TSTP Solution File: ITP341_1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP341_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:51:03 EDT 2024
% Result : Theorem 9.53s 3.14s
% Output : Refutation 10.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 360
% Syntax : Number of formulae : 653 ( 304 unt; 69 typ; 0 def)
% Number of atoms : 1237 (1153 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 4241 ( 138 ~; 49 |; 182 &;3450 @)
% ( 81 <=>; 341 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 21 ( 20 usr)
% Number of type conns : 67 ( 67 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 13 con; 0-4 aty)
% Number of variables : 1246 ( 0 ^1207 !; 39 ?;1246 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'A_n_vec_n_vec_set_set$\'_type',type,
'\'A_n_vec_n_vec_set_set$\'': $tType ).
thf('\'A_set_set$\'_type',type,
'\'A_set_set$\'': $tType ).
thf('\'A_n_vec_set$\'_type',type,
'\'A_n_vec_set$\'': $tType ).
thf('\'A_n_vec_n_vec_bool_fun$\'_type',type,
'\'A_n_vec_n_vec_bool_fun$\'': $tType ).
thf('\'A_n_vec_n_vec$\'_type',type,
'\'A_n_vec_n_vec$\'': $tType ).
thf('\'Nat$\'_type',type,
'\'Nat$\'': $tType ).
thf('\'A_n_vec_n_vec_set$\'_type',type,
'\'A_n_vec_n_vec_set$\'': $tType ).
thf('\'N$\'_type',type,
'\'N$\'': $tType ).
thf('\'Num$\'_type',type,
'\'Num$\'': $tType ).
thf('\'Num_set$\'_type',type,
'\'Num_set$\'': $tType ).
thf(tlbool_type,type,
tlbool: $tType ).
thf('\'A_bool_fun$\'_type',type,
'\'A_bool_fun$\'': $tType ).
thf('\'A_set$\'_type',type,
'\'A_set$\'': $tType ).
thf('\'A_n_vec_set_set$\'_type',type,
'\'A_n_vec_set_set$\'': $tType ).
thf('\'A$\'_type',type,
'\'A$\'': $tType ).
thf('\'A_n_vec$\'_type',type,
'\'A_n_vec$\'': $tType ).
thf('\'A_a_fun$\'_type',type,
'\'A_a_fun$\'': $tType ).
thf('\'A_n_vec_n_vec_n_vec$\'_type',type,
'\'A_n_vec_n_vec_n_vec$\'': $tType ).
thf('\'A_n_vec_bool_fun$\'_type',type,
'\'A_n_vec_bool_fun$\'': $tType ).
thf('\'N_a_n_vec_n_vec_fun$\'_type',type,
'\'N_a_n_vec_n_vec_fun$\'': $tType ).
thf('\'dbl_inc$a\'_type',type,
'\'dbl_inc$a\'': '\'A_n_vec$\'' > '\'A_n_vec$\'' ).
thf('\'mat$\'_type',type,
'\'mat$\'': '\'A$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'invertible$\'_type',type,
'\'invertible$\'': '\'A_n_vec_n_vec_bool_fun$\'' ).
thf('\'matrix_vector_mult$\'_type',type,
'\'matrix_vector_mult$\'': '\'A_n_vec_n_vec$\'' > '\'A_n_vec$\'' > '\'A_n_vec$\'' ).
thf('\'vector_matrix_mult$a\'_type',type,
'\'vector_matrix_mult$a\'': '\'A_n_vec$\'' > '\'A_n_vec_n_vec$\'' > '\'A_n_vec$\'' ).
thf('\'axis$\'_type',type,
'\'axis$\'': '\'N$\'' > '\'A_n_vec$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'columnvector$\'_type',type,
'\'columnvector$\'': '\'A_n_vec$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'gauss_Jordan$\'_type',type,
'\'gauss_Jordan$\'': '\'A_n_vec_n_vec$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'plus$g\'_type',type,
'\'plus$g\'': '\'A_n_vec_n_vec$\'' > '\'A_n_vec_n_vec$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'zero$c\'_type',type,
'\'zero$c\'': '\'A_n_vec$\'' ).
thf('\'axis$a\'_type',type,
'\'axis$a\'': '\'N$\'' > '\'A$\'' > '\'A_n_vec$\'' ).
thf('\'plus$i\'_type',type,
'\'plus$i\'': '\'A_n_vec_n_vec_n_vec$\'' > '\'A_n_vec_n_vec_n_vec$\'' > '\'A_n_vec_n_vec_n_vec$\'' ).
thf('\'vec$a\'_type',type,
'\'vec$a\'': '\'A_n_vec$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'times$a\'_type',type,
'\'times$a\'': '\'A_n_vec$\'' > '\'A_n_vec$\'' > '\'A_n_vec$\'' ).
thf('\'times$\'_type',type,
'\'times$\'': '\'A$\'' > '\'A$\'' > '\'A$\'' ).
thf('\'one$\'_type',type,
'\'one$\'': '\'A$\'' ).
thf('\'matrix_inv$\'_type',type,
'\'matrix_inv$\'': '\'A_n_vec_n_vec$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'equivalent_matrices$\'_type',type,
'\'equivalent_matrices$\'': '\'A_n_vec_n_vec$\'' > '\'A_n_vec_n_vec_bool_fun$\'' ).
thf(tltrue_type,type,
tltrue: tlbool ).
thf('\'plus$h\'_type',type,
'\'plus$h\'': '\'A$\'' > '\'A$\'' > '\'A$\'' ).
thf('\'row_add$\'_type',type,
'\'row_add$\'': '\'A_n_vec_n_vec$\'' > '\'N$\'' > '\'N$\'' > '\'A$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'rowvector$\'_type',type,
'\'rowvector$\'': '\'A_n_vec$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'gauss_Jordan_upt_k$\'_type',type,
'\'gauss_Jordan_upt_k$\'': '\'A_n_vec_n_vec$\'' > '\'Nat$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'a$\'_type',type,
'\'a$\'': '\'A_n_vec_n_vec$\'' ).
thf('\'mult_column$\'_type',type,
'\'mult_column$\'': '\'A_n_vec_n_vec$\'' > '\'N$\'' > '\'A$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'column_add$\'_type',type,
'\'column_add$\'': '\'A_n_vec_n_vec$\'' > '\'N$\'' > '\'N$\'' > '\'A$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'reduced_row_echelon_form$\'_type',type,
'\'reduced_row_echelon_form$\'': '\'A_n_vec_n_vec_bool_fun$\'' ).
thf('\'one$a\'_type',type,
'\'one$a\'': '\'A_n_vec$\'' ).
thf('\'divide$\'_type',type,
'\'divide$\'': '\'A$\'' > '\'A_a_fun$\'' ).
thf('\'zero$a\'_type',type,
'\'zero$a\'': '\'A_n_vec_n_vec$\'' ).
thf('\'matrix_matrix_mult$\'_type',type,
'\'matrix_matrix_mult$\'': '\'A_n_vec_n_vec$\'' > '\'A_n_vec_n_vec$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'transpose$\'_type',type,
'\'transpose$\'': '\'A_n_vec_n_vec$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'orthogonal_matrix$\'_type',type,
'\'orthogonal_matrix$\'': '\'A_n_vec_n_vec_bool_fun$\'' ).
