%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW503_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 : n018.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 09:10:42 AM UTC 2026
% Result : Theorem 94.27s 21.35s
% Output : Refutation 94.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 174
% Syntax : Number of formulae : 770 ( 294 unt; 0 typ; 2 def)
% Number of atoms : 1977 ( 884 equ; 0 cnn)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 11652 ( 825 ~; 606 |; 107 &;9740 @)
% ( 30 <=>; 344 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 8 con; 0-3 aty)
% Number of variables : 1196 ( 0 ^;1189 !; 5 ?;1196 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(power_decl,type,
power:
!>[TA: $tType] : $o ).
thf(field_decl,type,
field:
!>[TA: $tType] : $o ).
thf(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_0_decl,type,
semiring_0:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(division_ring_decl,type,
division_ring:
!>[TA: $tType] : $o ).
thf(real_field_decl,type,
real_field:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[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(linordered_field_decl,type,
linordered_field:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(field_inverse_zero_decl,type,
field_inverse_zero:
!>[TA: $tType] : $o ).
thf(real_algebra_1_decl,type,
real_algebra_1:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(real_normed_field_decl,type,
real_normed_field:
!>[TA: $tType] : $o ).
thf(real_normed_vector_decl,type,
real_normed_vector:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors:
!>[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_n2089651433ebra_1_decl,type,
real_n2089651433ebra_1:
!>[TA: $tType] : $o ).
thf(divisi14063676e_zero_decl,type,
divisi14063676e_zero:
!>[TA: $tType] : $o ).
thf(real_n1866405975lgebra_decl,type,
real_n1866405975lgebra:
!>[TA: $tType] : $o ).
thf(linord1117847801e_zero_decl,type,
linord1117847801e_zero:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_decl,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(inverse_divide_decl,type,
inverse_divide:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
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(root_decl,type,
root: nat > real > real ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(even_odd_even_decl,type,
even_odd_even:
!>[TA: $tType] : ( TA > $o ) ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(norm_norm_decl,type,
norm_norm:
!>[TA: $tType] : ( TA > real ) ).
thf(of_real_decl,type,
of_real:
!>[TA: $tType] : ( real > TA ) ).
thf(b_decl,type,
b: complex ).
thf(n_decl,type,
n: nat ).
thf(na_decl,type,
na: nat ).
thf(v_decl,type,
v: complex ).
thf(sk1_decl,type,
sk1: complex ).
thf(sk3_decl,type,
sk3: complex ).
thf(sk1_def,definition,
( sk1
= ( @+[A: complex] : ( real @ one_one @ ( na @ ( A @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: complex] : ( real @ one_one @ ( na @ ( A @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ) ) ) ).
thf(166,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_24_zero__less__norm__iff) ).
thf(629,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)],[166]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_power__less__imp__less__exp) ).
thf(365,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(107,axiom,
( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( real @ power_power ) ) )
= ( b @ ( complex @ norm_norm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096root_An_A_Icmod_Ab_J_A_094_An_A_061_Acmod_Ab_096) ).
thf(429,plain,
( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( real @ power_power ) ) )
= ( b @ ( complex @ norm_norm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(430,plain,
( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( real @ power_power ) ) )
= ( b @ ( complex @ norm_norm ) ) ),
inference(lifteq,[status(thm)],[429]) ).
thf(117,axiom,
! [A: nat,B: real] :
( ( A @ ( B @ ( complex @ of_real ) @ ( complex @ power_power ) ) )
= ( A @ ( B @ ( real @ power_power ) ) @ ( complex @ of_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_complex__of__real__power) ).
thf(460,plain,
! [A: nat,B: real] :
( ( A @ ( B @ ( complex @ of_real ) @ ( complex @ power_power ) ) )
= ( A @ ( B @ ( real @ power_power ) ) @ ( complex @ of_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(461,plain,
! [B: real,A: nat] :
( ( A @ ( B @ ( complex @ of_real ) @ ( complex @ power_power ) ) )
= ( A @ ( B @ ( real @ power_power ) ) @ ( complex @ of_real ) ) ),
inference(cnf,[status(esa)],[460]) ).
thf(462,plain,
! [B: real,A: nat] :
( ( A @ ( B @ ( real @ power_power ) ) @ ( complex @ of_real ) )
= ( A @ ( B @ ( complex @ of_real ) @ ( complex @ power_power ) ) ) ),
inference(lifteq,[status(thm)],[461]) ).
thf(1473,plain,
! [B: real,A: nat] :
( ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( real @ power_power ) ) )
!= ( A @ ( B @ ( real @ power_power ) ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
= ( A @ ( B @ ( complex @ of_real ) @ ( complex @ power_power ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[430,462]) ).
thf(1474,plain,
( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) ) ),
inference(pattern_uni,[status(thm)],[1473:[bind(A,$thf( na )),bind(B,$thf( b @ ( complex @ norm_norm ) @ ( na @ root ) ))]]) ).
thf(1,conjecture,
( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(174,plain,
( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(175,plain,
( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(1539,plain,
( ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,175]) ).
thf(1565,plain,
( ( na != na )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(simp,[status(thm)],[1539]) ).
thf(1583,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(simp,[status(thm)],[1565]) ).
thf(2484,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[1583]) ).
thf(2494,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(simp,[status(thm)],[2484]) ).
thf(2499,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(simp,[status(thm)],[2494]) ).
thf(28,axiom,
real @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) ).
thf(234,plain,
real @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(165,axiom,
? [A: complex] : ( real @ one_one @ ( na @ ( A @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14__096EX_Av_O_Acmod_A_Icomplex__of__real_A_Icmod_Ab_J_A_P_Ab_A_L_Av_A_094_An_J_A_060_A1_096) ).
thf(627,plain,
? [A: complex] : ( real @ one_one @ ( na @ ( A @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(628,plain,
real @ one_one @ ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ),
inference(cnf,[status(esa)],[627]) ).
thf(39,axiom,
! [A: nat] :
( ~ ( A @ ( nat @ even_odd_even ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_odd__pos) ).
thf(248,plain,
! [A: nat] :
( ~ ( A @ ( nat @ even_odd_even ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(249,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( A @ ( nat @ even_odd_even ) ) ),
inference(cnf,[status(esa)],[248]) ).
thf(142,axiom,
complex @ division_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Odivision__ring) ).
thf(544,plain,
complex @ division_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_divide__1) ).
thf(370,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(371,plain,
! [TA: $tType,A: TA] :
( ( ( TA @ one_one @ ( A @ ( TA @ inverse_divide ) ) )
= A )
| ~ ( TA @ division_ring ) ),
inference(cnf,[status(esa)],[370]) ).
thf(372,plain,
! [TA: $tType,A: TA] :
( ~ ( TA @ division_ring )
| ( ( TA @ one_one @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
inference(lifteq,[status(thm)],[371]) ).
thf(12042,plain,
! [TA: $tType,A: TA] :
( ( ( complex @ division_ring )
!= ( TA @ division_ring ) )
| ~ $true
| ( ( TA @ one_one @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[544,372]) ).
thf(12043,plain,
! [TA: $tType,A: TA] :
( ( ( complex @ division_ring )
!= ( TA @ division_ring ) )
| ( ( TA @ one_one @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
inference(simp,[status(thm)],[12042]) ).
thf(12044,plain,
! [A: complex] :
( ( complex @ one_one @ ( A @ ( complex @ inverse_divide ) ) )
= A ),
inference(pattern_uni,[status(thm)],[12043:[bind_type(TA,$thf( complex ))]]) ).
thf(12259,plain,
! [A: complex] :
( ( ( complex @ one_one @ ( A @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) )
| ( A
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12044,175]) ).
thf(12335,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ one_one ) )
| ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( na @ ( v @ ( complex @ power_power ) ) ) ) ),
inference(simp,[status(thm)],[12259]) ).
thf(12446,plain,
! [A: complex] :
( ( ( complex @ one_one @ ( A @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ one_one ) )
| ( ( na @ ( A @ ( complex @ power_power ) ) )
!= ( na @ ( v @ ( complex @ power_power ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12044,12335]) ).
thf(12469,plain,
! [A: complex] :
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= ( complex @ one_one ) )
| ( A != v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ one_one ) )
| ( na != na )
| ( A != v ) ),
inference(simp,[status(thm)],[12446]) ).
thf(12516,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= ( complex @ one_one ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ one_one ) ) ),
inference(simp,[status(thm)],[12469]) ).
thf(12540,plain,
( ( ( complex @ one_one )
!= ( complex @ one_one ) )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ one_one ) ) ),
inference(eqfactor_ordered,[status(thm)],[12516]) ).
thf(12549,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ one_one ) ) ),
inference(simp,[status(thm)],[12540]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ( ( real @ one_one @ ( TA @ of_real ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_of__real__1) ).
thf(481,plain,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ( ( real @ one_one @ ( TA @ of_real ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(9,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(197,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_add_Ocomm__neutral) ).
thf(190,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(191,plain,
! [TA: $tType,A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A )
| ~ ( TA @ comm_monoid_add ) ),
inference(cnf,[status(esa)],[190]) ).
thf(192,plain,
! [TA: $tType,A: TA] :
( ~ ( TA @ comm_monoid_add )
| ( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(774,plain,
! [TA: $tType,A: TA] :
( ( ( nat @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ~ $true
| ( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[197,192]) ).
thf(775,plain,
! [TA: $tType,A: TA] :
( ( ( nat @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(simp,[status(thm)],[774]) ).
thf(776,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[775:[bind_type(TA,$thf( nat ))]]) ).
thf(32,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(238,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(19,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_66_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(208,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)],[19]) ).
thf(209,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ ab_semigroup_add ) ),
inference(cnf,[status(esa)],[208]) ).
thf(210,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ~ ( TA @ ab_semigroup_add )
| ( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[209]) ).
thf(825,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( ( nat @ ab_semigroup_add )
!= ( TA @ ab_semigroup_add ) )
| ~ $true
| ( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[238,210]) ).
thf(826,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( ( nat @ ab_semigroup_add )
!= ( TA @ ab_semigroup_add ) )
| ( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[825]) ).
thf(827,plain,
! [C: nat,B: nat,A: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[826:[bind_type(TA,$thf( nat ))]]) ).
thf(1889,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
!= ( C @ ( D @ ( nat @ plus_plus ) ) ) )
| ( ( B @ ( A @ ( nat @ plus_plus ) ) )
= ( B @ ( C @ ( nat @ plus_plus ) ) @ ( D @ ( nat @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[776,827]) ).
thf(1890,plain,
! [B: nat,A: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[1889:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( nat @ zero_zero )),bind(D,$thf( A ))]]) ).
thf(2152,plain,
! [E: nat,D: nat,C: nat,B: nat,A: nat] :
( ( ( B @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) )
!= ( D @ ( E @ ( nat @ plus_plus ) ) ) )
| ( ( C @ ( B @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( C @ ( D @ ( nat @ plus_plus ) ) @ ( E @ ( nat @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1890,827]) ).
thf(2153,plain,
! [C: nat,B: nat,A: nat] :
( ( B @ ( C @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( B @ ( C @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[2152:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( G @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )),bind(E,$thf( A ))]]) ).
thf(2204,plain,
! [C: nat,B: nat,A: nat] :
( ( B @ ( C @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( B @ ( C @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[2153]) ).
thf(3038,plain,
! [C: nat,B: nat,A: nat] :
( ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) )
= ( B @ ( C @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[2204,827]) ).
thf(3086,plain,
! [F: nat,E: nat,D: nat,C: nat,B: nat,A: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) )
!= ( E @ ( F @ ( nat @ plus_plus ) ) ) )
| ( ( D @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( D @ ( E @ ( nat @ plus_plus ) ) @ ( F @ ( nat @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3038,827]) ).
thf(3087,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( B @ ( D @ ( C @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( B @ ( D @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[3086:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( I )),bind(D,$thf( D )),bind(E,$thf( J @ ( I @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )),bind(F,$thf( A ))]]) ).
thf(3136,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( B @ ( D @ ( C @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( B @ ( D @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[3087]) ).
thf(1885,plain,
! [F: nat,E: nat,D: nat,C: nat,B: nat,A: nat] :
( ( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( E @ ( F @ ( nat @ plus_plus ) ) ) )
| ( ( D @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( D @ ( E @ ( nat @ plus_plus ) ) @ ( F @ ( nat @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[827,827]) ).
thf(1886,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( B @ ( A @ ( D @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) @ ( D @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[1885:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( H @ ( G @ ( nat @ plus_plus ) ) ))]]) ).
thf(1930,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( B @ ( A @ ( D @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) @ ( D @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[1886]) ).
thf(3728,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( B @ ( A @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) @ ( D @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[1930,827]) ).
thf(5354,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( B @ ( D @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) )
= ( B @ ( D @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[3136,3728,827]) ).
thf(5461,plain,
! [E: nat,D: nat,C: nat,B: nat,A: nat] :
( ( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
!= ( C @ ( E @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) )
= ( C @ ( E @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[776,5354]) ).
thf(5462,plain,
! [C: nat,B: nat,A: nat] :
( ( C @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero @ ( C @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[5461:[bind(A,$thf( G @ ( F @ ( nat @ plus_plus ) ) )),bind(B,$thf( B )),bind(C,$thf( nat @ zero_zero )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(5564,plain,
! [C: nat,B: nat,A: nat] :
( ( C @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero @ ( C @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[5462]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_add__0) ).
thf(280,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(281,plain,
! [TA: $tType,A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A )
| ~ ( TA @ comm_monoid_add ) ),
inference(cnf,[status(esa)],[280]) ).
thf(282,plain,
! [TA: $tType,A: TA] :
( ~ ( TA @ comm_monoid_add )
| ( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(lifteq,[status(thm)],[281]) ).
thf(5979,plain,
! [TA: $tType,A: TA] :
( ( ( nat @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ~ $true
| ( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[197,282]) ).
thf(5980,plain,
! [TA: $tType,A: TA] :
( ( ( nat @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(simp,[status(thm)],[5979]) ).
thf(5981,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[5980:[bind_type(TA,$thf( nat ))]]) ).
thf(6791,plain,
! [C: nat,B: nat,A: nat] :
( ( nat @ zero_zero @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) )
= ( C @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[5564,3728,5981]) ).
thf(136,axiom,
! [TA: $tType] :
( ( TA @ field )
=> ! [A: nat,B: TA,C: TA] :
( ( C
!= ( TA @ zero_zero ) )
=> ( ( A @ ( C @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_nonzero__power__divide) ).
