__left__neg, arity_Polynomial_Opoly___Rings_Olinordered__ring, fact_2_th, fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, arity_Polynomial_Opoly___Rings_Omult__zero, fact_75_comm__mult__strict__left__mono, fact_47_zero__le__double__add__iff__zero__le__single__add, fact_4_poly__pCons, arity_HOL_Obool___Orderings_Olinorder, fact_78_order__le__less__trans, fact_24_add__le__imp__le__left, arity_RealDef_Oreal___Rings_Olinordered__ring, arity_Polynomial_Opoly___Rings_Olinordered__semiring__strict, fact_82_linorder__antisym__conv2, arity_Polynomial_Opoly___Rings_Oidom, arity_Polynomial_Opoly___Rings_Olinordered__comm__semiring__strict, fact_33_pCons, arity_Complex_Ocomplex___Groups_Ocomm__monoid__add, fact_74_ext, fact_52_norm__zero, fact_72_mult__strict__right__mono, arity_Polynomial_Opoly___Groups_Ocancel__semigroup__add, fact_86_linorder__antisym__conv1, arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_Polynomial_Opoly___Groups_Ozero, arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le, arity_RealDef_Oreal___Rings_Ocomm__semiring__1, arity_Polynomial_Opoly___Int_Oring__char__0, fact_27_add__left__mono, arity_Polynomial_Opoly___Rings_Olinordered__semidom, arity_RealDef_Oreal___Rings_Olinordered__semiring__strict, fact_7_add__pCons, fact_35_combine__common__factor, arity_fun___Orderings_Oorder, arity_Polynomial_Opoly___Groups_Oordered__ab__semigroup__add__imp__le, fact_60_mult__less__cancel__left__pos, fact_42_add__less__cancel__right, arity_Polynomial_Opoly___Groups_Ocancel__ab__semigroup__add, fact_34_crossproduct__eq, fact_6_poly__mult, fact_21_add__left__imp__eq, fact_36_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_55_norm__not__less__zero, fact_53_norm__le__zero__iff, arity_Complex_Ocomplex___Rings_Osemiring, fact_87_not__leE, arity_Polynomial_Opoly___Orderings_Oorder, arity_fun___Orderings_Opreorder, fact_50_double__add__less__zero__iff__single__add__less__zero, arity_Polynomial_Opoly___Rings_Ocomm__semiring__1, fact_65_pos__add__strict, fact_85_order__neq__le__trans, arity_RealDef_Oreal___Groups_Ocancel__comm__monoid__add, fact_20_add__imp__eq, arity_Polynomial_Opoly___Rings_Olinordered__idom, fact_67_zero__less__mult__pos2, fact_84_leD, fact_18_ab__semigroup__mult__class_Omult__ac_I1_J, arity_Polynomial_Opoly___Groups_Ocomm__monoid__add, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_70_mult__neg__neg, fact_76_mult__strict__right__mono__neg, arity_Complex_Ocomplex___Rings_Omult__zero, arity_RealDef_Oreal___Rings_Oidom, arity_RealDef_Oreal___Rings_Olinordered__semidom, fact_26_add__mono, arity_Polynomial_Opoly___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_89_order__le__less, arity_Complex_Ocomplex___Groups_Oab__semigroup__mult, arity_RealDef_Oreal___Groups_Oab__semigroup__add, arity_RealDef_Oreal___Rings_Omult__zero, arity_RealDef_Oreal___Int_Oring__char__0, fact_5_poly__add, arity_RealDef_Oreal___Rings_Ocomm__semiring__0, arity_RealDef_Oreal___Rings_Osemiring, arity_RealDef_Oreal___Groups_Ocancel__semigroup__add, arity_Polynomial_Opoly___Groups_Oab__semigroup__mult, fact_31_mult__left__idem, arity_RealDef_Oreal___Rings_Ono__zero__divisors, arity_RealDef_Oreal___Groups_Ocomm__monoid__add, arity_RealDef_Oreal___Orderings_Oorder, arity_Polynomial_Opoly___Rings_Osemiring, fact_15_add__left__cancel, fact_96_no__zero__divisors, fact_0__096cmod_A_Ic_A_L_Az_A_K_Apoly_Acs_Az_J_A_060_061_Acmod_Ac_A_L_Acmod_A_Iz_A_K_Apoly_Acs_Az_J_096, arity_Polynomial_Opoly___Groups_Ocancel__comm__monoid__add, arity_RealDef_Oreal___Orderings_Olinorder, arity_RealDef_Oreal___Groups_Olinordered__ab__group__add, arity_RealDef_Oreal___RealVector_Oreal__normed__vector, arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors, fact_90_less__le__not__le, fact_37_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, arity_RealDef_Oreal___Orderings_Opreorder, arity_RealDef_Oreal___RealVector_Oreal__normed__algebra, fact_95_divisors__zero, fact_22_ab__semigroup__add__class_Oadd__ac_I1_J, fact_40_mult__eq__0__iff, fact_43_add__less__cancel__left, fact_66_zero__less__mult__pos, fact_11_complex__mod__triangle__sub, arity_Polynomial_Opoly___Orderings_Opreorder, fact_13__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_93_linorder__not__le, fact_63_mult__pos__neg, fact_16_add__right__cancel, arity_Complex_Ocomplex___Groups_Ocancel__ab__semigroup__add, fact_92_linorder__le__less__linear, fact_17_mult__poly__add__left, fact_91_order__less__le, fact_23_poly__eq__iff, fact_56_not__square__less__zero, fact_59_mult__less__cancel__left__disj, fact_48_double__add__le__zero__iff__single__add__le__zero, arity_Polynomial_Opoly___Groups_Oab__semigroup__add, arity_Complex_Ocomplex___Groups_Ocancel__comm__monoid__add, fact_3_m, arity_RealDef_Oreal___Groups_Oab__semigroup__mult, fact_1_H, fact_51_norm__eq__zero, fact_79_order__less__le__trans, fact_25_add__le__imp__le__right, fact_62_mult__pos__pos, arity_Polynomial_Opoly___Orderings_Olinorder, fact_8_add__le__cancel__right, fact_32_order__refl, arity_Complex_Ocomplex___Groups_Ozero, fact_77_mult__strict__left__mono__neg, fact_61_add__pos__pos, fact_29_norm__mult, fact_57_zero__reorient, fact_83_order__less__imp__le, arity_Polynomial_Opoly___Rings_Ocomm__semiring__0, fact_10_norm__triangle__ineq, arity_Polynomial_Opoly___Rings_Olinordered__ring__strict, fact_94_linorder__not__less, fact_44_pCons__eq__0__iff, fact_73_mult__strict__left__mono, arity_Complex_Ocomplex___RealVector_Oreal__normed__vector
% 12.64/4.54 % No. of inferences in proof: 372
% 12.64/4.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4008 ms resp. 3230 ms w/o parsing
% 13.65/4.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.65/4.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------