thf('\'fun_app$d\'_type',type,
'\'fun_app$d\'': '\'A_a_fun$\'' > '\'A$\'' > '\'A$\'' ).
thf('\'matrix_vector_mult$a\'_type',type,
'\'matrix_vector_mult$a\'': '\'A_n_vec_n_vec_n_vec$\'' > '\'A_n_vec_n_vec$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'column$\'_type',type,
'\'column$\'': '\'N$\'' > '\'A_n_vec_n_vec$\'' > '\'A_n_vec$\'' ).
thf('\'vec$\'_type',type,
'\'vec$\'': '\'A$\'' > '\'A_n_vec$\'' ).
thf('\'zero$\'_type',type,
'\'zero$\'': '\'A$\'' ).
thf('\'plus$d\'_type',type,
'\'plus$d\'': '\'A_n_vec$\'' > '\'A_n_vec$\'' > '\'A_n_vec$\'' ).
thf('\'fun_app$c\'_type',type,
'\'fun_app$c\'': '\'N_a_n_vec_n_vec_fun$\'' > '\'N$\'' > '\'A_n_vec_n_vec$\'' ).
thf(tlfalse_type,type,
tlfalse: tlbool ).
thf('\'numeral$b\'_type',type,
'\'numeral$b\'': '\'Num$\'' > '\'A$\'' ).
thf('\'similar_matrices$\'_type',type,
'\'similar_matrices$\'': '\'A_n_vec_n_vec$\'' > '\'A_n_vec_n_vec_bool_fun$\'' ).
thf('\'interchange_columns$\'_type',type,
'\'interchange_columns$\'': '\'A_n_vec_n_vec$\'' > '\'N$\'' > '\'N$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'fun_app$\'_type',type,
'\'fun_app$\'': '\'A_n_vec_n_vec_bool_fun$\'' > '\'A_n_vec_n_vec$\'' > $o ).
thf('\'mult_row$\'_type',type,
'\'mult_row$\'': '\'A_n_vec_n_vec$\'' > '\'N$\'' > '\'A$\'' > '\'A_n_vec_n_vec$\'' ).
thf('\'dbl_inc$b\'_type',type,
'\'dbl_inc$b\'': '\'A$\'' > '\'A$\'' ).
thf('\'interchange_rows$\'_type',type,
'\'interchange_rows$\'': '\'A_n_vec_n_vec$\'' > '\'N$\'' > '\'N_a_n_vec_n_vec_fun$\'' ).
thf('\'p$\'_type',type,
'\'p$\'': '\'A_n_vec_n_vec$\'' ).
thf(154,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ C ) @ ( '\'times$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom312) ).
thf(1036,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ C ) @ ( '\'times$\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(264,axiom,
! [A: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ A )
= '\'one$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom267) ).
thf(1586,plain,
! [A: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ A )
= '\'one$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(180,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( '\'plus$g\'' @ A @ B )
= A )
<=> ( B = '\'zero$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom232) ).
thf(1190,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( ( '\'plus$g\'' @ A @ B )
= A )
=> ( B = '\'zero$a\'' ) )
& ( ( B = '\'zero$a\'' )
=> ( ( '\'plus$g\'' @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(235,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
=> ( ( ( '\'matrix_vector_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) @ C )
= '\'zero$c\'' )
<=> ( ( '\'matrix_vector_mult$\'' @ B @ C )
= '\'zero$c\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom193) ).
thf(1454,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
=> ( ( ( ( '\'matrix_vector_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) @ C )
= '\'zero$c\'' )
=> ( ( '\'matrix_vector_mult$\'' @ B @ C )
= '\'zero$c\'' ) )
& ( ( ( '\'matrix_vector_mult$\'' @ B @ C )
= '\'zero$c\'' )
=> ( ( '\'matrix_vector_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) @ C )
= '\'zero$c\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(278,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'N$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= '\'one$\'' )
& ( ( '\'times$\'' @ B @ A )
= '\'one$\'' ) )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mult_row$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom122) ).
thf(1633,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'N$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= '\'one$\'' )
& ( ( '\'times$\'' @ B @ A )
= '\'one$\'' ) )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mult_row$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(257,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
<=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20) ).
thf(1559,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) )
& ( ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(131,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( B = '\'zero$\'' )
=> ( ( '\'plus$h\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) @ C )
= C ) )
& ( ( B != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ A @ ( '\'times$\'' @ C @ B ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom271) ).
thf(909,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( B = '\'zero$\'' )
=> ( ( '\'plus$h\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) @ C )
= C ) )
& ( ( B != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ A @ ( '\'times$\'' @ C @ B ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(63,axiom,
! [A: '\'A_n_vec_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$a\'' @ ( '\'plus$i\'' @ A @ B ) @ C )
= ( '\'plus$g\'' @ ( '\'matrix_vector_mult$a\'' @ A @ C ) @ ( '\'matrix_vector_mult$a\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom329) ).
thf(555,plain,
! [A: '\'A_n_vec_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$a\'' @ ( '\'plus$i\'' @ A @ B ) @ C )
= ( '\'plus$g\'' @ ( '\'matrix_vector_mult$a\'' @ A @ C ) @ ( '\'matrix_vector_mult$a\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(255,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( '\'transpose$\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) )
= ( '\'matrix_matrix_mult$\'' @ ( '\'transpose$\'' @ B ) @ ( '\'transpose$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom43) ).
thf(1554,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( '\'transpose$\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) )
= ( '\'matrix_matrix_mult$\'' @ ( '\'transpose$\'' @ B ) @ ( '\'transpose$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(29,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( A
= ( '\'plus$d\'' @ A @ B ) )
<=> ( B = '\'zero$c\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom239) ).
thf(408,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( A
= ( '\'plus$d\'' @ A @ B ) )
=> ( B = '\'zero$c\'' ) )
& ( ( B = '\'zero$c\'' )
=> ( A
= ( '\'plus$d\'' @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(55,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( A
= ( '\'plus$h\'' @ B @ C ) )
=> ( ( '\'plus$h\'' @ A @ D )
= ( '\'plus$h\'' @ B @ ( '\'plus$h\'' @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom344) ).
thf(523,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( A
= ( '\'plus$h\'' @ B @ C ) )
=> ( ( '\'plus$h\'' @ A @ D )
= ( '\'plus$h\'' @ B @ ( '\'plus$h\'' @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(98,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom253) ).
thf(730,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(160,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ A @ C ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom93) ).
thf(1068,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ A @ C ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(143,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ '\'zero$a\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom244) ).
thf(994,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ '\'zero$a\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(259,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'interchange_columns$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ B @ C ) )
= ( '\'interchange_columns$\'' @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom47) ).
thf(1569,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'interchange_columns$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ B @ C ) )
= ( '\'interchange_columns$\'' @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(266,axiom,
( ( '\'matrix_matrix_mult$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ '\'a$\'' )
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ '\'p$\'' ) @ '\'a$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).
thf(1591,plain,
( ( '\'matrix_matrix_mult$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ '\'a$\'' )
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ '\'p$\'' ) @ '\'a$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(22,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( '\'plus$d\'' @ A @ B )
= A )
<=> ( B = '\'zero$c\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom233) ).