thf(523,plain,
! [TA: $tType] :
( ( TA @ field )
=> ! [A: nat,B: TA,C: TA] :
( ( C
!= ( TA @ zero_zero ) )
=> ( ( A @ ( C @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(122,axiom,
complex @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocomm__monoid__add) ).
thf(480,plain,
complex @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(861,plain,
! [TA: $tType,A: TA] :
( ( ( complex @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ~ $true
| ( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[480,192]) ).
thf(862,plain,
! [TA: $tType,A: TA] :
( ( ( complex @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(simp,[status(thm)],[861]) ).
thf(863,plain,
! [A: complex] :
( ( complex @ zero_zero @ ( A @ ( complex @ plus_plus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[862:[bind_type(TA,$thf( complex ))]]) ).
thf(91,axiom,
~ ! [A: complex] :
~ ( real @ one_one @ ( na @ ( A @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15__096_B_Bthesis_O_A_I_B_Bv_O_Acmod_A_Icomplex__of__real_A_Icmod_Ab_J_A_P_Ab_A_L_Av_A_094_An_J_A_060_A1_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(373,plain,
~ ! [A: complex] :
~ ( real @ one_one @ ( na @ ( A @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(374,plain,
~ ! [A: complex] :
~ ( real @ one_one @ ( na @ ( A @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ),
inference(polarity_switch,[status(thm)],[373]) ).
thf(375,plain,
~ ~ ? [A: complex] : ( real @ one_one @ ( na @ ( A @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ),
inference(miniscope,[status(thm)],[374]) ).
thf(376,plain,
real @ one_one @ ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ),
inference(cnf,[status(esa)],[375]) ).
thf(153,axiom,
( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
= ( real @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_th0) ).
thf(587,plain,
( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
= ( real @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(588,plain,
( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
= ( real @ one_one ) ),
inference(lifteq,[status(thm)],[587]) ).
thf(172,axiom,
complex @ real_normed_vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__vector) ).
thf(658,plain,
complex @ real_normed_vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(128,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_61_norm__not__less__zero) ).
thf(493,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)],[128]) ).
thf(494,plain,
! [TA: $tType,A: TA] :
( ~ ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) )
| ~ ( TA @ real_normed_vector ) ),
inference(cnf,[status(esa)],[493]) ).
thf(943,plain,
! [TA: $tType,A: TA] :
( ( ( complex @ real_normed_vector )
!= ( TA @ real_normed_vector ) )
| ~ ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[658,494]) ).
thf(944,plain,
! [TA: $tType,A: TA] :
( ( ( complex @ real_normed_vector )
!= ( TA @ real_normed_vector ) )
| ~ ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) ) ),
inference(simp,[status(thm)],[943]) ).
thf(945,plain,
! [A: complex] :
~ ( real @ zero_zero @ ( A @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ),
inference(pattern_uni,[status(thm)],[944:[bind_type(TA,$thf( complex ))]]) ).
thf(1092,plain,
! [A: complex] :
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
!= ( A @ ( complex @ norm_norm ) ) )
| ~ ( real @ zero_zero @ ( real @ one_one @ ( real @ ord_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[588,945]) ).
thf(1093,plain,
~ ( real @ zero_zero @ ( real @ one_one @ ( real @ ord_less ) ) ),
inference(pattern_uni,[status(thm)],[1092:[bind(A,$thf( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ))]]) ).
thf(1328,plain,
( ( ( real @ one_one @ ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ one_one @ ( real @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[376,1093]) ).
thf(1329,plain,
( ( real @ one_one @ ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ one_one @ ( real @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1328]) ).
thf(1332,plain,
( ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[1329]) ).
thf(3644,plain,
! [A: complex] :
( ( ( complex @ zero_zero @ ( A @ ( complex @ plus_plus ) ) )
!= ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[863,1332]) ).
thf(3671,plain,
! [A: complex] :
( ( ( na @ ( sk1 @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( A
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[3644]) ).
thf(3681,plain,
( ( ( na @ ( sk1 @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[3671]) ).
thf(6691,plain,
( ( ( na @ ( sk1 @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ one_one ) ) ),
inference(rewrite,[status(thm)],[3681,588]) ).
thf(6692,plain,
( ( ( na @ ( sk1 @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[6691]) ).
thf(6693,plain,
( ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) )
!= ( na @ ( sk1 @ ( complex @ power_power ) ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[1474,6692]) ).
thf(6694,plain,
( ( na != na )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= sk1 )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[6693]) ).
thf(6695,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= sk1 )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[6694]) ).
thf(66,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_one__reorient) ).
thf(308,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1543,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
= ( real @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[1474,588]) ).
thf(1544,plain,
( ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
= ( real @ one_one ) ),
inference(pattern_uni,[status(thm)],[1543:[]]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) )
<=> ( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_divide__less__0__iff) ).
thf(449,plain,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( ( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) )
=> ( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(38,axiom,
real @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(247,plain,
real @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: real,B: real] :
( ( A @ ( B @ ( real @ plus_plus ) ) @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) @ ( B @ ( TA @ of_real ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_of__real__add) ).
thf(377,plain,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: real,B: real] :
( ( A @ ( B @ ( real @ plus_plus ) ) @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) @ ( B @ ( TA @ of_real ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(378,plain,
! [TA: $tType,B: real,A: real] :
( ( ( A @ ( B @ ( real @ plus_plus ) ) @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) @ ( B @ ( TA @ of_real ) @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ real_algebra_1 ) ),
inference(cnf,[status(esa)],[377]) ).
thf(379,plain,
! [TA: $tType,B: real,A: real] :
( ~ ( TA @ real_algebra_1 )
| ( ( A @ ( B @ ( real @ plus_plus ) ) @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) @ ( B @ ( TA @ of_real ) @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[378]) ).
thf(1103,plain,
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[588,175]) ).
thf(1113,plain,
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(simp,[status(thm)],[1103]) ).
thf(1532,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,1113]) ).
thf(1533,plain,
( ( ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1532:[]]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_add__0__right) ).
thf(267,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(268,plain,
! [TA: $tType,A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A )
| ~ ( TA @ monoid_add ) ),
inference(cnf,[status(esa)],[267]) ).
thf(269,plain,
! [TA: $tType,A: TA] :
( ~ ( TA @ monoid_add )
| ( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(lifteq,[status(thm)],[268]) ).
thf(13,axiom,
~ ( nat @ one_one @ ( nat @ even_odd_even ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_odd__1__nat) ).
thf(201,plain,
~ ( nat @ one_one @ ( nat @ even_odd_even ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(202,plain,
~ ( nat @ one_one @ ( nat @ even_odd_even ) ),
inference(polarity_switch,[status(thm)],[201]) ).
thf(22,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_82_add__pos__pos) ).
thf(216,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)],[22]) ).
thf(217,plain,
! [TA: $tType,B: TA,A: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere216010020id_add ) ),
inference(cnf,[status(esa)],[216]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__strict__mono) ).
thf(275,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(276,plain,
! [TA: $tType,D: TA,C: TA,B: TA,A: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( A @ ( B @ ( TA @ ord_less ) ) )
| ~ ( C @ ( D @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere223160158up_add ) ),
inference(cnf,[status(esa)],[275]) ).
thf(5965,plain,
! [TA: $tType,A: TA] :
( ( ( complex @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ~ $true
| ( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[480,282]) ).
thf(5966,plain,
! [TA: $tType,A: TA] :
( ( ( complex @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(simp,[status(thm)],[5965]) ).
thf(5967,plain,
! [A: complex] :
( ( A @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[5966:[bind_type(TA,$thf( complex ))]]) ).
thf(96,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_norm__zero) ).
thf(385,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_field__power__not__zero) ).
thf(382,plain,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(383,plain,
! [TA: $tType,B: TA,A: nat] :
( ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) )
| ~ ( TA @ ring_11004092258visors ) ),
inference(cnf,[status(esa)],[382]) ).
thf(384,plain,
! [TA: $tType,B: TA,A: nat] :
( ~ ( TA @ ring_11004092258visors )
| ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[383]) ).
thf(75,axiom,
real @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__add) ).
thf(342,plain,
real @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(6051,plain,
! [TA: $tType,A: TA] :
( ( ( real @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ~ $true
| ( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[342,282]) ).
thf(6052,plain,
! [TA: $tType,A: TA] :
( ( ( real @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(simp,[status(thm)],[6051]) ).
thf(6053,plain,
! [A: real] :
( ( A @ ( real @ zero_zero @ ( real @ plus_plus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[6052:[bind_type(TA,$thf( real ))]]) ).
thf(93,axiom,
complex @ real_algebra_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__algebra__1) ).
thf(380,plain,
complex @ real_algebra_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(12572,plain,
! [TA: $tType,B: real,A: real] :
( ( ( complex @ real_algebra_1 )
!= ( TA @ real_algebra_1 ) )
| ~ $true
| ( ( A @ ( B @ ( real @ plus_plus ) ) @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) @ ( B @ ( TA @ of_real ) @ ( TA @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[380,379]) ).
thf(12573,plain,
! [TA: $tType,B: real,A: real] :
( ( ( complex @ real_algebra_1 )
!= ( TA @ real_algebra_1 ) )
| ( ( A @ ( B @ ( real @ plus_plus ) ) @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) @ ( B @ ( TA @ of_real ) @ ( TA @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[12572]) ).
thf(12574,plain,
! [B: real,A: real] :
( ( A @ ( B @ ( real @ plus_plus ) ) @ ( complex @ of_real ) )
= ( A @ ( complex @ of_real ) @ ( B @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[12573:[bind_type(TA,$thf( complex ))]]) ).
thf(12829,plain,
! [C: real,B: real,A: real] :
( ( ( A @ ( real @ zero_zero @ ( real @ plus_plus ) ) )
!= ( B @ ( C @ ( real @ plus_plus ) ) ) )
| ( ( A @ ( complex @ of_real ) )
= ( B @ ( complex @ of_real ) @ ( C @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6053,12574]) ).
thf(12830,plain,
! [A: real] :
( ( A @ ( complex @ of_real ) @ ( real @ zero_zero @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) )
= ( A @ ( complex @ of_real ) ) ),
inference(pattern_uni,[status(thm)],[12829:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( real @ zero_zero ))]]) ).
thf(13078,plain,
! [A: real] :
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( A @ ( complex @ of_real ) ) )
| ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( real @ zero_zero @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) )
= ( A @ ( complex @ of_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,12830]) ).
thf(13079,plain,
( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( real @ zero_zero @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) )
= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ),
inference(pattern_uni,[status(thm)],[13078:[bind(A,$thf( b @ ( complex @ norm_norm ) ))]]) ).
thf(13674,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( real @ zero_zero @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
= ( real @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[13079,588]) ).
thf(13675,plain,
( ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( real @ zero_zero @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
= ( real @ one_one ) ),
inference(pattern_uni,[status(thm)],[13674:[]]) ).
thf(3,axiom,
! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
<=> ~ ( ~ ( B @ ( nat @ even_odd_even ) )
<=> ~ ( A @ ( nat @ even_odd_even ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_odd__add) ).
thf(176,plain,
! [A: nat,B: nat] :
( ( ~ ( ( ~ ( A @ ( nat @ even_odd_even ) )
=> ~ ( B @ ( nat @ even_odd_even ) ) )
& ( ~ ( B @ ( nat @ even_odd_even ) )
=> ~ ( A @ ( nat @ even_odd_even ) ) ) )
=> ~ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) )
& ( ~ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
=> ~ ( ( ~ ( A @ ( nat @ even_odd_even ) )
=> ~ ( B @ ( nat @ even_odd_even ) ) )
& ( ~ ( B @ ( nat @ even_odd_even ) )
=> ~ ( A @ ( nat @ even_odd_even ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(177,plain,
( ! [A: nat,B: nat] :
( ~ ( ( ~ ( A @ ( nat @ even_odd_even ) )
=> ~ ( B @ ( nat @ even_odd_even ) ) )
& ( ~ ( B @ ( nat @ even_odd_even ) )
=> ~ ( A @ ( nat @ even_odd_even ) ) ) )
=> ~ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) )
& ! [A: nat,B: nat] :
( ~ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
=> ~ ( ( ~ ( A @ ( nat @ even_odd_even ) )
=> ~ ( B @ ( nat @ even_odd_even ) ) )
& ( ~ ( B @ ( nat @ even_odd_even ) )
=> ~ ( A @ ( nat @ even_odd_even ) ) ) ) ) ),
inference(miniscope,[status(thm)],[176]) ).
thf(178,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ~ ( C @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ~ ( D @ ( nat @ even_odd_even ) )
| ( C @ ( nat @ even_odd_even ) ) )
& ( ~ ( C @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ~ ( C @ ( nat @ even_odd_even ) )
| ( D @ ( nat @ even_odd_even ) ) )
& ( ( B @ ( nat @ even_odd_even ) )
| ( A @ ( nat @ even_odd_even ) )
| ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) )
& ( ~ ( A @ ( nat @ even_odd_even ) )
| ( A @ ( nat @ even_odd_even ) )
| ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) )
& ( ( B @ ( nat @ even_odd_even ) )
| ~ ( B @ ( nat @ even_odd_even ) )
| ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) )
& ( ~ ( A @ ( nat @ even_odd_even ) )
| ~ ( B @ ( nat @ even_odd_even ) )
| ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ) ),
inference(cnf,[status(esa)],[177]) ).
thf(181,plain,
! [B: nat,A: nat] :
( ~ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ~ ( B @ ( nat @ even_odd_even ) )
| ( A @ ( nat @ even_odd_even ) ) ),
inference(cnfConj,[status(thm)],[178]) ).
thf(185,plain,
! [B: nat,A: nat] :
( ~ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ~ ( B @ ( nat @ even_odd_even ) )
| ( A @ ( nat @ even_odd_even ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(30,axiom,
real @ real_normed_vector,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__vector) ).
thf(236,plain,
real @ real_normed_vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(630,plain,
! [TA: $tType,A: TA] :
( ( ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
| ( A
= ( TA @ zero_zero ) )
| ~ ( TA @ real_normed_vector ) )
& ( ( A
!= ( TA @ zero_zero ) )
| ~ ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
| ~ ( TA @ real_normed_vector ) ) ),
inference(cnf,[status(esa)],[629]) ).
thf(631,plain,
! [TA: $tType,A: TA] :
( ( A
!= ( TA @ zero_zero ) )
| ~ ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
| ~ ( TA @ real_normed_vector ) ),
inference(cnfConj,[status(thm)],[630]) ).