thf(379,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( ( '\'plus$d\'' @ A @ B )
= A )
=> ( B = '\'zero$c\'' ) )
& ( ( B = '\'zero$c\'' )
=> ( ( '\'plus$d\'' @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(287,axiom,
( ! [A: '\'A_n_vec_n_vec$\''] :
( ( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
& ( ( '\'gauss_Jordan$\'' @ '\'a$\'' )
= ( '\'matrix_matrix_mult$\'' @ A @ '\'a$\'' ) ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).
thf(1692,plain,
~ ! [A: '\'A_n_vec_n_vec$\''] :
~ ( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
& ( ( '\'gauss_Jordan$\'' @ '\'a$\'' )
= ( '\'matrix_matrix_mult$\'' @ A @ '\'a$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(90,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ C @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom361) ).
thf(677,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ C @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(228,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'A$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'mult_column$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ B @ C ) )
= ( '\'mult_column$\'' @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom36) ).
thf(1426,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'A$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'mult_column$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ B @ C ) )
= ( '\'mult_column$\'' @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(44,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom365) ).
thf(472,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(205,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'plus$h\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ A @ ( '\'plus$h\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom338) ).
thf(1327,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'plus$h\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ A @ ( '\'plus$h\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(93,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom255) ).
thf(698,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(280,axiom,
! [A: '\'A$\'',B: '\'N$\''] :
( ( A != '\'zero$\'' )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mult_column$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom56) ).
thf(1640,plain,
! [A: '\'A$\'',B: '\'N$\''] :
( ( A != '\'zero$\'' )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mult_column$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(14,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ C ) @ ( '\'times$a\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom298) ).
thf(340,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ C ) @ ( '\'times$a\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(212,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
= B )
<=> ( ( B = '\'zero$\'' )
| ( A = '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom128) ).
thf(1354,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= B )
=> ( ( B = '\'zero$\'' )
| ( A = '\'one$\'' ) ) )
& ( ( ( B = '\'zero$\'' )
| ( A = '\'one$\'' ) )
=> ( ( '\'times$\'' @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(89,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'plus$h\'' @ A @ B )
= A )
<=> ( B = '\'zero$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom231) ).
thf(670,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( ( '\'plus$h\'' @ A @ B )
= A )
=> ( B = '\'zero$\'' ) )
& ( ( B = '\'zero$\'' )
=> ( ( '\'plus$h\'' @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(241,axiom,
! [A: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ '\'one$\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom256) ).
thf(1497,plain,
! [A: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ '\'one$\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(291,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'mat$\'' @ '\'one$\'' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
thf(1705,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'mat$\'' @ '\'one$\'' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(231,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec$\''] :
( ( '\'columnvector$\'' @ ( '\'matrix_vector_mult$\'' @ A @ B ) )
= ( '\'matrix_matrix_mult$\'' @ A @ ( '\'columnvector$\'' @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom194) ).
thf(1441,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec$\''] :
( ( '\'columnvector$\'' @ ( '\'matrix_vector_mult$\'' @ A @ B ) )
= ( '\'matrix_matrix_mult$\'' @ A @ ( '\'columnvector$\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(219,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ ( '\'equivalent_matrices$\'' @ A ) @ B )
<=> ? [C: '\'A_n_vec_n_vec$\'',D: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ C )
& ( '\'fun_app$\'' @ '\'invertible$\'' @ D )
& ( B
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ C ) @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom29) ).
thf(1386,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( '\'fun_app$\'' @ ( '\'equivalent_matrices$\'' @ A ) @ B )
=> ? [C: '\'A_n_vec_n_vec$\'',D: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ C )
& ( '\'fun_app$\'' @ '\'invertible$\'' @ D )
& ( B
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ C ) @ A ) @ D ) ) ) )
& ( ? [C: '\'A_n_vec_n_vec$\'',D: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ C )
& ( '\'fun_app$\'' @ '\'invertible$\'' @ D )
& ( B
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ C ) @ A ) @ D ) ) )
=> ( '\'fun_app$\'' @ ( '\'equivalent_matrices$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(5,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\'',D: '\'A_n_vec$\''] :
( ( A
= ( '\'plus$d\'' @ B @ C ) )
=> ( ( '\'plus$d\'' @ D @ A )
= ( '\'plus$d\'' @ B @ ( '\'plus$d\'' @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom347) ).
thf(301,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\'',D: '\'A_n_vec$\''] :
( ( A
= ( '\'plus$d\'' @ B @ C ) )
=> ( ( '\'plus$d\'' @ D @ A )
= ( '\'plus$d\'' @ B @ ( '\'plus$d\'' @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(65,axiom,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ A @ '\'zero$\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).
thf(565,plain,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ A @ '\'zero$\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(275,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ A @ ( '\'mat$\'' @ '\'one$\'' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom35) ).
thf(1623,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ A @ ( '\'mat$\'' @ '\'one$\'' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(87,axiom,
! [A: '\'N$\'',B: '\'A_n_vec$\'',C: '\'N$\'',D: '\'A_n_vec$\''] :
( ( ( '\'axis$\'' @ A @ B )
= ( '\'axis$\'' @ C @ D ) )
<=> ( ( ( B = D )
& ( A = C ) )
| ( ( B = '\'zero$c\'' )
& ( D = '\'zero$c\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom191) ).
thf(651,plain,
! [A: '\'N$\'',B: '\'A_n_vec$\'',C: '\'N$\'',D: '\'A_n_vec$\''] :
( ( ( ( '\'axis$\'' @ A @ B )
= ( '\'axis$\'' @ C @ D ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( ( B = '\'zero$c\'' )
& ( D = '\'zero$c\'' ) ) ) )
& ( ( ( ( B = D )
& ( A = C ) )
| ( ( B = '\'zero$c\'' )
& ( D = '\'zero$c\'' ) ) )
=> ( ( '\'axis$\'' @ A @ B )
= ( '\'axis$\'' @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(139,axiom,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ '\'zero$\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom293) ).
thf(973,plain,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ '\'zero$\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(156,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ A @ '\'zero$a\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom398) ).
thf(1046,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ A @ '\'zero$a\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(284,axiom,
! [A: tlbool,B: '\'A$\''] :
( ( ( A = tltrue )
=> ( ( ( A = tltrue )
=> ( ( '\'times$\'' @ '\'one$\'' @ B )
= B ) )
& ( ( A != tltrue )
=> ( ( '\'times$\'' @ '\'one$\'' @ B )
= '\'zero$\'' ) ) ) )
& ( ( A != tltrue )
=> ( ( ( A = tltrue )
=> ( ( '\'times$\'' @ '\'zero$\'' @ B )
= B ) )
& ( ( A != tltrue )
=> ( ( '\'times$\'' @ '\'zero$\'' @ B )
= '\'zero$\'' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom153) ).
thf(1660,plain,
! [A: tlbool,B: '\'A$\''] :
( ( ( A = tltrue )
=> ( ( ( A = tltrue )
=> ( ( '\'times$\'' @ '\'one$\'' @ B )
= B ) )
& ( ( A != tltrue )
=> ( ( '\'times$\'' @ '\'one$\'' @ B )
= '\'zero$\'' ) ) ) )
& ( ( A != tltrue )
=> ( ( ( A = tltrue )
=> ( ( '\'times$\'' @ '\'zero$\'' @ B )
= B ) )
& ( ( A != tltrue )
=> ( ( '\'times$\'' @ '\'zero$\'' @ B )
= '\'zero$\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(206,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ C ) @ ( '\'times$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom297) ).
thf(1330,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ C ) @ ( '\'times$\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(71,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ ( '\'plus$g\'' @ A @ B ) @ C )
= ( '\'plus$g\'' @ A @ ( '\'plus$g\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom355) ).
thf(587,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ ( '\'plus$g\'' @ A @ B ) @ C )
= ( '\'plus$g\'' @ A @ ( '\'plus$g\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(132,axiom,
! [A: '\'A$\'',B: '\'Num$\'',C: '\'A$\''] :
( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'numeral$b\'' @ B ) )
= C )
<=> ( ( ( ( '\'numeral$b\'' @ B )
!= '\'zero$\'' )
=> ( A
= ( '\'times$\'' @ C @ ( '\'numeral$b\'' @ B ) ) ) )
& ( ( ( '\'numeral$b\'' @ B )
!= '\'zero$\'' )
=> ( C = '\'zero$\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom415) ).
thf(917,plain,
! [A: '\'A$\'',B: '\'Num$\'',C: '\'A$\''] :
( ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'numeral$b\'' @ B ) )
= C )
=> ( ( ( ( '\'numeral$b\'' @ B )
!= '\'zero$\'' )
=> ( A
= ( '\'times$\'' @ C @ ( '\'numeral$b\'' @ B ) ) ) )
& ( ( ( '\'numeral$b\'' @ B )
= '\'zero$\'' )
=> ( C = '\'zero$\'' ) ) ) )
& ( ( ( ( ( '\'numeral$b\'' @ B )
!= '\'zero$\'' )
=> ( A
= ( '\'times$\'' @ C @ ( '\'numeral$b\'' @ B ) ) ) )
& ( ( ( '\'numeral$b\'' @ B )
= '\'zero$\'' )
=> ( C = '\'zero$\'' ) ) )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'numeral$b\'' @ B ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(170,axiom,
! [A: '\'A$\''] :
( ( '\'times$\'' @ '\'zero$\'' @ A )
= '\'zero$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom134) ).
thf(1132,plain,
! [A: '\'A$\''] :
( ( '\'times$\'' @ '\'zero$\'' @ A )
= '\'zero$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(252,axiom,
'\'zero$\'' != '\'one$\'',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom150) ).
thf(1545,plain,
'\'zero$\'' != '\'one$\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(217,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\'',D: '\'A$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'column_add$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ B @ C @ D ) )
= ( '\'column_add$\'' @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom33) ).
thf(1379,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\'',D: '\'A$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'column_add$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ B @ C @ D ) )
= ( '\'column_add$\'' @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(191,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ '\'zero$a\'' @ A )
= '\'zero$c\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom181) ).
thf(1247,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ '\'zero$a\'' @ A )
= '\'zero$c\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(260,axiom,
! [A: '\'A$\''] :
( ( '\'one$\'' = A )
<=> ( A = '\'one$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom23) ).
thf(1572,plain,
! [A: '\'A$\''] :
( ( ( '\'one$\'' = A )
=> ( A = '\'one$\'' ) )
& ( ( A = '\'one$\'' )
=> ( '\'one$\'' = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(149,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\''] :
( ( '\'interchange_columns$\'' @ A @ B @ C )
= ( '\'transpose$\'' @ ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ ( '\'transpose$\'' @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).
thf(1013,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\''] :
( ( '\'interchange_columns$\'' @ A @ B @ C )
= ( '\'transpose$\'' @ ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ ( '\'transpose$\'' @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(240,axiom,
! [A: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ A )
= '\'one$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom264) ).
thf(1494,plain,
! [A: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ A )
= '\'one$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(113,axiom,
! [A: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ '\'zero$\'' ) @ A )
= '\'zero$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom247) ).
thf(817,plain,
! [A: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ '\'zero$\'' ) @ A )
= '\'zero$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(130,axiom,
! [A: '\'N$\'',B: '\'A$\''] :
( ( ( '\'axis$a\'' @ A @ B )
= '\'zero$c\'' )
<=> ( B = '\'zero$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom161) ).
thf(902,plain,
! [A: '\'N$\'',B: '\'A$\''] :
( ( ( ( '\'axis$a\'' @ A @ B )
= '\'zero$c\'' )
=> ( B = '\'zero$\'' ) )
& ( ( B = '\'zero$\'' )
=> ( ( '\'axis$a\'' @ A @ B )
= '\'zero$c\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(82,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( ( '\'times$\'' @ B @ A )
= ( '\'times$\'' @ C @ A ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom91) ).
thf(638,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( ( '\'times$\'' @ B @ A )
= ( '\'times$\'' @ C @ A ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(121,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ ( '\'times$\'' @ A @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom262) ).
thf(853,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ ( '\'times$\'' @ A @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(224,axiom,
! [A: '\'N$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'column$\'' @ A @ ( '\'matrix_matrix_mult$\'' @ B @ C ) )
= ( '\'matrix_vector_mult$\'' @ B @ ( '\'column$\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom195) ).
thf(1415,plain,
! [A: '\'N$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'column$\'' @ A @ ( '\'matrix_matrix_mult$\'' @ B @ C ) )
= ( '\'matrix_vector_mult$\'' @ B @ ( '\'column$\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(45,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'dbl_inc$a\'' @ A )
= ( '\'plus$d\'' @ ( '\'plus$d\'' @ A @ A ) @ '\'one$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom394) ).
thf(475,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'dbl_inc$a\'' @ A )
= ( '\'plus$d\'' @ ( '\'plus$d\'' @ A @ A ) @ '\'one$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(11,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ '\'zero$c\'' )
= '\'zero$c\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom136) ).
thf(321,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ '\'zero$c\'' )
= '\'zero$c\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ '\'one$a\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom115) ).
thf(376,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ '\'one$a\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(225,axiom,
! [A: '\'A$\''] :
( ( '\'transpose$\'' @ ( '\'mat$\'' @ A ) )
= ( '\'mat$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom41) ).
thf(1418,plain,
! [A: '\'A$\''] :
( ( '\'transpose$\'' @ ( '\'mat$\'' @ A ) )
= ( '\'mat$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(85,axiom,
tltrue != tlfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_419) ).
thf(646,plain,
tltrue != tlfalse,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(286,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) )
<=> ! [B: '\'A_n_vec$\''] :
( ( ( '\'matrix_vector_mult$\'' @ A @ B )
= '\'zero$c\'' )
=> ( B = '\'zero$c\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom159) ).
thf(1682,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) )
=> ! [B: '\'A_n_vec$\''] :
( ( ( '\'matrix_vector_mult$\'' @ A @ B )
= '\'zero$c\'' )
=> ( B = '\'zero$c\'' ) ) )
& ( ! [B: '\'A_n_vec$\''] :
( ( ( '\'matrix_vector_mult$\'' @ A @ B )
= '\'zero$c\'' )
=> ( B = '\'zero$c\'' ) )
=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(47,axiom,
! [A: '\'A_n_vec_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$a\'' @ A @ ( '\'plus$g\'' @ B @ C ) )
= ( '\'plus$g\'' @ ( '\'matrix_vector_mult$a\'' @ A @ B ) @ ( '\'matrix_vector_mult$a\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom319) ).