thf(633,plain,
! [TA: $tType,A: TA] :
( ~ ( A @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
| ~ ( TA @ real_normed_vector )
| ( A
!= ( TA @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[631]) ).
thf(634,plain,
! [TA: $tType] :
( ~ ( TA @ zero_zero @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
| ~ ( TA @ real_normed_vector ) ),
inference(simp,[status(thm)],[633]) ).
thf(694,plain,
! [TA: $tType] :
( ( ( real @ real_normed_vector )
!= ( TA @ real_normed_vector ) )
| ~ ( TA @ zero_zero @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,634]) ).
thf(695,plain,
! [TA: $tType] :
( ( ( real @ real_normed_vector )
!= ( TA @ real_normed_vector ) )
| ~ ( TA @ zero_zero @ ( TA @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ),
inference(simp,[status(thm)],[694]) ).
thf(696,plain,
~ ( real @ zero_zero @ ( real @ norm_norm ) @ ( real @ zero_zero @ ( real @ ord_less ) ) ),
inference(pattern_uni,[status(thm)],[695:[bind_type(TA,$thf( real ))]]) ).
thf(386,plain,
! [TA: $tType] :
( ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) )
| ~ ( TA @ real_normed_vector ) ),
inference(cnf,[status(esa)],[385]) ).
thf(387,plain,
! [TA: $tType] :
( ~ ( TA @ real_normed_vector )
| ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[386]) ).
thf(989,plain,
! [TA: $tType] :
( ( ( real @ real_normed_vector )
!= ( TA @ real_normed_vector ) )
| ~ $true
| ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[236,387]) ).
thf(990,plain,
! [TA: $tType] :
( ( ( real @ real_normed_vector )
!= ( TA @ real_normed_vector ) )
| ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[989]) ).
thf(991,plain,
( ( real @ zero_zero @ ( real @ norm_norm ) )
= ( real @ zero_zero ) ),
inference(pattern_uni,[status(thm)],[990:[bind_type(TA,$thf( real ))]]) ).
thf(1046,plain,
~ ( real @ zero_zero @ ( real @ zero_zero @ ( real @ ord_less ) ) ),
inference(rewrite,[status(thm)],[696,991]) ).
thf(60,axiom,
real @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
thf(301,plain,
real @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(160,axiom,
complex @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oab__semigroup__add) ).
thf(599,plain,
complex @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(900,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( ( complex @ ab_semigroup_add )
!= ( TA @ ab_semigroup_add ) )
| ~ $true
| ( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[599,210]) ).
thf(901,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( ( complex @ ab_semigroup_add )
!= ( TA @ ab_semigroup_add ) )
| ( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[900]) ).
thf(902,plain,
! [C: complex,B: complex,A: complex] :
( ( A @ ( B @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( A @ ( B @ ( complex @ plus_plus ) ) @ ( C @ ( complex @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[901:[bind_type(TA,$thf( complex ))]]) ).
thf(2624,plain,
! [D: complex,C: complex,B: complex,A: complex] :
( ( ( complex @ zero_zero @ ( A @ ( complex @ plus_plus ) ) )
!= ( C @ ( D @ ( complex @ plus_plus ) ) ) )
| ( ( B @ ( A @ ( complex @ plus_plus ) ) )
= ( B @ ( C @ ( complex @ plus_plus ) ) @ ( D @ ( complex @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[863,902]) ).
thf(2625,plain,
! [B: complex,A: complex] :
( ( B @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) )
= ( B @ ( A @ ( complex @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[2624:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( complex @ zero_zero )),bind(D,$thf( A ))]]) ).
thf(2686,plain,
! [E: complex,D: complex,C: complex,B: complex,A: complex] :
( ( ( B @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) )
!= ( D @ ( E @ ( complex @ plus_plus ) ) ) )
| ( ( C @ ( B @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( C @ ( D @ ( complex @ plus_plus ) ) @ ( E @ ( complex @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2625,902]) ).
thf(2687,plain,
! [C: complex,B: complex,A: complex] :
( ( B @ ( C @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( B @ ( C @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[2686:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( G @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) )),bind(E,$thf( A ))]]) ).
thf(2779,plain,
! [C: complex,B: complex,A: complex] :
( ( B @ ( C @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( B @ ( C @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[2687]) ).
thf(3490,plain,
! [C: complex,B: complex,A: complex] :
( ( B @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) )
= ( B @ ( C @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[2779,902]) ).
thf(3501,plain,
! [F: complex,E: complex,D: complex,C: complex,B: complex,A: complex] :
( ( ( B @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) )
!= ( E @ ( F @ ( complex @ plus_plus ) ) ) )
| ( ( D @ ( B @ ( C @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( D @ ( E @ ( complex @ plus_plus ) ) @ ( F @ ( complex @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3490,902]) ).
thf(3502,plain,
! [D: complex,C: complex,B: complex,A: complex] :
( ( B @ ( D @ ( C @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( B @ ( D @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[3501:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( I )),bind(D,$thf( D )),bind(E,$thf( J @ ( I @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) )),bind(F,$thf( A ))]]) ).
thf(3612,plain,
! [D: complex,C: complex,B: complex,A: complex] :
( ( B @ ( D @ ( C @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( B @ ( D @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[3502]) ).
thf(2598,plain,
! [F: complex,E: complex,D: complex,C: complex,B: complex,A: complex] :
( ( ( A @ ( B @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
!= ( E @ ( F @ ( complex @ plus_plus ) ) ) )
| ( ( D @ ( A @ ( B @ ( complex @ plus_plus ) ) @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( D @ ( E @ ( complex @ plus_plus ) ) @ ( F @ ( complex @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[902,902]) ).
thf(2599,plain,
! [D: complex,C: complex,B: complex,A: complex] :
( ( B @ ( A @ ( D @ ( complex @ plus_plus ) ) @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( B @ ( A @ ( complex @ plus_plus ) ) @ ( D @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[2598:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( H @ ( G @ ( complex @ plus_plus ) ) ))]]) ).
thf(2670,plain,
! [D: complex,C: complex,B: complex,A: complex] :
( ( B @ ( A @ ( D @ ( complex @ plus_plus ) ) @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( B @ ( A @ ( complex @ plus_plus ) ) @ ( D @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[2599]) ).
thf(4841,plain,
! [D: complex,C: complex,B: complex,A: complex] :
( ( B @ ( A @ ( D @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( C @ ( complex @ plus_plus ) ) )
= ( B @ ( A @ ( complex @ plus_plus ) ) @ ( D @ ( complex @ plus_plus ) ) @ ( C @ ( complex @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[2670,902]) ).
thf(9279,plain,
! [D: complex,C: complex,B: complex,A: complex] :
( ( B @ ( D @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) )
= ( B @ ( D @ ( C @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[3612,902,4841]) ).
thf(9353,plain,
! [E: complex,D: complex,C: complex,B: complex,A: complex] :
( ( ( complex @ zero_zero @ ( A @ ( complex @ plus_plus ) ) )
!= ( C @ ( E @ ( D @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( A @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) )
= ( C @ ( E @ ( D @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[863,9279]) ).
thf(9354,plain,
! [C: complex,B: complex,A: complex] :
( ( C @ ( B @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) )
= ( complex @ zero_zero @ ( C @ ( B @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[9353:[bind(A,$thf( G @ ( F @ ( complex @ plus_plus ) ) )),bind(B,$thf( B )),bind(C,$thf( complex @ zero_zero )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(9482,plain,
! [C: complex,B: complex,A: complex] :
( ( C @ ( B @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) )
= ( complex @ zero_zero @ ( C @ ( B @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[9354]) ).
thf(9301,plain,
! [E: complex,D: complex,C: complex,B: complex,A: complex] :
( ( ( A @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) )
!= ( E @ ( D @ ( complex @ plus_plus ) ) ) )
| ( ( C @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) )
= ( C @ ( E @ ( D @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5967,9279]) ).
thf(9302,plain,
! [C: complex,B: complex,A: complex] :
( ( C @ ( A @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) )
= ( C @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[9301:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( complex @ zero_zero )),bind(E,$thf( A ))]]) ).
thf(9556,plain,
! [C: complex,B: complex,A: complex] :
( ( C @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) )
= ( C @ ( A @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[9302,4841,5967]) ).
thf(10248,plain,
! [C: complex,B: complex,A: complex] :
( ( complex @ zero_zero @ ( C @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) )
= ( C @ ( B @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[9482,9556,4841]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_zero__reorient) ).
thf(320,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)],[70]) ).
thf(150,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: nat,B: TA] :
( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
<=> ( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
& ~ ( A @ ( nat @ even_odd_even ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_power__less__zero__eq) ).
thf(565,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: nat,B: TA] :
( ( ( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
& ~ ( A @ ( nat @ even_odd_even ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
& ~ ( A @ ( nat @ even_odd_even ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(171,axiom,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) ) )
& ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_divide__self__if) ).
thf(651,plain,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) ) )
& ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(41,axiom,
( n
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_assms_I2_J) ).
thf(257,plain,
( n
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ even_odd_even ) )
<=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ even_odd_even ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_even__power__nat) ).
thf(570,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ even_odd_even ) ) )
=> ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ even_odd_even ) ) )
& ( ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ even_odd_even ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ even_odd_even ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(184,plain,
! [B: nat,A: nat] :
( ~ ( A @ ( nat @ even_odd_even ) )
| ~ ( B @ ( nat @ even_odd_even ) )
| ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(cnfConj,[status(thm)],[178]) ).
thf(133,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ inverse_divide ) ) @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_divide__strict__right__mono__neg) ).
thf(504,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ inverse_divide ) ) @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(77,axiom,
real @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(344,plain,
real @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(8,axiom,
real @ real_n1866405975lgebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__div__algebra) ).
thf(196,plain,
real @ real_n1866405975lgebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,axiom,
real @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__semigroup__add) ).
thf(235,plain,
real @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(836,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( ( real @ ab_semigroup_add )
!= ( TA @ ab_semigroup_add ) )
| ~ $true
| ( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[235,210]) ).
thf(837,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( ( real @ ab_semigroup_add )
!= ( TA @ ab_semigroup_add ) )
| ( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[836]) ).
thf(838,plain,
! [C: real,B: real,A: real] :
( ( A @ ( B @ ( C @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) )
= ( A @ ( B @ ( real @ plus_plus ) ) @ ( C @ ( real @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[837:[bind_type(TA,$thf( real ))]]) ).
thf(81,axiom,
nat @ ordere216010020id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
thf(357,plain,
nat @ ordere216010020id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1422,plain,
( ( ( real @ one_one @ ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ zero_zero @ ( real @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,1046]) ).
thf(1423,plain,
( ( real @ one_one @ ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1422]) ).
thf(1452,plain,
( ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[1423]) ).
thf(6260,plain,
! [A: complex] :
( ( ( A @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) )
!= ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[5967,1452]) ).
thf(6299,plain,
! [A: complex] :
( ( A
!= ( na @ ( sk3 @ ( complex @ power_power ) ) ) )
| ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[6260]) ).
thf(6332,plain,
( ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[6299]) ).
thf(147,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_power__strict__increasing__iff) ).
thf(559,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add__less__imp__less__left) ).
thf(188,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(189,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
| ~ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere236663937imp_le ) ),
inference(cnf,[status(esa)],[188]) ).
thf(55,axiom,
real @ real_n2089651433ebra_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__algebra__1) ).
thf(284,plain,
real @ real_n2089651433ebra_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(67,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_74_add__less__imp__less__right) ).
thf(316,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(5465,plain,
! [E: nat,D: nat,C: nat,B: nat,A: nat] :
( ( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
!= ( E @ ( D @ ( nat @ plus_plus ) ) ) )
| ( ( C @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) )
= ( C @ ( E @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[776,5354]) ).
thf(5466,plain,
! [C: nat,B: nat,A: nat] :
( ( C @ ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) )
= ( C @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[5465:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( nat @ zero_zero ))]]) ).
thf(5590,plain,
! [C: nat,B: nat,A: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) )
= ( C @ ( A @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[5466,3728,3038]) ).
thf(179,plain,
! [B: nat,A: nat] :
( ( B @ ( nat @ even_odd_even ) )
| ( A @ ( nat @ even_odd_even ) )
| ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(cnfConj,[status(thm)],[178]) ).
thf(2138,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( B @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) )
!= ( C @ ( D @ ( nat @ plus_plus ) ) ) )
| ( D @ ( nat @ even_odd_even ) )
| ( C @ ( nat @ even_odd_even ) )
| ( B @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(paramod_ordered,[status(thm)],[1890,179]) ).
thf(2139,plain,
! [B: nat,A: nat] :
( ( A @ ( nat @ even_odd_even ) )
| ( B @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( B @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(pattern_uni,[status(thm)],[2138:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( F @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )),bind(D,$thf( A ))]]) ).
thf(2199,plain,
! [B: nat,A: nat] :
( ( A @ ( nat @ even_odd_even ) )
| ( B @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( B @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(simp,[status(thm)],[2139]) ).
thf(2848,plain,
! [B: nat,A: nat] :
( ~ $true
| ( ( B @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
!= ( A @ ( nat @ even_odd_even ) ) )
| ( A @ ( nat @ even_odd_even ) )
| ( B @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(eqfactor_ordered,[status(thm)],[2199]) ).
thf(2852,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( A @ ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(pattern_uni,[status(thm)],[2848:[bind(A,$thf( D @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )),bind(B,$thf( D ))]]) ).
thf(2868,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( A @ ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(simp,[status(thm)],[2852]) ).
thf(3959,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( A @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(rewrite,[status(thm)],[2868,827]) ).
thf(5595,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( C @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) )
!= ( D @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) ) )
| ( D @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( C @ ( A @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(paramod_ordered,[status(thm)],[5590,3959]) ).
thf(5596,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( A @ ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(pattern_uni,[status(thm)],[5595:[bind(A,$thf( F @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )),bind(B,$thf( nat @ zero_zero )),bind(C,$thf( F )),bind(D,$thf( F @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) ))]]) ).
thf(5786,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( A @ ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(simp,[status(thm)],[5596]) ).
thf(8379,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( A @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(rewrite,[status(thm)],[5786,3728,5981]) ).
thf(156,axiom,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_power__divide) ).
thf(591,plain,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ inverse_divide ) ) @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_less__half__sum) ).
thf(443,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ inverse_divide ) ) @ ( B @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(994,plain,
! [TA: $tType] :
( ( ( complex @ real_normed_vector )
!= ( TA @ real_normed_vector ) )
| ~ $true
| ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[658,387]) ).