thf(485,plain,
! [A: '\'A_n_vec_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$a\'' @ A @ ( '\'plus$g\'' @ B @ C ) )
= ( '\'plus$g\'' @ ( '\'matrix_vector_mult$a\'' @ A @ B ) @ ( '\'matrix_vector_mult$a\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(117,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
= '\'zero$\'' )
=> ( ( A = '\'zero$\'' )
| ( B = '\'zero$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom144) ).
thf(834,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
= '\'zero$\'' )
=> ( ( A = '\'zero$\'' )
| ( B = '\'zero$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(173,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( B != '\'zero$\'' ) )
=> ( ( '\'plus$h\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A ) @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ D ) @ B ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ ( '\'times$\'' @ C @ B ) @ ( '\'times$\'' @ D @ A ) ) ) @ ( '\'times$\'' @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom273) ).
thf(1151,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( B != '\'zero$\'' ) )
=> ( ( '\'plus$h\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A ) @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ D ) @ B ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ ( '\'times$\'' @ C @ B ) @ ( '\'times$\'' @ D @ A ) ) ) @ ( '\'times$\'' @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(133,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ ( '\'transpose$\'' @ A ) @ B )
= ( '\'vector_matrix_mult$a\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom185) ).
thf(937,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ ( '\'transpose$\'' @ A ) @ B )
= ( '\'vector_matrix_mult$a\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(262,axiom,
( '\'a$\''
= ( '\'matrix_matrix_mult$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ '\'a$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom11) ).
thf(1581,plain,
( '\'a$\''
= ( '\'matrix_matrix_mult$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ '\'a$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(138,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( A
= ( '\'plus$g\'' @ B @ A ) )
<=> ( B = '\'zero$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom235) ).
thf(966,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( A
= ( '\'plus$g\'' @ B @ A ) )
=> ( B = '\'zero$a\'' ) )
& ( ( B = '\'zero$a\'' )
=> ( A
= ( '\'plus$g\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(105,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
= '\'zero$\'' )
<=> ( ( A = '\'zero$\'' )
| ( B = '\'zero$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom76) ).
thf(766,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= '\'zero$\'' )
=> ( ( A = '\'zero$\'' )
| ( B = '\'zero$\'' ) ) )
& ( ( ( A = '\'zero$\'' )
| ( B = '\'zero$\'' ) )
=> ( ( '\'times$\'' @ A @ B )
= '\'zero$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1,conjecture,
( ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ ( '\'mat$\'' @ '\'one$\'' ) )
= ( '\'matrix_inv$\'' @ '\'p$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture3) ).
thf(2,negated_conjecture,
( ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ ( '\'mat$\'' @ '\'one$\'' ) )
!= ( '\'matrix_inv$\'' @ '\'p$\'' ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(293,plain,
( ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ ( '\'mat$\'' @ '\'one$\'' ) )
!= ( '\'matrix_inv$\'' @ '\'p$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ A @ ( '\'plus$d\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom335) ).
thf(396,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ A @ ( '\'plus$d\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(230,axiom,
! [A: '\'A$\''] :
( ( ( A = '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ A )
= '\'zero$\'' ) )
& ( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ A )
= '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom268) ).
thf(1433,plain,
! [A: '\'A$\''] :
( ( ( A = '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ A )
= '\'zero$\'' ) )
& ( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ A )
= '\'one$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(182,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ '\'zero$a\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom282) ).
thf(1201,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ '\'zero$a\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(270,axiom,
! [A: '\'N$\'',B: '\'N$\'',C: '\'A$\''] :
( ( A != B )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'row_add$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom62) ).
thf(1600,plain,
! [A: '\'N$\'',B: '\'N$\'',C: '\'A$\''] :
( ( A != B )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'row_add$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(247,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A )
= '\'one$\'' )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom390) ).
thf(1521,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A )
= '\'one$\'' )
=> ( B = A ) )
& ( ( B = A )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A )
= '\'one$\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(8,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ ( '\'vector_matrix_mult$a\'' @ A @ C ) @ ( '\'vector_matrix_mult$a\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom382) ).
thf(312,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ ( '\'vector_matrix_mult$a\'' @ A @ C ) @ ( '\'vector_matrix_mult$a\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(271,axiom,
! [A: '\'A$\''] :
( ( '\'times$\'' @ '\'one$\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom81) ).
thf(1604,plain,
! [A: '\'A$\''] :
( ( '\'times$\'' @ '\'one$\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(292,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ B )
& ( ( '\'gauss_Jordan$\'' @ A )
= ( '\'matrix_matrix_mult$\'' @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom27) ).
thf(1708,plain,
! [A: '\'A_n_vec_n_vec$\''] :
? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ B )
& ( ( '\'gauss_Jordan$\'' @ A )
= ( '\'matrix_matrix_mult$\'' @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(202,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
= '\'zero$\'' )
<=> ( ( A = '\'zero$\'' )
| ( B = '\'zero$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom138) ).
thf(1311,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= '\'zero$\'' )
=> ( ( A = '\'zero$\'' )
| ( B = '\'zero$\'' ) ) )
& ( ( ( A = '\'zero$\'' )
| ( B = '\'zero$\'' ) )
=> ( ( '\'times$\'' @ A @ B )
= '\'zero$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(58,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).
thf(534,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(158,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( A
= ( '\'plus$g\'' @ A @ B ) )
<=> ( B = '\'zero$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom238) ).
thf(1057,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( A
= ( '\'plus$g\'' @ A @ B ) )
=> ( B = '\'zero$a\'' ) )
& ( ( B = '\'zero$a\'' )
=> ( A
= ( '\'plus$g\'' @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(175,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom379) ).
thf(1163,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(129,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ A @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom358) ).
thf(894,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(246,axiom,
( ( '\'vec$\'' @ '\'one$\'' )
= '\'one$a\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom174) ).
thf(1519,plain,
( ( '\'vec$\'' @ '\'one$\'' )
= '\'one$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(261,axiom,
'\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mat$\'' @ '\'one$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom28) ).
thf(1580,plain,
'\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mat$\'' @ '\'one$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(178,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ C @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom218) ).
thf(1174,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ C @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(73,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'plus$h\'' @ ( '\'times$\'' @ A @ B ) @ ( '\'plus$h\'' @ ( '\'times$\'' @ C @ B ) @ D ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ ( '\'plus$h\'' @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom315) ).
thf(598,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'plus$h\'' @ ( '\'times$\'' @ A @ B ) @ ( '\'plus$h\'' @ ( '\'times$\'' @ C @ B ) @ D ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ ( '\'plus$h\'' @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(114,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A
= ( '\'plus$h\'' @ A @ B ) )
<=> ( B = '\'zero$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom237) ).
thf(820,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( A
= ( '\'plus$h\'' @ A @ B ) )
=> ( B = '\'zero$\'' ) )
& ( ( B = '\'zero$\'' )
=> ( A
= ( '\'plus$h\'' @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(33,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ '\'zero$c\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom245) ).
thf(429,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ '\'zero$c\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(188,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( A != '\'zero$a\'' )
=> ( ( '\'gauss_Jordan$\'' @ A )
!= '\'zero$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom119) ).