thf(995,plain,
! [TA: $tType] :
( ( ( complex @ real_normed_vector )
!= ( TA @ real_normed_vector ) )
| ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[994]) ).
thf(996,plain,
( ( complex @ zero_zero @ ( complex @ norm_norm ) )
= ( real @ zero_zero ) ),
inference(pattern_uni,[status(thm)],[995:[bind_type(TA,$thf( complex ))]]) ).
thf(3641,plain,
( ( ( complex @ zero_zero @ ( complex @ norm_norm ) )
!= ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[996,1332]) ).
thf(3642,plain,
( ( ( complex @ zero_zero @ ( complex @ norm_norm ) )
!= ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[3641]) ).
thf(3675,plain,
( ( ( complex @ zero_zero )
!= ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[3642]) ).
thf(3689,plain,
! [A: complex] :
( ( ( complex @ zero_zero @ ( A @ ( complex @ plus_plus ) ) )
!= ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( A
!= ( complex @ zero_zero ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[863,3675]) ).
thf(3703,plain,
( ( ( na @ ( sk1 @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[3689]) ).
thf(12228,plain,
! [A: complex] :
( ( ( complex @ one_one @ ( A @ ( complex @ inverse_divide ) ) )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( na @ ( sk1 @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( A
!= ( complex @ zero_zero ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[12044,3703]) ).
thf(12276,plain,
( ( b
!= ( complex @ one_one ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ zero_zero ) )
| ( ( na @ ( sk1 @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[12228]) ).
thf(80,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_42_double__add__less__zero__iff__single__add__less__zero) ).
thf(353,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)],[80]) ).
thf(20,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_46_add__less__cancel__right) ).
thf(211,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)],[20]) ).
thf(169,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_one__less__power) ).
thf(646,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(2880,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(simp,[status(thm)],[2499]) ).
thf(125,axiom,
! [TA: $tType] :
( ( ( TA @ real_field )
& ( TA @ field_inverse_zero ) )
=> ! [A: real,B: real] :
( ( A @ ( B @ ( real @ inverse_divide ) ) @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) @ ( B @ ( TA @ of_real ) @ ( TA @ inverse_divide ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_of__real__divide) ).
thf(485,plain,
! [TA: $tType] :
( ( ( TA @ real_field )
& ( TA @ field_inverse_zero ) )
=> ! [A: real,B: real] :
( ( A @ ( B @ ( real @ inverse_divide ) ) @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) @ ( B @ ( TA @ of_real ) @ ( TA @ inverse_divide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(6347,plain,
! [B: nat,A: nat] :
( ( A @ ( nat @ even_odd_even ) )
| ( B @ ( nat @ even_odd_even ) )
| ( B @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(rewrite,[status(thm)],[2199,5981]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_nat__zero__less__power__iff) ).
thf(419,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(420,plain,
( ! [A: nat,B: nat] :
( ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(miniscope,[status(thm)],[419]) ).
thf(421,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( C @ ( D @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( C
!= ( nat @ zero_zero ) ) )
& ( ( C @ ( D @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ~ ( D @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ~ ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[420]) ).
thf(424,plain,
! [B: nat,A: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( A
!= ( nat @ zero_zero ) ) ),
inference(cnfConj,[status(thm)],[421]) ).
thf(427,plain,
! [B: nat,A: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( A
!= ( nat @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[424]) ).
thf(428,plain,
! [A: nat] : ( nat @ zero_zero @ ( A @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ),
inference(simp,[status(thm)],[427]) ).
thf(94,axiom,
real @ one_one @ ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_v) ).
thf(381,plain,
real @ one_one @ ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(1397,plain,
( ( ( real @ one_one @ ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ one_one @ ( real @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[381,1093]) ).
thf(1398,plain,
( ( real @ one_one @ ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ one_one @ ( real @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1397]) ).
thf(1407,plain,
( ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[1398]) ).
thf(6235,plain,
! [A: complex] :
( ( ( A @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) )
!= ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[5967,1407]) ).
thf(6294,plain,
! [A: complex] :
( ( A
!= ( na @ ( v @ ( complex @ power_power ) ) ) )
| ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[6235]) ).
thf(6327,plain,
( ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[6294]) ).
thf(17,axiom,
real @ divisi14063676e_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero) ).
thf(206,plain,
real @ divisi14063676e_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(784,plain,
! [TA: $tType,A: TA] :
( ( ( real @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ~ $true
| ( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[342,192]) ).
thf(785,plain,
! [TA: $tType,A: TA] :
( ( ( real @ comm_monoid_add )
!= ( TA @ comm_monoid_add ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(simp,[status(thm)],[784]) ).
thf(786,plain,
! [A: real] :
( ( real @ zero_zero @ ( A @ ( real @ plus_plus ) ) )
= A ),
inference(pattern_uni,[status(thm)],[785:[bind_type(TA,$thf( real ))]]) ).
thf(2294,plain,
! [D: real,C: real,B: real,A: real] :
( ( ( real @ zero_zero @ ( A @ ( real @ plus_plus ) ) )
!= ( C @ ( D @ ( real @ plus_plus ) ) ) )
| ( ( B @ ( A @ ( real @ plus_plus ) ) )
= ( B @ ( C @ ( real @ plus_plus ) ) @ ( D @ ( real @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[786,838]) ).
thf(2295,plain,
! [B: real,A: real] :
( ( B @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) )
= ( B @ ( A @ ( real @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[2294:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( real @ zero_zero )),bind(D,$thf( A ))]]) ).
thf(2337,plain,
! [E: real,D: real,C: real,B: real,A: real] :
( ( ( B @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) )
!= ( D @ ( E @ ( real @ plus_plus ) ) ) )
| ( ( C @ ( B @ ( A @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) )
= ( C @ ( D @ ( real @ plus_plus ) ) @ ( E @ ( real @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2295,838]) ).
thf(2338,plain,
! [C: real,B: real,A: real] :
( ( B @ ( C @ ( A @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) )
= ( B @ ( C @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[2337:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( G @ ( real @ zero_zero @ ( real @ plus_plus ) ) )),bind(E,$thf( A ))]]) ).
thf(2398,plain,
! [C: real,B: real,A: real] :
( ( B @ ( C @ ( A @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) )
= ( B @ ( C @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[2338]) ).
thf(3183,plain,
! [C: real,B: real,A: real] :
( ( B @ ( C @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) )
= ( B @ ( C @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[2398,838]) ).
thf(3198,plain,
! [F: real,E: real,D: real,C: real,B: real,A: real] :
( ( ( B @ ( C @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) )
!= ( E @ ( F @ ( real @ plus_plus ) ) ) )
| ( ( D @ ( B @ ( C @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) )
= ( D @ ( E @ ( real @ plus_plus ) ) @ ( F @ ( real @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3183,838]) ).
thf(3199,plain,
! [D: real,C: real,B: real,A: real] :
( ( B @ ( D @ ( C @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) )
= ( B @ ( D @ ( C @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[3198:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( I )),bind(D,$thf( D )),bind(E,$thf( J @ ( I @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) )),bind(F,$thf( A ))]]) ).
thf(3295,plain,
! [D: real,C: real,B: real,A: real] :
( ( B @ ( D @ ( C @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) )
= ( B @ ( D @ ( C @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[3199]) ).
thf(2268,plain,
! [F: real,E: real,D: real,C: real,B: real,A: real] :
( ( ( A @ ( B @ ( C @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) )
!= ( E @ ( F @ ( real @ plus_plus ) ) ) )
| ( ( D @ ( A @ ( B @ ( real @ plus_plus ) ) @ ( C @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) )
= ( D @ ( E @ ( real @ plus_plus ) ) @ ( F @ ( real @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[838,838]) ).
thf(2269,plain,
! [D: real,C: real,B: real,A: real] :
( ( B @ ( A @ ( D @ ( real @ plus_plus ) ) @ ( C @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) )
= ( B @ ( A @ ( real @ plus_plus ) ) @ ( D @ ( C @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[2268:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( H @ ( G @ ( real @ plus_plus ) ) ))]]) ).
thf(2328,plain,
! [D: real,C: real,B: real,A: real] :
( ( B @ ( A @ ( D @ ( real @ plus_plus ) ) @ ( C @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) )
= ( B @ ( A @ ( real @ plus_plus ) ) @ ( D @ ( C @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[2269]) ).
thf(4676,plain,
! [D: real,C: real,B: real,A: real] :
( ( B @ ( A @ ( D @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( C @ ( real @ plus_plus ) ) )
= ( B @ ( A @ ( real @ plus_plus ) ) @ ( D @ ( real @ plus_plus ) ) @ ( C @ ( real @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[2328,838]) ).
thf(7609,plain,
! [D: real,C: real,B: real,A: real] :
( ( B @ ( D @ ( C @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) )
= ( B @ ( D @ ( C @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[3295,4676,838]) ).
thf(7711,plain,
! [E: real,D: real,C: real,B: real,A: real] :
( ( ( real @ zero_zero @ ( A @ ( real @ plus_plus ) ) )
!= ( C @ ( E @ ( D @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) ) )
| ( ( A @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) )
= ( C @ ( E @ ( D @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[786,7609]) ).
thf(7712,plain,
! [C: real,B: real,A: real] :
( ( C @ ( B @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) )
= ( real @ zero_zero @ ( C @ ( B @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[7711:[bind(A,$thf( G @ ( F @ ( real @ plus_plus ) ) )),bind(B,$thf( B )),bind(C,$thf( real @ zero_zero )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(7763,plain,
! [C: real,B: real,A: real] :
( ( C @ ( B @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) )
= ( real @ zero_zero @ ( C @ ( B @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[7712]) ).
thf(7672,plain,
! [E: real,D: real,C: real,B: real,A: real] :
( ( ( A @ ( real @ zero_zero @ ( real @ plus_plus ) ) )
!= ( E @ ( D @ ( real @ plus_plus ) ) ) )
| ( ( C @ ( A @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) )
= ( C @ ( E @ ( D @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6053,7609]) ).
thf(7673,plain,
! [C: real,B: real,A: real] :
( ( C @ ( A @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) )
= ( C @ ( A @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[7672:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( real @ zero_zero )),bind(E,$thf( A ))]]) ).
thf(7982,plain,
! [C: real,B: real,A: real] :
( ( C @ ( A @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) )
= ( C @ ( A @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[7673,4676,6053]) ).
thf(8554,plain,
! [C: real,B: real,A: real] :
( ( real @ zero_zero @ ( C @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) )
= ( C @ ( B @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[7763,4676,7982]) ).
thf(45,axiom,
real @ linordered_field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Olinordered__field) ).
thf(265,plain,
real @ linordered_field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(65,axiom,
real @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__add) ).
thf(307,plain,
real @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(27,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__strict__left__mono) ).
thf(232,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(233,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( B @ ( C @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere223160158up_add ) ),
inference(cnf,[status(esa)],[232]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zero__less__power) ).
thf(439,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(48,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_47_add__less__cancel__left) ).
thf(270,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)],[48]) ).
thf(144,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ power_power ) ) @ ( C @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_power__strict__increasing) ).
thf(546,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ power_power ) ) @ ( C @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(2883,plain,
( ( ( b @ ( complex @ norm_norm ) )
!= ( complex @ zero_zero @ ( complex @ norm_norm ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[996,2499]) ).
thf(2906,plain,
( ( ( b @ ( complex @ norm_norm ) )
!= ( complex @ zero_zero @ ( complex @ norm_norm ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(simp,[status(thm)],[2883]) ).
thf(6588,plain,
( ( ( b @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(rewrite,[status(thm)],[2906,996]) ).
thf(366,plain,
! [TA: $tType,C: TA,B: nat,A: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
| ~ ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
| ~ ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_semidom ) ),
inference(cnf,[status(esa)],[365]) ).
thf(140,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_divide__zero__left) ).
thf(534,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(73,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_65_add__left__imp__eq) ).
thf(332,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)],[73]) ).
thf(333,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( B = A )
| ( ( B @ ( C @ ( TA @ plus_plus ) ) )
!= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ cancel_semigroup_add ) ),
inference(cnf,[status(esa)],[332]) ).
thf(334,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ~ ( TA @ cancel_semigroup_add )
| ( B = A )
| ( ( B @ ( C @ ( TA @ plus_plus ) ) )
!= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[333]) ).
thf(1371,plain,
( ( ( real @ one_one @ ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ zero_zero @ ( real @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[381,1046]) ).
thf(1372,plain,
( ( real @ one_one @ ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1371]) ).
thf(1403,plain,
( ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[1372]) ).
thf(6243,plain,
! [A: complex] :
( ( ( A @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) )
!= ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[5967,1403]) ).
thf(6295,plain,
! [A: complex] :
( ( A
!= ( na @ ( v @ ( complex @ power_power ) ) ) )
| ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[6243]) ).
thf(6328,plain,
( ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[6295]) ).
thf(2812,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( B @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) )
!= ( D @ ( C @ ( nat @ plus_plus ) ) ) )
| ( C @ ( nat @ even_odd_even ) )
| ( D @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( B @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(paramod_ordered,[status(thm)],[1890,2199]) ).
thf(2813,plain,
! [B: nat,A: nat] :
( ( A @ ( nat @ even_odd_even ) )
| ( B @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( B @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(pattern_uni,[status(thm)],[2812:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) ))]]) ).
thf(2878,plain,
! [B: nat,A: nat] :
( ( A @ ( nat @ even_odd_even ) )
| ( B @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( B @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(simp,[status(thm)],[2813]) ).
thf(10975,plain,
! [B: nat,A: nat] :
( ( A @ ( nat @ even_odd_even ) )
| ( B @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ( B @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(rewrite,[status(thm)],[2878,5981]) ).
thf(61,axiom,
real @ ordere223160158up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(302,plain,
real @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(42,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_63_add__right__imp__eq) ).
thf(260,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)],[42]) ).
thf(159,axiom,
complex @ real_n1866405975lgebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__div__algebra) ).
thf(598,plain,
complex @ real_n1866405975lgebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1104,plain,
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( real @ one_one @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[588,175]) ).
thf(1111,plain,
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( real @ one_one @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) ) ) ),
inference(simp,[status(thm)],[1104]) ).
thf(1501,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( real @ one_one @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,1111]) ).
thf(1502,plain,
( ( ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( real @ one_one @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1501:[]]) ).
thf(10,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(198,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(120,axiom,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: nat,B: TA] :
( ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_power__eq__0__iff) ).
thf(467,plain,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: nat,B: TA] :
( ( ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(468,plain,
! [TA: $tType,B: TA,A: nat] :
( ( ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
| ( A
= ( nat @ zero_zero ) )
| ( B
!= ( TA @ zero_zero ) )
| ~ ( TA @ zero_neq_one )
| ~ ( TA @ no_zero_divisors )
| ~ ( TA @ mult_zero )
| ~ ( TA @ power ) )
& ( ( A
!= ( nat @ zero_zero ) )
| ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) )
| ~ ( TA @ zero_neq_one )
| ~ ( TA @ no_zero_divisors )
| ~ ( TA @ mult_zero )
| ~ ( TA @ power ) )
& ( ( B
= ( TA @ zero_zero ) )
| ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) )
| ~ ( TA @ zero_neq_one )
| ~ ( TA @ no_zero_divisors )
| ~ ( TA @ mult_zero )
| ~ ( TA @ power ) ) ),
inference(cnf,[status(esa)],[467]) ).
thf(470,plain,
! [TA: $tType,B: TA,A: nat] :
( ( A
!= ( nat @ zero_zero ) )
| ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) )
| ~ ( TA @ zero_neq_one )
| ~ ( TA @ no_zero_divisors )
| ~ ( TA @ mult_zero )
| ~ ( TA @ power ) ),
inference(cnfConj,[status(thm)],[468]) ).
thf(473,plain,
! [TA: $tType,B: TA,A: nat] :
( ~ ( TA @ zero_neq_one )
| ~ ( TA @ no_zero_divisors )
| ~ ( TA @ mult_zero )
| ~ ( TA @ power )
| ( A
!= ( nat @ zero_zero ) )
| ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[470]) ).
thf(474,plain,
! [TA: $tType,A: TA] :
( ~ ( TA @ zero_neq_one )
| ~ ( TA @ no_zero_divisors )
| ~ ( TA @ mult_zero )
| ~ ( TA @ power )
| ( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ),
inference(simp,[status(thm)],[473]) ).
thf(740,plain,
! [TA: $tType,A: TA] :
( ( ( nat @ mult_zero )
!= ( TA @ mult_zero ) )
| ~ ( TA @ zero_neq_one )
| ~ ( TA @ no_zero_divisors )
| ~ $true
| ~ ( TA @ power )
| ( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[198,474]) ).
thf(741,plain,
! [TA: $tType,A: TA] :
( ( ( nat @ mult_zero )
!= ( TA @ mult_zero ) )
| ~ ( TA @ zero_neq_one )
| ~ ( TA @ no_zero_divisors )
| ~ ( TA @ power )
| ( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ),
inference(simp,[status(thm)],[740]) ).
thf(742,plain,
! [A: nat] :
( ~ ( nat @ zero_neq_one )
| ~ ( nat @ no_zero_divisors )
| ~ ( nat @ power )
| ( ( nat @ zero_zero @ ( A @ ( nat @ power_power ) ) )
!= ( nat @ zero_zero ) ) ),
inference(pattern_uni,[status(thm)],[741:[bind_type(TA,$thf( nat ))]]) ).
thf(23,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(218,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(56,axiom,
nat @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(285,plain,
nat @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(69,axiom,
nat @ power,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(319,plain,
nat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(787,plain,
! [A: nat] :
( ~ $true
| ~ $true
| ~ $true
| ( ( nat @ zero_zero @ ( A @ ( nat @ power_power ) ) )
!= ( nat @ zero_zero ) ) ),
inference(rewrite,[status(thm)],[742,218,285,319]) ).
thf(788,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ power_power ) ) )
!= ( nat @ zero_zero ) ),
inference(simp,[status(thm)],[787]) ).
thf(124,axiom,
complex @ power,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Power_Opower) ).
thf(484,plain,
complex @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: real,B: TA,C: real,D: TA] :
( ( C @ ( D @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) )
=> ( A @ ( C @ ( real @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_norm__add__less) ).
thf(360,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: real,B: TA,C: real,D: TA] :
( ( C @ ( D @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) )
=> ( A @ ( C @ ( real @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(361,plain,
! [TA: $tType,D: TA,C: real,B: TA,A: real] :
( ( A @ ( C @ ( real @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) )
| ~ ( A @ ( B @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) )
| ~ ( C @ ( D @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) )
| ~ ( TA @ real_normed_vector ) ),
inference(cnf,[status(esa)],[360]) ).
thf(163,axiom,
complex @ real_n2089651433ebra_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1) ).
thf(625,plain,
complex @ real_n2089651433ebra_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(72,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add__0__left) ).
thf(329,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1530,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,1113]) ).
thf(1531,plain,
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1530:[]]) ).
thf(11157,plain,
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[588,1531]) ).
thf(11162,plain,
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(simp,[status(thm)],[11157]) ).
thf(11174,plain,
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(simp,[status(thm)],[11162]) ).
thf(12438,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ one_one ) )
| ( na != na )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) )
!= v ) ),
inference(simp,[status(thm)],[12335]) ).
thf(12506,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ one_one ) )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) )
!= v ) ),
inference(simp,[status(thm)],[12438]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ one_one @ ( TA @ inverse_divide ) ) )
= ( A @ ( B @ ( TA @ one_one @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_power__one__over) ).
thf(388,plain,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ one_one @ ( TA @ inverse_divide ) ) )
= ( A @ ( B @ ( TA @ one_one @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(354,plain,
! [TA: $tType,A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
| ~ ( TA @ linord219039673up_add ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
| ~ ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linord219039673up_add ) ) ),
inference(cnf,[status(esa)],[353]) ).
thf(356,plain,
! [TA: $tType,A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
| ~ ( TA @ linord219039673up_add ) ),
inference(cnfConj,[status(thm)],[354]) ).
thf(131,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_power__one__right) ).
thf(499,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(126,axiom,
! [A: nat] :
( ( na @ ( A @ ( nat @ ord_less ) ) )
=> ( ( A
!= ( nat @ zero_zero ) )
=> ? [B: complex] : ( real @ one_one @ ( A @ ( B @ ( complex @ power_power ) ) @ ( b @ ( complex @ times_times ) ) @ ( complex @ one_one @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_IH) ).
thf(488,plain,
! [A: nat] :
( ( na @ ( A @ ( nat @ ord_less ) ) )
=> ( ( A
!= ( nat @ zero_zero ) )
=> ? [B: complex] : ( real @ one_one @ ( A @ ( B @ ( complex @ power_power ) ) @ ( b @ ( complex @ times_times ) ) @ ( complex @ one_one @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(74,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_53_double__zero__sym) ).
thf(335,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)],[74]) ).
thf(336,plain,
! [TA: $tType,A: TA] :
( ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
| ( A
!= ( TA @ zero_zero ) )
| ~ ( TA @ linord219039673up_add ) )
& ( ( A
= ( TA @ zero_zero ) )
| ( ( TA @ zero_zero )
!= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ linord219039673up_add ) ) ),
inference(cnf,[status(esa)],[335]) ).
thf(337,plain,
! [TA: $tType,A: TA] :
( ( A
= ( TA @ zero_zero ) )
| ( ( TA @ zero_zero )
!= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ linord219039673up_add ) ),
inference(cnfConj,[status(thm)],[336]) ).
thf(339,plain,
! [TA: $tType,A: TA] :
( ~ ( TA @ linord219039673up_add )
| ( A
= ( TA @ zero_zero ) )
| ( ( TA @ zero_zero )
!= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[337]) ).
thf(137,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_divide__pos__pos) ).
thf(526,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(1935,plain,
! [A: nat] :
( ( ( A @ ( nat @ even_odd_even ) )
!= ( nat @ one_one @ ( nat @ even_odd_even ) ) )
| ~ $true
| ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[249,202]) ).
thf(1936,plain,
! [A: nat] :
( ( ( A @ ( nat @ even_odd_even ) )
!= ( nat @ one_one @ ( nat @ even_odd_even ) ) )
| ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1935]) ).
thf(1937,plain,
nat @ one_one @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(pattern_uni,[status(thm)],[1936:[bind(A,$thf( nat @ one_one ))]]) ).
thf(155,axiom,
complex @ ring_11004092258visors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors) ).
thf(590,plain,
complex @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(71,axiom,
nat @ ordere223160158up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(328,plain,
nat @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(7,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_64_add__imp__eq) ).
thf(193,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)],[7]) ).
thf(1448,plain,
( ( ( real @ one_one @ ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ one_one @ ( real @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[628,1093]) ).
thf(1449,plain,
( ( real @ one_one @ ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ one_one @ ( real @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1448]) ).
thf(1461,plain,
( ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[1449]) ).
thf(141,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_18_norm__eq__zero) ).
thf(537,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)],[141]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_power__one) ).
thf(457,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1171,plain,
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( real @ one_one @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[588,1111]) ).
thf(1173,plain,
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( real @ one_one @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(simp,[status(thm)],[1171]) ).
thf(1177,plain,
( ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( real @ one_one @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(simp,[status(thm)],[1173]) ).
thf(1524,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( real @ one_one @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,1177]) ).
thf(1525,plain,
( ( ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= b )
| ( ( na @ ( real @ one_one @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( real @ one_one @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1524:[]]) ).
thf(36,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_41_zero__less__double__add__iff__zero__less__single__add) ).
thf(242,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)],[36]) ).
thf(243,plain,
! [TA: $tType,A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ linord219039673up_add ) )
& ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ linord219039673up_add ) ) ),
inference(cnf,[status(esa)],[242]) ).
thf(244,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ linord219039673up_add ) ),
inference(cnfConj,[status(thm)],[243]) ).
thf(46,axiom,
real @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(266,plain,
real @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(16,axiom,
nat @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(205,plain,
nat @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12873,plain,
! [C: real,B: real,A: real] :
( ( ( real @ zero_zero @ ( A @ ( real @ plus_plus ) ) )
!= ( B @ ( C @ ( real @ plus_plus ) ) ) )
| ( ( A @ ( complex @ of_real ) )
= ( B @ ( complex @ of_real ) @ ( C @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[786,12574]) ).
thf(12874,plain,
! [A: real] :
( ( real @ zero_zero @ ( complex @ of_real ) @ ( A @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) )
= ( A @ ( complex @ of_real ) ) ),
inference(pattern_uni,[status(thm)],[12873:[bind(A,$thf( A )),bind(B,$thf( real @ zero_zero )),bind(C,$thf( A ))]]) ).
thf(13313,plain,
! [A: real] :
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( A @ ( complex @ of_real ) ) )
| ( ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ plus_plus ) ) )
= ( A @ ( complex @ of_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,12874]) ).
thf(13314,plain,
( ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ plus_plus ) ) )
= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ),
inference(pattern_uni,[status(thm)],[13313:[bind(A,$thf( b @ ( complex @ norm_norm ) ))]]) ).
thf(14179,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ plus_plus ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
= ( real @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[13314,588]) ).
thf(14180,plain,
( ( b @ ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ plus_plus ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
= ( real @ one_one ) ),
inference(pattern_uni,[status(thm)],[14179:[]]) ).
thf(99,axiom,
( na
!= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_n) ).
thf(398,plain,
( na
!= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(76,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(343,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(31,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(237,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(103,axiom,
( b
!= ( complex @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_b) ).
thf(412,plain,
( b
!= ( complex @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(44,axiom,
real @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(264,plain,
real @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(52,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__strict__right__mono) ).
thf(278,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(279,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( B @ ( C @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere223160158up_add ) ),
inference(cnf,[status(esa)],[278]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ real_normed_field )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( B @ ( A @ ( TA @ inverse_divide ) ) @ ( TA @ norm_norm ) )
= ( B @ ( TA @ norm_norm ) @ ( A @ ( TA @ norm_norm ) @ ( real @ inverse_divide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_nonzero__norm__divide) ).
thf(402,plain,
! [TA: $tType] :
( ( TA @ real_normed_field )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( B @ ( A @ ( TA @ inverse_divide ) ) @ ( TA @ norm_norm ) )
= ( B @ ( TA @ norm_norm ) @ ( A @ ( TA @ norm_norm ) @ ( real @ inverse_divide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
<=> ( ( B @ ( nat @ even_odd_even ) )
<=> ( A @ ( nat @ even_odd_even ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_even__add) ).
thf(286,plain,
! [A: nat,B: nat] :
( ( ( ( ( A @ ( nat @ even_odd_even ) )
=> ( B @ ( nat @ even_odd_even ) ) )
& ( ( B @ ( nat @ even_odd_even ) )
=> ( A @ ( nat @ even_odd_even ) ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) )
& ( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
=> ( ( ( A @ ( nat @ even_odd_even ) )
=> ( B @ ( nat @ even_odd_even ) ) )
& ( ( B @ ( nat @ even_odd_even ) )
=> ( A @ ( nat @ even_odd_even ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( A
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_zero__less__power__nat__eq) ).
thf(577,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( A
= ( nat @ zero_zero ) ) )
=> ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( A
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(15,axiom,
real @ ring_11004092258visors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
thf(204,plain,
real @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(143,axiom,
complex @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__add) ).
thf(545,plain,
complex @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(258,plain,
( n
!= ( nat @ zero_zero ) ),
inference(polarity_switch,[status(thm)],[257]) ).
thf(259,plain,
( n
!= ( nat @ zero_zero ) ),
inference(lifteq,[status(thm)],[258]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: real] :
( ( ( A @ ( TA @ of_real ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( real @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_of__real__eq__0__iff) ).
thf(391,plain,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: real] :
( ( ( A
= ( real @ zero_zero ) )
=> ( ( A @ ( TA @ of_real ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ of_real ) )
= ( TA @ zero_zero ) )
=> ( A
= ( real @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_gt__half__sum) ).
thf(445,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(119,axiom,
complex @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Omult__zero) ).
thf(466,plain,
complex @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(100,axiom,
complex @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ono__zero__divisors) ).
thf(401,plain,
complex @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(812,plain,
! [TA: $tType,A: TA] :
( ( ( complex @ no_zero_divisors )
!= ( TA @ no_zero_divisors ) )
| ~ ( TA @ zero_neq_one )
| ~ $true
| ~ ( TA @ mult_zero )
| ~ ( TA @ power )
| ( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[401,474]) ).
thf(813,plain,
! [TA: $tType,A: TA] :
( ( ( complex @ no_zero_divisors )
!= ( TA @ no_zero_divisors ) )
| ~ ( TA @ zero_neq_one )
| ~ ( TA @ mult_zero )
| ~ ( TA @ power )
| ( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ),
inference(simp,[status(thm)],[812]) ).