thf(1238,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( A != '\'zero$a\'' )
=> ( ( '\'gauss_Jordan$\'' @ A )
!= '\'zero$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(101,axiom,
! [A: '\'A$\''] :
( ( '\'times$\'' @ A @ '\'zero$\'' )
= '\'zero$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom74) ).
thf(746,plain,
! [A: '\'A$\''] :
( ( '\'times$\'' @ A @ '\'zero$\'' )
= '\'zero$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(162,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'vec$\'' @ A )
= ( '\'vec$\'' @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom170) ).
thf(1091,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( ( '\'vec$\'' @ A )
= ( '\'vec$\'' @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( '\'vec$\'' @ A )
= ( '\'vec$\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(227,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'matrix_matrix_mult$\'' @ B @ C ) )
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom26) ).
thf(1423,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'matrix_matrix_mult$\'' @ B @ C ) )
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(119,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ C ) @ ( '\'times$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom300) ).
thf(847,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ C ) @ ( '\'times$\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(35,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ ( '\'times$a\'' @ A @ B ) @ C )
= ( '\'times$a\'' @ A @ ( '\'times$a\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom103) ).
thf(435,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ ( '\'times$a\'' @ A @ B ) @ C )
= ( '\'times$a\'' @ A @ ( '\'times$a\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(199,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ B @ A ) ) @ ( '\'times$\'' @ A @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom259) ).
thf(1296,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ B @ A ) ) @ ( '\'times$\'' @ A @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(42,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ '\'one$a\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).
thf(461,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ '\'one$a\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(198,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( A
= ( '\'plus$h\'' @ B @ C ) )
=> ( ( '\'plus$h\'' @ D @ A )
= ( '\'plus$h\'' @ B @ ( '\'plus$h\'' @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom350) ).
thf(1291,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( A
= ( '\'plus$h\'' @ B @ C ) )
=> ( ( '\'plus$h\'' @ D @ A )
= ( '\'plus$h\'' @ B @ ( '\'plus$h\'' @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(12,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( '\'vec$a\'' @ A )
= ( '\'vec$a\'' @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom171) ).
thf(324,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( ( '\'vec$a\'' @ A )
= ( '\'vec$a\'' @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( '\'vec$a\'' @ A )
= ( '\'vec$a\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(165,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ C @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom362) ).
thf(1106,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ C @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(222,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( '\'one$\''
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) )
<=> ( ( B != '\'zero$\'' )
& ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom266) ).
thf(1402,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'one$\''
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) )
=> ( ( B != '\'zero$\'' )
& ( A = B ) ) )
& ( ( ( B != '\'zero$\'' )
& ( A = B ) )
=> ( '\'one$\''
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(68,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'transpose$\'' @ ( '\'columnvector$\'' @ A ) )
= ( '\'rowvector$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom203) ).
thf(578,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'transpose$\'' @ ( '\'columnvector$\'' @ A ) )
= ( '\'rowvector$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(194,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ A @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom215) ).
thf(1270,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(250,axiom,
( ( '\'gauss_Jordan$\'' @ '\'a$\'' )
= ( '\'matrix_matrix_mult$\'' @ '\'p$\'' @ '\'a$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom14) ).
thf(1534,plain,
( ( '\'gauss_Jordan$\'' @ '\'a$\'' )
= ( '\'matrix_matrix_mult$\'' @ '\'p$\'' @ '\'a$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(76,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'times$\'' @ A @ B ) @ C )
= ( '\'times$\'' @ A @ ( '\'times$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom110) ).
thf(615,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'times$\'' @ A @ B ) @ C )
= ( '\'times$\'' @ A @ ( '\'times$\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(168,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A )
= C )
<=> ( B
= ( '\'times$\'' @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom384) ).
thf(1121,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A )
= C )
=> ( B
= ( '\'times$\'' @ C @ A ) ) )
& ( ( B
= ( '\'times$\'' @ C @ A ) )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(159,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom380) ).
thf(1064,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(185,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'transpose$\'' @ ( '\'rowvector$\'' @ A ) )
= ( '\'columnvector$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom202) ).
thf(1227,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'transpose$\'' @ ( '\'rowvector$\'' @ A ) )
= ( '\'columnvector$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(147,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ ( '\'times$\'' @ C @ A ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom261) ).
thf(1006,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ ( '\'times$\'' @ C @ A ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(122,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ A @ ( '\'plus$g\'' @ B @ C ) )
= ( '\'plus$g\'' @ B @ ( '\'plus$g\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom373) ).
thf(857,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ A @ ( '\'plus$g\'' @ B @ C ) )
= ( '\'plus$g\'' @ B @ ( '\'plus$g\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(126,axiom,
! [A: tlbool,B: '\'A_n_vec$\''] :
( ( ( A = tltrue )
=> ( ( ( A = tltrue )
=> ( ( '\'times$a\'' @ '\'one$a\'' @ B )
= B ) )
& ( ( A != tltrue )
=> ( ( '\'times$a\'' @ '\'one$a\'' @ B )
= '\'zero$c\'' ) ) ) )
& ( ( A != tltrue )
=> ( ( ( A = tltrue )
=> ( ( '\'times$a\'' @ '\'zero$c\'' @ B )
= B ) )
& ( ( A != tltrue )
=> ( ( '\'times$a\'' @ '\'zero$c\'' @ B )
= '\'zero$c\'' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom152) ).
thf(874,plain,
! [A: tlbool,B: '\'A_n_vec$\''] :
( ( ( A = tltrue )
=> ( ( ( A = tltrue )
=> ( ( '\'times$a\'' @ '\'one$a\'' @ B )
= B ) )
& ( ( A != tltrue )
=> ( ( '\'times$a\'' @ '\'one$a\'' @ B )
= '\'zero$c\'' ) ) ) )
& ( ( A != tltrue )
=> ( ( ( A = tltrue )
=> ( ( '\'times$a\'' @ '\'zero$c\'' @ B )
= B ) )
& ( ( A != tltrue )
=> ( ( '\'times$a\'' @ '\'zero$c\'' @ B )
= '\'zero$c\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(172,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( A = '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ ( '\'times$\'' @ A @ C ) )
= '\'zero$\'' ) )
& ( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ ( '\'times$\'' @ A @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom263) ).
thf(1143,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( A = '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ ( '\'times$\'' @ A @ C ) )
= '\'zero$\'' ) )
& ( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ ( '\'times$\'' @ A @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(48,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\'',D: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ B ) @ ( '\'plus$d\'' @ ( '\'times$a\'' @ C @ B ) @ D ) )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ ( '\'plus$d\'' @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom313) ).
thf(488,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\'',D: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ B ) @ ( '\'plus$d\'' @ ( '\'times$a\'' @ C @ B ) @ D ) )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ ( '\'plus$d\'' @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(179,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'zero$c\'' = A )
<=> ( A = '\'zero$c\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom90) ).
thf(1182,plain,
! [A: '\'A_n_vec$\''] :
( ( ( '\'zero$c\'' = A )
=> ( A = '\'zero$c\'' ) )
& ( ( A = '\'zero$c\'' )
=> ( '\'zero$c\'' = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(289,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
& ( '\'fun_app$\'' @ '\'invertible$\'' @ B ) )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).