thf(814,plain,
! [A: complex] :
( ~ ( complex @ zero_neq_one )
| ~ ( complex @ mult_zero )
| ~ ( complex @ power )
| ( ( nat @ zero_zero @ ( A @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) ) ),
inference(pattern_uni,[status(thm)],[813:[bind_type(TA,$thf( complex ))]]) ).
thf(892,plain,
! [A: complex] :
( ~ ( complex @ zero_neq_one )
| ~ $true
| ~ $true
| ( ( nat @ zero_zero @ ( A @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) ) ),
inference(rewrite,[status(thm)],[814,466,484]) ).
thf(893,plain,
! [A: complex] :
( ~ ( complex @ zero_neq_one )
| ( ( nat @ zero_zero @ ( A @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) ) ),
inference(simp,[status(thm)],[892]) ).
thf(173,axiom,
complex @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ozero__neq__one) ).
thf(659,plain,
complex @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(946,plain,
! [A: complex] :
( ~ $true
| ( ( nat @ zero_zero @ ( A @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) ) ),
inference(rewrite,[status(thm)],[893,659]) ).
thf(947,plain,
! [A: complex] :
( ( nat @ zero_zero @ ( A @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) ),
inference(simp,[status(thm)],[946]) ).
thf(9355,plain,
! [E: complex,D: complex,C: complex,B: complex,A: complex] :
( ( ( complex @ zero_zero @ ( A @ ( complex @ plus_plus ) ) )
!= ( E @ ( D @ ( complex @ plus_plus ) ) ) )
| ( ( C @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) )
= ( C @ ( E @ ( D @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[863,9279]) ).
thf(9356,plain,
! [C: complex,B: complex,A: complex] :
( ( C @ ( complex @ zero_zero @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) )
= ( C @ ( A @ ( complex @ plus_plus ) ) @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[9355:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( complex @ zero_zero ))]]) ).
thf(9808,plain,
! [C: complex,B: complex,A: complex] :
( ( C @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) @ ( A @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) )
= ( C @ ( A @ ( complex @ plus_plus ) ) @ ( B @ ( complex @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[9356,9556,4841]) ).
thf(4,axiom,
real @ division_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Odivision__ring) ).
thf(187,plain,
real @ division_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
<=> ( ( ~ ( A @ ( nat @ even_odd_even ) )
& ~ ( B @ ( nat @ even_odd_even ) ) )
| ( ( A @ ( nat @ even_odd_even ) )
& ( B @ ( nat @ even_odd_even ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_even__sum__nat) ).
thf(219,plain,
! [A: nat,B: nat] :
( ( ( ( ~ ( A @ ( nat @ even_odd_even ) )
& ~ ( B @ ( nat @ even_odd_even ) ) )
| ( ( A @ ( nat @ even_odd_even ) )
& ( B @ ( nat @ even_odd_even ) ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) )
& ( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
=> ( ( ~ ( A @ ( nat @ even_odd_even ) )
& ~ ( B @ ( nat @ even_odd_even ) ) )
| ( ( A @ ( nat @ even_odd_even ) )
& ( B @ ( nat @ even_odd_even ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(49,axiom,
real @ semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__0) ).
thf(274,plain,
real @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(2884,plain,
( ( ( b @ ( complex @ norm_norm ) )
!= ( complex @ zero_zero @ ( complex @ norm_norm ) ) )
| ( ( real @ zero_zero @ ( na @ root ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[996,2499]) ).
thf(2902,plain,
( ( ( b @ ( complex @ norm_norm ) )
!= ( complex @ zero_zero @ ( complex @ norm_norm ) ) )
| ( ( real @ zero_zero @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(simp,[status(thm)],[2884]) ).
thf(5103,plain,
( ( ( b @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) )
| ( ( real @ zero_zero @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(rewrite,[status(thm)],[2902,996]) ).
thf(25,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(230,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(245,plain,
! [TA: $tType,A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ linord219039673up_add ) ),
inference(cnfConj,[status(thm)],[243]) ).
thf(62,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_81_add__neg__neg) ).
thf(303,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)],[62]) ).
thf(85,axiom,
complex @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocancel__semigroup__add) ).
thf(362,plain,
complex @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(6244,plain,
! [A: complex] :
( ( ( A @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) )
!= ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[5967,1332]) ).
thf(6311,plain,
! [A: complex] :
( ( A
!= ( na @ ( sk1 @ ( complex @ power_power ) ) ) )
| ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[6244]) ).
thf(6340,plain,
( ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( complex @ norm_norm ) )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[6311]) ).
thf(2942,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,2880]) ).
thf(2943,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(pattern_uni,[status(thm)],[2942:[]]) ).
thf(68,axiom,
nat @ semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(318,plain,
nat @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1536,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( na @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,175]) ).
thf(1571,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(simp,[status(thm)],[1536]) ).
thf(121,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_divide__self) ).
thf(477,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(157,axiom,
complex @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(594,plain,
complex @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(212,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( A @ ( C @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere236663937imp_le ) )
& ( ( A @ ( C @ ( TA @ ord_less ) ) )
| ~ ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere236663937imp_le ) ) ),
inference(cnf,[status(esa)],[211]) ).
thf(213,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( A @ ( C @ ( TA @ ord_less ) ) )
| ~ ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere236663937imp_le ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(34,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(240,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(164,axiom,
complex @ field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Ofield) ).
thf(626,plain,
complex @ field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(78,axiom,
real @ real_normed_field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__field) ).
thf(345,plain,
real @ real_normed_field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(88,axiom,
~ ( na @ ( nat @ even_odd_even ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_o) ).
thf(367,plain,
~ ( na @ ( nat @ even_odd_even ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(368,plain,
~ ( na @ ( nat @ even_odd_even ) ),
inference(polarity_switch,[status(thm)],[367]) ).
thf(1950,plain,
! [A: nat] :
( ( ( A @ ( nat @ even_odd_even ) )
!= ( na @ ( nat @ even_odd_even ) ) )
| ~ $true
| ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[249,368]) ).
thf(1951,plain,
! [A: nat] :
( ( ( A @ ( nat @ even_odd_even ) )
!= ( na @ ( nat @ even_odd_even ) ) )
| ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1950]) ).
thf(1952,plain,
na @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(pattern_uni,[status(thm)],[1951:[bind(A,$thf( na ))]]) ).
thf(135,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ power_power ) ) @ ( B @ ( C @ ( nat @ power_power ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_nat__power__less__imp__less) ).
thf(521,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ power_power ) ) @ ( B @ ( C @ ( nat @ power_power ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(167,axiom,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ( ( real @ zero_zero @ ( TA @ of_real ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_of__real__0) ).
thf(636,plain,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ( ( real @ zero_zero @ ( TA @ of_real ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(64,axiom,
real @ field_inverse_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Ofield__inverse__zero) ).
thf(306,plain,
real @ field_inverse_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(58,axiom,
real @ linord219039673up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
thf(299,plain,
real @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(109,axiom,
complex @ field_inverse_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Ofield__inverse__zero) ).
thf(438,plain,
complex @ field_inverse_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(108,axiom,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: real,B: real] :
( ( ( B @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_of__real__eq__iff) ).
thf(431,plain,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: real,B: real] :
( ( ( B = A )
=> ( ( B @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) ) ) )
& ( ( ( B @ ( TA @ of_real ) )
= ( A @ ( TA @ of_real ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(35,axiom,
real @ real_algebra_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__algebra__1) ).
thf(241,plain,
real @ real_algebra_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(4246,plain,
! [A: complex] :
( ( ( complex @ zero_zero @ ( A @ ( complex @ plus_plus ) ) )
!= ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[863,1403]) ).
thf(4266,plain,
! [A: complex] :
( ( ( na @ ( v @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( A
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[4246]) ).
thf(4280,plain,
( ( ( na @ ( v @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[4266]) ).
thf(7323,plain,
( ( ( na @ ( v @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(rewrite,[status(thm)],[4280,588]) ).
thf(7324,plain,
( ( ( na @ ( v @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[7323]) ).
thf(148,axiom,
complex @ semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__0) ).
thf(563,plain,
complex @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(12019,plain,
! [TA: $tType,A: TA] :
( ( ( real @ division_ring )
!= ( TA @ division_ring ) )
| ~ $true
| ( ( TA @ one_one @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[187,372]) ).
thf(12020,plain,
! [TA: $tType,A: TA] :
( ( ( real @ division_ring )
!= ( TA @ division_ring ) )
| ( ( TA @ one_one @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
inference(simp,[status(thm)],[12019]) ).
thf(12021,plain,
! [A: real] :
( ( real @ one_one @ ( A @ ( real @ inverse_divide ) ) )
= A ),
inference(pattern_uni,[status(thm)],[12020:[bind_type(TA,$thf( real ))]]) ).
thf(154,axiom,
complex @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocancel__ab__semigroup__add) ).
thf(589,plain,
complex @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(139,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ inverse_divide ) ) )
= ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( A @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_add__divide__distrib) ).
thf(531,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ inverse_divide ) ) )
= ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( A @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(145,axiom,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( 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_91_zero__less__divide__iff) ).
thf(548,plain,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( 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)],[145]) ).
thf(170,axiom,
! [TA: $tType] :
( ( ( TA @ real_normed_field )
& ( TA @ field_inverse_zero ) )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ norm_norm ) )
= ( A @ ( TA @ norm_norm ) @ ( B @ ( TA @ norm_norm ) @ ( real @ inverse_divide ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_norm__divide) ).
thf(648,plain,
! [TA: $tType] :
( ( ( TA @ real_normed_field )
& ( TA @ field_inverse_zero ) )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ norm_norm ) )
= ( A @ ( TA @ norm_norm ) @ ( B @ ( TA @ norm_norm ) @ ( real @ inverse_divide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(1508,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( real @ one_one @ ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,376]) ).
thf(1509,plain,
real @ one_one @ ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ),
inference(pattern_uni,[status(thm)],[1508:[]]) ).
thf(355,plain,
! [TA: $tType,A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
| ~ ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linord219039673up_add ) ),
inference(cnfConj,[status(thm)],[354]) ).
thf(413,plain,
( b
!= ( complex @ zero_zero ) ),
inference(polarity_switch,[status(thm)],[412]) ).
thf(414,plain,
( b
!= ( complex @ zero_zero ) ),
inference(lifteq,[status(thm)],[413]) ).
thf(43,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(263,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(11,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(199,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(330,plain,
! [TA: $tType,A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A )
| ~ ( TA @ monoid_add ) ),
inference(cnf,[status(esa)],[329]) ).
thf(331,plain,
! [TA: $tType,A: TA] :
( ~ ( TA @ monoid_add )
| ( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(lifteq,[status(thm)],[330]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( A @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_divide__strict__right__mono) ).
thf(441,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( A @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(132,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_divide__pos__neg) ).
thf(502,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ real_n1866405975lgebra )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ norm_norm ) )
= ( A @ ( B @ ( TA @ norm_norm ) @ ( real @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_norm__power) ).
thf(463,plain,
! [TA: $tType] :
( ( TA @ real_n1866405975lgebra )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ norm_norm ) )
= ( A @ ( B @ ( TA @ norm_norm ) @ ( real @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1537,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,175]) ).
thf(1538,plain,
( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ),
inference(pattern_uni,[status(thm)],[1537:[]]) ).
thf(83,axiom,
complex @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
thf(359,plain,
complex @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1302,plain,
( ( ( real @ one_one @ ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ zero_zero @ ( real @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[376,1046]) ).
thf(1303,plain,
( ( real @ one_one @ ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) )
!= ( real @ zero_zero @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1302]) ).
thf(1336,plain,
( ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[1303]) ).
thf(6261,plain,
! [A: complex] :
( ( ( A @ ( complex @ zero_zero @ ( complex @ plus_plus ) ) )
!= ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[5967,1336]) ).
thf(6302,plain,
! [A: complex] :
( ( A
!= ( na @ ( sk1 @ ( complex @ power_power ) ) ) )
| ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[6261]) ).
thf(6333,plain,
( ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( na @ ( sk1 @ ( complex @ power_power ) ) @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[6302]) ).
thf(161,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( ( B @ ( C @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_power__inject__exp) ).
thf(600,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(1505,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( real @ one_one @ ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,628]) ).
thf(1506,plain,
real @ one_one @ ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ),
inference(pattern_uni,[status(thm)],[1505:[]]) ).
thf(12548,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ one_one ) ) ),
inference(simp,[status(thm)],[12540]) ).
thf(10546,plain,
( ( ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ norm_norm ) )
!= ( complex @ zero_zero @ ( complex @ norm_norm ) ) )
| ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[996,6327]) ).
thf(10547,plain,
( ( ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ norm_norm ) )
!= ( complex @ zero_zero @ ( complex @ norm_norm ) ) )
| ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[10546]) ).
thf(10568,plain,
( ( ( na @ ( v @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( complex @ zero_zero )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[10547]) ).
thf(158,axiom,
! [TA: $tType] :
( ( TA @ real_field )
=> ! [A: real,B: real] :
( ( B
!= ( real @ zero_zero ) )
=> ( ( B @ ( A @ ( real @ inverse_divide ) ) @ ( TA @ of_real ) )
= ( B @ ( TA @ of_real ) @ ( A @ ( TA @ of_real ) @ ( TA @ inverse_divide ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_nonzero__of__real__divide) ).
thf(595,plain,
! [TA: $tType] :
( ( TA @ real_field )
=> ! [A: real,B: real] :
( ( B
!= ( real @ zero_zero ) )
=> ( ( B @ ( A @ ( real @ inverse_divide ) ) @ ( TA @ of_real ) )
= ( B @ ( TA @ of_real ) @ ( A @ ( TA @ of_real ) @ ( TA @ inverse_divide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(14,axiom,
real @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) ).
thf(203,plain,
real @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(63,axiom,
nat @ zero_zero @ ( nat @ even_odd_even ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_even__zero__nat) ).
thf(305,plain,
nat @ zero_zero @ ( nat @ even_odd_even ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(955,plain,
( ( ( nat @ zero_zero @ ( nat @ even_odd_even ) )
!= ( nat @ one_one @ ( nat @ even_odd_even ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[305,202]) ).
thf(956,plain,
( ( nat @ zero_zero @ ( nat @ even_odd_even ) )
!= ( nat @ one_one @ ( nat @ even_odd_even ) ) ),
inference(simp,[status(thm)],[955]) ).
thf(976,plain,
( ( nat @ zero_zero )
!= ( nat @ one_one ) ),
inference(simp,[status(thm)],[956]) ).
thf(734,plain,
! [TA: $tType,A: TA] :
( ( ( real @ mult_zero )
!= ( TA @ mult_zero ) )
| ~ ( TA @ zero_neq_one )
| ~ ( TA @ no_zero_divisors )
| ~ $true
| ~ ( TA @ power )
| ( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[264,474]) ).
thf(735,plain,
! [TA: $tType,A: TA] :
( ( ( real @ mult_zero )
!= ( TA @ mult_zero ) )
| ~ ( TA @ zero_neq_one )
| ~ ( TA @ no_zero_divisors )
| ~ ( TA @ power )
| ( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ),
inference(simp,[status(thm)],[734]) ).
thf(736,plain,
! [A: real] :
( ~ ( real @ zero_neq_one )
| ~ ( real @ no_zero_divisors )
| ~ ( real @ power )
| ( ( nat @ zero_zero @ ( A @ ( real @ power_power ) ) )
!= ( real @ zero_zero ) ) ),
inference(pattern_uni,[status(thm)],[735:[bind_type(TA,$thf( real ))]]) ).
thf(26,axiom,
real @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
thf(231,plain,
real @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(54,axiom,
real @ power,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(283,plain,
real @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(758,plain,
! [A: real] :
( ~ $true
| ~ $true
| ~ $true
| ( ( nat @ zero_zero @ ( A @ ( real @ power_power ) ) )
!= ( real @ zero_zero ) ) ),
inference(rewrite,[status(thm)],[736,231,266,283]) ).
thf(759,plain,
! [A: real] :
( ( nat @ zero_zero @ ( A @ ( real @ power_power ) ) )
!= ( real @ zero_zero ) ),
inference(simp,[status(thm)],[758]) ).
thf(40,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_48_add__right__cancel) ).
thf(250,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)],[40]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_divide__neg__pos) ).
thf(363,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(146,axiom,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_divide__zero) ).
thf(556,plain,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(13579,plain,
! [A: real] :
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( A @ ( complex @ of_real ) ) )
| ( ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( real @ zero_zero @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( A @ ( complex @ of_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[13079,12874]) ).
thf(13580,plain,
( ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( real @ zero_zero @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) @ ( complex @ plus_plus ) ) )
= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ),
inference(pattern_uni,[status(thm)],[13579:[bind(A,$thf( b @ ( complex @ norm_norm ) ))]]) ).
thf(15548,plain,
( ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ plus_plus ) ) @ ( real @ zero_zero @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) )
= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ),
inference(rewrite,[status(thm)],[13580,902]) ).
thf(129,axiom,
complex @ real_normed_field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__field) ).
thf(495,plain,
complex @ real_normed_field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(304,plain,
! [TA: $tType,B: TA,A: TA] :
( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
| ~ ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere216010020id_add ) ),
inference(cnf,[status(esa)],[303]) ).
thf(389,plain,
! [TA: $tType,B: TA,A: nat] :
( ( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ one_one @ ( TA @ inverse_divide ) ) )
= ( A @ ( B @ ( TA @ one_one @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) ) )
| ~ ( TA @ field_inverse_zero ) ),
inference(cnf,[status(esa)],[388]) ).
thf(390,plain,
! [TA: $tType,B: TA,A: nat] :
( ~ ( TA @ field_inverse_zero )
| ( ( A @ ( B @ ( TA @ one_one @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ one_one @ ( TA @ inverse_divide ) ) ) ) ),
inference(lifteq,[status(thm)],[389]) ).
thf(183,plain,
! [B: nat,A: nat] :
( ~ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ~ ( A @ ( nat @ even_odd_even ) )
| ( B @ ( nat @ even_odd_even ) ) ),
inference(cnfConj,[status(thm)],[178]) ).
thf(186,plain,
! [B: nat,A: nat] :
( ~ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) )
| ~ ( A @ ( nat @ even_odd_even ) )
| ( B @ ( nat @ even_odd_even ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(105,axiom,
complex @ real_field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__field) ).
thf(418,plain,
complex @ real_field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(7325,plain,
( ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) )
!= ( na @ ( v @ ( complex @ power_power ) ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[1474,7324]) ).
thf(7326,plain,
( ( na != na )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[7325]) ).
thf(7327,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[7326]) ).
thf(7709,plain,
! [E: real,D: real,C: real,B: real,A: real] :
( ( ( real @ zero_zero @ ( A @ ( real @ plus_plus ) ) )
!= ( E @ ( D @ ( real @ plus_plus ) ) ) )
| ( ( C @ ( A @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) )
= ( C @ ( E @ ( D @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[786,7609]) ).
thf(7710,plain,
! [C: real,B: real,A: real] :
( ( C @ ( real @ zero_zero @ ( A @ ( real @ plus_plus ) ) @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) )
= ( C @ ( A @ ( real @ plus_plus ) ) @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[7709:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( real @ zero_zero ))]]) ).
thf(8172,plain,
! [C: real,B: real,A: real] :
( ( C @ ( real @ zero_zero @ ( real @ plus_plus ) ) @ ( A @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) )
= ( C @ ( A @ ( real @ plus_plus ) ) @ ( B @ ( real @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[7710,4676,7982]) ).
thf(18,axiom,
real @ field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Ofield) ).
thf(207,plain,
real @ field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5825,plain,
! [A: complex] :
( ( ( complex @ zero_zero @ ( A @ ( complex @ plus_plus ) ) )
!= ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[863,1452]) ).
thf(5843,plain,
! [A: complex] :
( ( ( na @ ( sk3 @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( A
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( A @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[5825]) ).
thf(5859,plain,
( ( ( na @ ( sk3 @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ norm_norm ) )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[5843]) ).
thf(8789,plain,
( ( ( na @ ( sk3 @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(rewrite,[status(thm)],[5859,588]) ).
thf(8790,plain,
( ( ( na @ ( sk3 @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[8789]) ).
thf(8791,plain,
( ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) )
!= ( na @ ( sk3 @ ( complex @ power_power ) ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[1474,8790]) ).
thf(8792,plain,
( ( na != na )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= sk3 )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[8791]) ).
thf(8793,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= sk3 )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ zero_zero ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[8792]) ).
thf(79,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_49_add__left__cancel) ).
thf(346,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)],[79]) ).
thf(2885,plain,
! [TA: $tType] :
( ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ~ ( TA @ real_normed_vector ) ),
inference(paramod_ordered,[status(thm)],[387,2499]) ).
thf(2917,plain,
! [TA: $tType] :
( ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( real @ zero_zero @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ~ ( TA @ real_normed_vector ) ),
inference(simp,[status(thm)],[2885]) ).
thf(37,axiom,
real @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
thf(246,plain,
real @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(714,plain,
! [TA: $tType,A: TA] :
( ( ( real @ real_normed_vector )
!= ( TA @ real_normed_vector ) )
| ~ ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,494]) ).
thf(715,plain,
! [TA: $tType,A: TA] :
( ( ( real @ real_normed_vector )
!= ( TA @ real_normed_vector ) )
| ~ ( real @ zero_zero @ ( A @ ( TA @ norm_norm ) @ ( real @ ord_less ) ) ) ),
inference(simp,[status(thm)],[714]) ).
thf(716,plain,
! [A: real] :
~ ( real @ zero_zero @ ( A @ ( real @ norm_norm ) @ ( real @ ord_less ) ) ),
inference(pattern_uni,[status(thm)],[715:[bind_type(TA,$thf( real ))]]) ).
thf(214,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( A @ ( C @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere236663937imp_le ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(12257,plain,
! [A: complex] :
( ( ( complex @ one_one @ ( A @ ( complex @ inverse_divide ) ) )
!= ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( A
!= ( complex @ zero_zero ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[12044,10568]) ).
thf(12293,plain,
( ( b
!= ( complex @ one_one ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( complex @ zero_zero ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= ( complex @ zero_zero ) )
| ( ( real @ zero_zero )
!= ( real @ one_one ) ) ),
inference(simp,[status(thm)],[12257]) ).
thf(1511,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( real @ one_one @ ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,381]) ).
thf(1512,plain,
real @ one_one @ ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) @ ( real @ ord_less ) ),
inference(pattern_uni,[status(thm)],[1511:[]]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ one_one @ ( A @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ power_power ) ) @ ( B @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_power__strict__decreasing) ).
thf(447,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ one_one @ ( A @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ power_power ) ) @ ( B @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(15756,plain,
( ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) ) )
| ( ( real @ zero_zero @ ( complex @ of_real ) @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) @ ( real @ zero_zero @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) )
= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,15548]) ).
thf(15757,plain,
( ( real @ zero_zero @ ( complex @ of_real ) @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) @ ( real @ zero_zero @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) )
= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ),
inference(pattern_uni,[status(thm)],[15756:[]]) ).
thf(16130,plain,
( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( real @ zero_zero @ ( complex @ of_real ) @ ( complex @ plus_plus ) ) )
= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) ),
inference(rewrite,[status(thm)],[15757,12874]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ( TA @ semiring_0 )
& ( TA @ power ) )
=> ! [A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_power__0__left) ).
thf(405,plain,
! [TA: $tType] :
( ( ( TA @ semiring_0 )
& ( TA @ power ) )
=> ! [A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(271,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( A @ ( B @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere236663937imp_le ) )
& ( ( A @ ( B @ ( TA @ ord_less ) ) )
| ~ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere236663937imp_le ) ) ),
inference(cnf,[status(esa)],[270]) ).
thf(273,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
| ~ ( A @ ( B @ ( TA @ ord_less ) ) )
| ~ ( TA @ ordere236663937imp_le ) ),
inference(cnfConj,[status(thm)],[271]) ).
thf(5823,plain,
( ( ( complex @ zero_zero @ ( complex @ norm_norm ) )
!= ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( real @ zero_zero )
!= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[996,1452]) ).
thf(5824,plain,
( ( ( complex @ zero_zero @ ( complex @ norm_norm ) )
!= ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[5823]) ).
thf(5852,plain,
( ( ( complex @ zero_zero )
!= ( na @ ( sk3 @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[5824]) ).
thf(59,axiom,
real @ real_field,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__field) ).
thf(300,plain,
real @ real_field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(149,axiom,
complex @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oone) ).
thf(564,plain,
complex @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(338,plain,
! [TA: $tType,A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
| ( A
!= ( TA @ zero_zero ) )
| ~ ( TA @ linord219039673up_add ) ),
inference(cnfConj,[status(thm)],[336]) ).
thf(340,plain,
! [TA: $tType,A: TA] :
( ~ ( TA @ linord219039673up_add )
| ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
| ( A
!= ( TA @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[338]) ).
thf(341,plain,
! [TA: $tType] :
( ~ ( TA @ linord219039673up_add )
| ( ( TA @ zero_zero @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(134,axiom,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ inverse_divide ) ) @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) )
<=> ( ( B
!= ( TA @ zero_zero ) )
& ( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_divide__less__cancel) ).
thf(506,plain,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( B
!= ( TA @ zero_zero ) )
& ( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) )
=> ( B @ ( A @ ( TA @ inverse_divide ) ) @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( A @ ( TA @ inverse_divide ) ) @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) )
=> ( ( B
!= ( TA @ zero_zero ) )
& ( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(82,axiom,
real @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(358,plain,
real @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(194,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( B = A )
| ( ( B @ ( C @ ( TA @ plus_plus ) ) )
!= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ cancel146912293up_add ) ),
inference(cnf,[status(esa)],[193]) ).
thf(195,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ~ ( TA @ cancel146912293up_add )
| ( B = A )
| ( ( B @ ( C @ ( TA @ plus_plus ) ) )
!= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[194]) ).
thf(399,plain,
( na
!= ( nat @ zero_zero ) ),
inference(polarity_switch,[status(thm)],[398]) ).
thf(400,plain,
( na
!= ( nat @ zero_zero ) ),
inference(lifteq,[status(thm)],[399]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ power )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_power__0) ).
thf(415,plain,
! [TA: $tType] :
( ( TA @ power )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(33,axiom,
real @ linord1117847801e_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero) ).
thf(239,plain,
real @ linord1117847801e_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(2886,plain,
! [TA: $tType] :
( ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( real @ zero_zero @ ( na @ root ) @ ( complex @ of_real ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ~ ( TA @ real_normed_vector ) ),
inference(paramod_ordered,[status(thm)],[387,2499]) ).
thf(2898,plain,
! [TA: $tType] :
( ( ( TA @ zero_zero @ ( TA @ norm_norm ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( real @ zero_zero @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( v @ ( complex @ power_power ) ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) ) )
| ~ ( TA @ real_normed_vector ) ),
inference(simp,[status(thm)],[2886]) ).
thf(1540,plain,
( ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) )
!= ( na @ ( v @ ( complex @ power_power ) ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,175]) ).
thf(1564,plain,
( ( na != na )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) ) ) ),
inference(simp,[status(thm)],[1540]) ).
thf(1582,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) )
!= v )
| ( ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) ) ) ),
inference(simp,[status(thm)],[1564]) ).
thf(138,axiom,
! [TA: $tType] :
( ( TA @ real_n2089651433ebra_1 )
=> ( ( TA @ one_one @ ( TA @ norm_norm ) )
= ( real @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_norm__one) ).
thf(528,plain,
! [TA: $tType] :
( ( TA @ real_n2089651433ebra_1 )
=> ( ( TA @ one_one @ ( TA @ norm_norm ) )
= ( real @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(6348,plain,
! [A: nat] :
( ( A @ ( nat @ even_odd_even ) )
| ( A @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ even_odd_even ) ) ),
inference(rewrite,[status(thm)],[3959,5981]) ).
thf(12,axiom,
real @ ordere216010020id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) ).
thf(200,plain,
real @ ordere216010020id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(51,axiom,
real @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oone) ).
thf(277,plain,
real @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(4244,plain,
( ( ( complex @ zero_zero @ ( complex @ norm_norm ) )
!= ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) )
| ( ( real @ zero_zero )
!= ( real @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[996,1403]) ).
thf(4245,plain,
( ( ( complex @ zero_zero @ ( complex @ norm_norm ) )
!= ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) @ ( complex @ norm_norm ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[4244]) ).
thf(4271,plain,
( ( ( complex @ zero_zero )
!= ( na @ ( v @ ( complex @ power_power ) ) @ ( b @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( complex @ inverse_divide ) ) @ ( complex @ plus_plus ) ) ) )
| ( ( real @ one_one )
!= ( real @ zero_zero ) ) ),
inference(simp,[status(thm)],[4245]) ).