thf(1700,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
& ( '\'fun_app$\'' @ '\'invertible$\'' @ B ) )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(281,axiom,
! [A: '\'N$\'',B: '\'A$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ ( '\'mult_row$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A @ B ) @ C )
= ( '\'mult_row$\'' @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom57) ).
thf(1644,plain,
! [A: '\'N$\'',B: '\'A$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ ( '\'mult_row$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A @ B ) @ C )
= ( '\'mult_row$\'' @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(155,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A
= ( '\'plus$h\'' @ A @ B ) )
<=> ( B = '\'zero$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom400) ).
thf(1039,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( A
= ( '\'plus$h\'' @ A @ B ) )
=> ( B = '\'zero$\'' ) )
& ( ( B = '\'zero$\'' )
=> ( A
= ( '\'plus$h\'' @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(174,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( A = B )
<=> ! [C: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ C )
= ( '\'matrix_vector_mult$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom187) ).
thf(1155,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( A = B )
=> ! [C: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ C )
= ( '\'matrix_vector_mult$\'' @ B @ C ) ) )
& ( ! [C: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ C )
= ( '\'matrix_vector_mult$\'' @ B @ C ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(236,axiom,
! [A: '\'N$\'',B: '\'N$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A ) @ B ) @ C )
= ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom61) ).
thf(1461,plain,
! [A: '\'N$\'',B: '\'N$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A ) @ B ) @ C )
= ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(59,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( ( '\'times$\'' @ B @ A )
= C ) )
=> ( B
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom385) ).
thf(537,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( ( '\'times$\'' @ B @ A )
= C ) )
=> ( B
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(150,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'plus$h\'' @ A @ B )
= B )
<=> ( A = '\'zero$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom228) ).
thf(1016,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( ( '\'plus$h\'' @ A @ B )
= B )
=> ( A = '\'zero$\'' ) )
& ( ( A = '\'zero$\'' )
=> ( ( '\'plus$h\'' @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(184,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'Num$\''] :
( ( A
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ ( '\'numeral$b\'' @ C ) ) )
<=> ( ( ( ( '\'numeral$b\'' @ C )
!= '\'zero$\'' )
=> ( ( '\'times$\'' @ A @ ( '\'numeral$b\'' @ C ) )
= B ) )
& ( ( ( '\'numeral$b\'' @ C )
!= '\'zero$\'' )
=> ( A = '\'zero$\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom416) ).
thf(1207,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'Num$\''] :
( ( ( A
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ ( '\'numeral$b\'' @ C ) ) )
=> ( ( ( ( '\'numeral$b\'' @ C )
!= '\'zero$\'' )
=> ( ( '\'times$\'' @ A @ ( '\'numeral$b\'' @ C ) )
= B ) )
& ( ( ( '\'numeral$b\'' @ C )
= '\'zero$\'' )
=> ( A = '\'zero$\'' ) ) ) )
& ( ( ( ( ( '\'numeral$b\'' @ C )
!= '\'zero$\'' )
=> ( ( '\'times$\'' @ A @ ( '\'numeral$b\'' @ C ) )
= B ) )
& ( ( ( '\'numeral$b\'' @ C )
= '\'zero$\'' )
=> ( A = '\'zero$\'' ) ) )
=> ( A
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ ( '\'numeral$b\'' @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(72,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ A @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom359) ).
thf(590,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(118,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ B ) )
<=> ( ( B = '\'zero$\'' )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom250) ).
thf(837,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ B ) )
=> ( ( B = '\'zero$\'' )
| ( A = C ) ) )
& ( ( ( B = '\'zero$\'' )
| ( A = C ) )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(144,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) ) @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ D ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ D ) ) @ ( '\'times$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom279) ).
thf(997,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) ) @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ D ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ D ) ) @ ( '\'times$\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(163,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ A @ '\'zero$a\'' )
= '\'zero$c\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom69) ).
thf(1099,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ A @ '\'zero$a\'' )
= '\'zero$c\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(94,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ B @ A ) ) @ ( '\'times$\'' @ C @ A ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom260) ).
thf(701,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ B @ A ) ) @ ( '\'times$\'' @ C @ A ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(218,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'times$\'' @ A @ B ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ '\'one$\'' ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom269) ).
thf(1382,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'times$\'' @ A @ B ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ '\'one$\'' ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(193,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ B @ ( '\'times$\'' @ C @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom274) ).
thf(1266,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ B @ ( '\'times$\'' @ C @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(229,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'times$\'' @ B @ A ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ '\'one$\'' ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom270) ).
thf(1429,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'times$\'' @ B @ A ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ '\'one$\'' ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(107,axiom,
! [A: '\'N$\'',B: '\'A_n_vec$\''] :
( ( ( '\'axis$\'' @ A @ B )
= '\'zero$a\'' )
<=> ( B = '\'zero$c\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom160) ).
thf(779,plain,
! [A: '\'N$\'',B: '\'A_n_vec$\''] :
( ( ( ( '\'axis$\'' @ A @ B )
= '\'zero$a\'' )
=> ( B = '\'zero$c\'' ) )
& ( ( B = '\'zero$c\'' )
=> ( ( '\'axis$\'' @ A @ B )
= '\'zero$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(204,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\''] :
( ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ ( '\'transpose$\'' @ A ) @ B ) @ C )
= ( '\'transpose$\'' @ ( '\'interchange_columns$\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom125) ).
thf(1324,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\''] :
( ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ ( '\'transpose$\'' @ A ) @ B ) @ C )
= ( '\'transpose$\'' @ ( '\'interchange_columns$\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(24,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ A @ '\'zero$c\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom289) ).
thf(393,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ A @ '\'zero$c\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(166,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'transpose$\'' @ ( '\'transpose$\'' @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom40) ).
thf(1114,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'transpose$\'' @ ( '\'transpose$\'' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(207,axiom,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ A @ '\'zero$\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom397) ).
thf(1333,plain,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ A @ '\'zero$\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(15,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ C @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom360) ).
thf(343,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ C @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(189,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'plus$h\'' @ B @ C ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ B ) @ ( '\'times$\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom296) ).
thf(1241,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'plus$h\'' @ B @ C ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ B ) @ ( '\'times$\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(60,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( A = '\'zero$a\'' )
=> ( ( '\'gauss_Jordan$\'' @ A )
= '\'zero$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom120) ).
thf(541,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( A = '\'zero$a\'' )
=> ( ( '\'gauss_Jordan$\'' @ A )
= '\'zero$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(177,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ B @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ ( '\'times$\'' @ B @ A ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom276) ).
thf(1170,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ B @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ ( '\'times$\'' @ B @ A ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(273,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'N$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= '\'one$\'' )
& ( ( '\'times$\'' @ B @ A )
= '\'one$\'' ) )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mult_column$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom58) ).
thf(1616,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'N$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= '\'one$\'' )
& ( ( '\'times$\'' @ B @ A )
= '\'one$\'' ) )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mult_column$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(110,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ A @ C ) )
<=> ( ( A = '\'zero$\'' )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom139) ).
thf(794,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ A @ C ) )
=> ( ( A = '\'zero$\'' )
| ( B = C ) ) )
& ( ( ( A = '\'zero$\'' )
| ( B = C ) )
=> ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(127,axiom,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ '\'zero$\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom243) ).