thf(89,axiom,
complex @ divisi14063676e_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Odivision__ring__inverse__zero) ).
thf(369,plain,
complex @ divisi14063676e_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(162,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ~ ( A @ ( nat @ even_odd_even ) ) )
| ( ( B
!= ( TA @ zero_zero ) )
& ( A @ ( nat @ even_odd_even ) ) )
| ( A
= ( nat @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_zero__less__power__eq) ).
thf(607,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: nat,B: TA] :
( ( ( ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ~ ( A @ ( nat @ even_odd_even ) ) )
| ( ( B
!= ( TA @ zero_zero ) )
& ( A @ ( nat @ even_odd_even ) ) )
| ( A
= ( nat @ zero_zero ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ~ ( A @ ( nat @ even_odd_even ) ) )
| ( ( B
!= ( TA @ zero_zero ) )
& ( A @ ( nat @ even_odd_even ) ) )
| ( A
= ( nat @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(251,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
| ( C != A )
| ~ ( TA @ cancel_semigroup_add ) )
& ( ( C = A )
| ( ( B @ ( C @ ( TA @ plus_plus ) ) )
!= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ cancel_semigroup_add ) ) ),
inference(cnf,[status(esa)],[250]) ).
thf(252,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( C = A )
| ( ( B @ ( C @ ( TA @ plus_plus ) ) )
!= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ cancel_semigroup_add ) ),
inference(cnfConj,[status(thm)],[251]) ).
thf(254,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ~ ( TA @ cancel_semigroup_add )
| ( C = A )
| ( ( B @ ( C @ ( TA @ plus_plus ) ) )
!= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[252]) ).
thf(21,axiom,
nat @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(215,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(168,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( ( B @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_right__inverse__eq) ).
thf(639,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) ) )
& ( ( ( B @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(7266,plain,
( ( ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) )
!= ( na @ ( b @ ( complex @ norm_norm ) @ ( na @ root ) @ ( complex @ of_real ) @ ( complex @ power_power ) ) ) )
| ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1474,1571]) ).
thf(7267,plain,
( ( ( b @ ( complex @ norm_norm ) @ ( na @ root ) )
!= ( b @ ( complex @ norm_norm ) ) )
| ( ( na @ ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( v @ ( complex @ inverse_divide ) ) @ ( complex @ power_power ) ) )
!= ( b @ ( complex @ norm_norm ) @ ( complex @ of_real ) @ ( na @ ( v @ ( complex @ power_power ) ) @ ( complex @ inverse_divide ) ) ) ) ),
inference(pattern_uni,[status(thm)],[7266:[]]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_divide__neg__neg) ).
thf(491,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(130,axiom,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: nat,B: real] :
( ( A @ ( B @ ( real @ power_power ) ) @ ( TA @ of_real ) )
= ( A @ ( B @ ( TA @ of_real ) @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_of__real__power) ).
thf(496,plain,
! [TA: $tType] :
( ( TA @ real_algebra_1 )
=> ! [A: nat,B: real] :
( ( A @ ( B @ ( real @ power_power ) ) @ ( TA @ of_real ) )
= ( A @ ( B @ ( TA @ of_real ) @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(364,plain,
! [TA: $tType,B: TA,A: TA] :
( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) )
| ~ ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_field ) ),
inference(cnf,[status(esa)],[363]) ).
thf(3752,plain,
! [F: nat,E: nat,D: nat,C: nat,B: nat,A: nat] :
( ( ( B @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) )
!= ( C @ ( F @ ( nat @ plus_plus ) ) ) )
| ( ( D @ ( B @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( E @ ( nat @ plus_plus ) ) )
= ( D @ ( C @ ( nat @ plus_plus ) ) @ ( F @ ( nat @ plus_plus ) ) @ ( E @ ( nat @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1890,3728]) ).
thf(3753,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( B @ ( D @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( D @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[3752:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( H @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( A ))]]) ).
thf(3852,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( B @ ( D @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( D @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[3753]) ).
thf(11631,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( D @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[3852,3728]) ).
thf(22345,plain,
$false,
inference(e,[status(thm)],[629,365,2499,234,628,249,12549,481,6791,523,6695,308,1544,449,247,379,1533,269,202,217,276,5967,385,384,13675,945,174,185,1046,301,10248,320,565,651,257,570,184,372,504,344,196,460,587,838,357,6332,902,559,189,284,316,216,8379,179,591,443,376,238,12276,353,480,211,646,2880,485,280,634,6347,428,6327,206,8554,265,307,9556,233,248,380,439,270,546,201,6588,381,366,534,334,6328,10975,302,260,598,1502,192,429,275,788,467,484,197,361,625,329,11174,493,1407,285,12506,1111,188,388,356,499,488,339,3728,526,1937,590,328,4676,193,1461,537,3703,457,1525,244,266,360,205,14180,398,3675,343,237,412,6053,264,279,12874,430,176,402,286,577,1403,204,545,259,391,445,382,12830,1332,466,335,947,9808,236,187,219,13079,274,5103,419,230,245,303,208,863,377,996,362,6340,2943,318,1571,599,477,387,494,12044,594,213,240,626,345,367,198,1177,6692,462,1952,521,1474,827,636,278,306,299,267,438,431,241,658,1113,7324,563,1583,12021,589,531,548,648,1509,342,355,7982,776,282,414,1531,263,199,1452,331,441,370,502,463,1538,359,1336,544,6333,600,1506,12548,10568,175,595,991,5981,627,203,976,759,218,368,250,231,363,556,15548,495,588,319,304,12574,12516,390,186,401,418,786,7327,8172,207,8793,346,2917,235,246,716,214,12293,1512,447,16130,13314,405,273,373,5852,300,190,4841,564,305,210,8790,341,506,358,195,474,400,12335,283,415,239,242,1093,332,2898,1582,528,6348,200,277,4271,369,607,254,215,639,7267,491,496,364,232,659,11631]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW503_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n018.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 16:11:51 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.46/1.29 % [INFO] Parsing done (297ms).
% 1.96/1.31 % [INFO] Running in sequential loop mode.
% 2.89/1.71 % [INFO] eprover registered as external prover.
% 2.89/1.72 % [INFO] Scanning for conjecture ...
% 3.10/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 173 axioms. Running axiom selection ...
% 3.31/2.02 % [INFO] Axiom selection finished. Selected 171 axioms (removed 2 axioms).
% 4.21/2.23 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.21/2.26 % [INFO] Type checking passed.
% 4.21/2.26 % [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 ...
% 94.27/21.34 % External prover 'e' found a proof!
% 94.27/21.34 % [INFO] Killing All external provers ...
% 94.27/21.34 % Time passed: 20784ms (effective reasoning time: 20029ms)
% 94.27/21.34 % 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)>
% 94.27/21.35 % Axioms used in derivation (171): fact_48_add__right__cancel, arity_RealDef_Oreal___RealVector_Oreal__normed__div__algebra, fact_81_add__neg__neg, arity_RealDef_Oreal___RealVector_Oreal__field, arity_Nat_Onat___Groups_Omonoid__mult, fact_16_power__one, fact_49_add__left__cancel, fact_52_odd__add, fact_61_norm__not__less__zero, fact_87_divide__pos__neg, fact_19_of__real__0, arity_Complex_Ocomplex___Groups_Oab__semigroup__add, fact_6_of__real__power, fact_69_add_Ocomm__neutral, arity_RealDef_Oreal___RealVector_Oreal__normed__field, fact_67_one__reorient, arity_RealDef_Oreal___Fields_Olinordered__field, arity_Complex_Ocomplex___RealVector_Oreal__normed__div__algebra, fact_79_divide__1, fact_18_norm__eq__zero, arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add, arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add, fact_29_power__inject__exp, arity_Complex_Ocomplex___Fields_Odivision__ring__inverse__zero, arity_RealDef_Oreal___Rings_Osemiring__0, fact_75_add__strict__mono, arity_Complex_Ocomplex___Power_Opower, arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors, arity_RealDef_Oreal___Groups_Ozero, arity_Complex_Ocomplex___Groups_Ocancel__semigroup__add, arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero, fact_44_divide__zero, arity_Nat_Onat___Power_Opower, fact_45_divide__zero__left, arity_RealDef_Oreal___Fields_Ofield__inverse__zero, arity_Complex_Ocomplex___Rings_Ono__zero__divisors, fact_56_zero__less__power__nat__eq, fact_32_power__less__imp__less__exp, fact_0__096root_An_A_Icmod_Ab_J_A_094_An_A_061_Acmod_Ab_096, fact_43_zero__less__power__eq, fact_28_zero__less__power, arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add, fact_60_odd__pos, fact_12_norm__power, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_86_divide__neg__pos, fact_15__096_B_Bthesis_O_A_I_B_Bv_O_Acmod_A_Icomplex__of__real_A_Icmod_Ab_J_A_P_Ab_A_L_Av_A_094_An_J_A_060_A1_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_7_th0, fact_53_double__zero__sym, fact_90_divide__less__0__iff, fact_91_zero__less__divide__iff, fact_9_of__real__eq__iff, fact_24_zero__less__norm__iff, fact_11_norm__divide, fact_4_assms_I2_J, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_68_nonzero__of__real__divide, fact_23_power__0, fact_13_power__divide, fact_14__096EX_Av_O_Acmod_A_Icomplex__of__real_A_Icmod_Ab_J_A_P_Ab_A_L_Av_A_094_An_J_A_060_A1_096, fact_17_norm__zero, arity_Nat_Onat___Rings_Omult__zero, fact_5_of__real__divide, fact_59_power__one__right, arity_RealDef_Oreal___RealVector_Oreal__algebra__1, arity_Complex_Ocomplex___Groups_Ocomm__monoid__add, fact_63_add__right__imp__eq, fact_26_of__real__1, arity_Complex_Ocomplex___Rings_Ozero__neq__one, fact_65_add__left__imp__eq, fact_64_add__imp__eq, fact_93_divide__self, fact_95_less__half__sum, fact_46_add__less__cancel__right, arity_RealDef_Oreal___Groups_Omonoid__add, arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le, fact_73_add__less__imp__less__left, arity_Complex_Ocomplex___Fields_Ofield__inverse__zero, fact_80_even__zero__nat, fact_39_nonzero__norm__divide, fact_92_right__inverse__eq, fact_62_zero__reorient, arity_RealDef_Oreal___Fields_Odivision__ring, arity_Complex_Ocomplex___RealVector_Oreal__normed__field, arity_Complex_Ocomplex___Rings_Osemiring__0, fact_35_norm__add__less, arity_Complex_Ocomplex___RealVector_Oreal__algebra__1, fact_88_divide__pos__pos, arity_Nat_Onat___Rings_Osemiring__0, arity_RealDef_Oreal___Fields_Ofield, fact_42_double__add__less__zero__iff__single__add__less__zero, fact_3_o, fact_51_even__add, fact_89_divide__less__cancel, fact_34_power__strict__decreasing, fact_55_even__power__nat, fact_40_divide__self__if, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_82_add__pos__pos, fact_41_zero__less__double__add__iff__zero__less__single__add, arity_Complex_Ocomplex___Rings_Omult__zero, arity_Nat_Onat___Rings_Olinordered__semidom, fact_30_power__strict__increasing__iff, arity_RealDef_Oreal___Rings_Olinordered__semidom, fact_58_nat__power__less__imp__less, fact_2_b, fact_50_even__sum__nat, arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1, arity_Nat_Onat___Groups_Ozero, arity_Nat_Onat___Groups_Oordered__comm__monoid__add, fact_31_one__less__power, arity_RealDef_Oreal___Groups_Oab__semigroup__add, arity_RealDef_Oreal___Rings_Omult__zero, arity_RealDef_Oreal___Groups_Ocancel__semigroup__add, arity_Complex_Ocomplex___Fields_Ofield, fact_97_IH, arity_RealDef_Oreal___Rings_Ono__zero__divisors, arity_RealDef_Oreal___Groups_Ocomm__monoid__add, fact_54_nat__zero__less__power__iff, fact_96_power__less__zero__eq, arity_RealDef_Oreal___Groups_Olinordered__ab__group__add, arity_RealDef_Oreal___RealVector_Oreal__normed__vector, fact_83_divide__strict__right__mono__neg, arity_RealDef_Oreal___Rings_Ozero__neq__one, fact_38_nonzero__power__divide, arity_RealDef_Oreal___Groups_Oone, arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors, fact_1_n, arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_66_ab__semigroup__add__class_Oadd__ac_I1_J, fact_25_norm__one, fact_72_add__0__left, fact_57_odd__1__nat, arity_Complex_Ocomplex___Groups_Oone, fact_27_power__0__left, fact_36_field__power__not__zero, arity_RealDef_Oreal___Groups_Omonoid__mult, arity_Nat_Onat___Groups_Oone, arity_Complex_Ocomplex___Groups_Omonoid__mult, arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero, arity_RealDef_Oreal___Power_Opower, fact_47_add__less__cancel__left, fact_94_gt__half__sum, arity_Complex_Ocomplex___Groups_Ocancel__ab__semigroup__add, fact_33_power__strict__increasing, fact_77_add__strict__right__mono, fact_22_power__eq__0__iff, fact_76_add__strict__left__mono, arity_Nat_Onat___Rings_Ono__zero__divisors, arity_RealDef_Oreal___RealVector_Oreal__normed__algebra__1, fact_85_divide__neg__neg, arity_Complex_Ocomplex___Groups_Omonoid__add, fact_8_complex__of__real__power, fact_20_of__real__eq__0__iff, fact_84_divide__strict__right__mono, arity_Nat_Onat___Groups_Omonoid__add, arity_Nat_Onat___Groups_Oab__semigroup__add, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_10_v, fact_74_add__less__imp__less__right, fact_37_power__one__over, arity_Nat_Onat___Rings_Ozero__neq__one, arity_Complex_Ocomplex___Groups_Ozero, fact_71_add__0, fact_70_add__0__right, fact_78_add__divide__distrib, arity_Nat_Onat___Groups_Ocancel__semigroup__add, arity_Complex_Ocomplex___RealVector_Oreal__normed__vector, arity_Complex_Ocomplex___RealVector_Oreal__field, arity_Complex_Ocomplex___Fields_Odivision__ring, fact_21_of__real__add
% 94.27/21.35 % No. of inferences in proof: 768
% 94.27/21.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 20784 ms resp. 20029 ms w/o parsing
% 94.66/21.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 94.66/21.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------