thf(888,plain,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ '\'zero$\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(64,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( A
= ( '\'plus$g\'' @ A @ B ) )
<=> ( B = '\'zero$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom401) ).
thf(558,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( A
= ( '\'plus$g\'' @ A @ B ) )
=> ( B = '\'zero$a\'' ) )
& ( ( B = '\'zero$a\'' )
=> ( A
= ( '\'plus$g\'' @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(161,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= C )
<=> ( ( ( B != '\'zero$\'' )
=> ( A
= ( '\'times$\'' @ C @ B ) ) )
& ( ( B != '\'zero$\'' )
=> ( C = '\'zero$\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom388) ).
thf(1071,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= C )
=> ( ( ( B != '\'zero$\'' )
=> ( A
= ( '\'times$\'' @ C @ B ) ) )
& ( ( B = '\'zero$\'' )
=> ( C = '\'zero$\'' ) ) ) )
& ( ( ( ( B != '\'zero$\'' )
=> ( A
= ( '\'times$\'' @ C @ B ) ) )
& ( ( B = '\'zero$\'' )
=> ( C = '\'zero$\'' ) ) )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(152,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ A @ C ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom142) ).
thf(1026,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(176,axiom,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ '\'zero$\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom281) ).
thf(1167,plain,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ '\'zero$\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(171,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ A @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom214) ).
thf(1135,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(77,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ A @ '\'zero$a\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom288) ).
thf(618,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ A @ '\'zero$a\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(288,axiom,
( ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ '\'p$\'' ) @ '\'a$\'' )
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ ( '\'matrix_matrix_mult$\'' @ '\'p$\'' @ '\'a$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).
thf(1698,plain,
( ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ '\'p$\'' ) @ '\'a$\'' )
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ ( '\'matrix_matrix_mult$\'' @ '\'p$\'' @ '\'a$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(253,axiom,
! [A: '\'N$\'',B: '\'N$\'',C: '\'A$\'',D: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ ( '\'row_add$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A @ B @ C ) @ D )
= ( '\'row_add$\'' @ D @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom63) ).
thf(1548,plain,
! [A: '\'N$\'',B: '\'N$\'',C: '\'A$\'',D: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ ( '\'row_add$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A @ B @ C ) @ D )
= ( '\'row_add$\'' @ D @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(268,axiom,
( '\'a$\''
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ ( '\'mat$\'' @ '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).
thf(1595,plain,
( '\'a$\''
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ ( '\'mat$\'' @ '\'one$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(38,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( '\'plus$d\'' @ A @ B )
= B )
<=> ( A = '\'zero$c\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom230) ).
thf(444,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( ( '\'plus$d\'' @ A @ B )
= B )
=> ( A = '\'zero$c\'' ) )
& ( ( A = '\'zero$c\'' )
=> ( ( '\'plus$d\'' @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(215,axiom,
( ( '\'gauss_Jordan$\'' @ '\'a$\'' )
= ( '\'mat$\'' @ '\'one$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).
thf(1374,plain,
( ( '\'gauss_Jordan$\'' @ '\'a$\'' )
= ( '\'mat$\'' @ '\'one$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(99,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'times$\'' @ B @ C ) )
= ( '\'times$\'' @ B @ ( '\'times$\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom98) ).
thf(733,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'times$\'' @ B @ C ) )
= ( '\'times$\'' @ B @ ( '\'times$\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(74,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= '\'zero$\'' )
<=> ( ( A = '\'zero$\'' )
| ( B = '\'zero$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom248) ).
thf(601,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= '\'zero$\'' )
=> ( ( A = '\'zero$\'' )
| ( B = '\'zero$\'' ) ) )
& ( ( ( A = '\'zero$\'' )
| ( B = '\'zero$\'' ) )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= '\'zero$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(195,axiom,
( ( '\'dbl_inc$a\'' @ '\'zero$c\'' )
= '\'one$a\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).
thf(1278,plain,
( ( '\'dbl_inc$a\'' @ '\'zero$c\'' )
= '\'one$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(4,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ ( '\'plus$d\'' @ B @ C ) )
= ( '\'plus$d\'' @ ( '\'matrix_vector_mult$\'' @ A @ B ) @ ( '\'matrix_vector_mult$\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom320) ).
thf(298,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ ( '\'plus$d\'' @ B @ C ) )
= ( '\'plus$d\'' @ ( '\'matrix_vector_mult$\'' @ A @ B ) @ ( '\'matrix_vector_mult$\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(70,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ '\'zero$c\'' @ A )
= '\'zero$c\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom71) ).
thf(584,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ '\'zero$c\'' @ A )
= '\'zero$c\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(27,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ ( '\'plus$d\'' @ B @ C ) )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ B ) @ ( '\'times$a\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom301) ).
thf(402,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ ( '\'plus$d\'' @ B @ C ) )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ B ) @ ( '\'times$a\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(274,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
=> ( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'matrix_inv$\'' @ A ) )
= ( '\'mat$\'' @ '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom24) ).
thf(1620,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
=> ( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'matrix_inv$\'' @ A ) )
= ( '\'mat$\'' @ '\'one$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(137,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( C = '\'zero$\'' )
=> ( ( '\'plus$h\'' @ A @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) )
= A ) )
& ( ( C != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ A @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ ( '\'times$\'' @ A @ C ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom272) ).
thf(958,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( C = '\'zero$\'' )
=> ( ( '\'plus$h\'' @ A @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) )
= A ) )
& ( ( C != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ A @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ ( '\'times$\'' @ A @ C ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(61,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
!= '\'zero$\'' )
=> ( ( A != '\'zero$\'' )
& ( B != '\'zero$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom147) ).
thf(545,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
!= '\'zero$\'' )
=> ( ( A != '\'zero$\'' )
& ( B != '\'zero$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(83,axiom,
! [A: '\'Num$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'numeral$b\'' @ A ) @ ( '\'plus$h\'' @ B @ C ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ ( '\'numeral$b\'' @ A ) @ B ) @ ( '\'times$\'' @ ( '\'numeral$b\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom411) ).
thf(641,plain,
! [A: '\'Num$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'numeral$b\'' @ A ) @ ( '\'plus$h\'' @ B @ C ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ ( '\'numeral$b\'' @ A ) @ B ) @ ( '\'times$\'' @ ( '\'numeral$b\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(75,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ B @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ C @ ( '\'times$\'' @ B @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom275) ).
thf(611,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ B @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ C @ ( '\'times$\'' @ B @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(111,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom367) ).
thf(804,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(237,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
= A )
<=> ( ( A = '\'zero$\'' )
| ( B = '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom130) ).
thf(1464,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= A )
=> ( ( A = '\'zero$\'' )
| ( B = '\'one$\'' ) ) )
& ( ( ( A = '\'zero$\'' )
| ( B = '\'one$\'' ) )
=> ( ( '\'times$\'' @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(141,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( ( '\'times$\'' @ B @ A )
= ( '\'times$\'' @ C @ A ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom141) ).
thf(979,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( ( ( '\'times$\'' @ B @ A )
= ( '\'times$\'' @ C @ A ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( '\'times$\'' @ B @ A )
= ( '\'times$\'' @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(116,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'times$\'' @ B @ C ) )
= ( '\'times$\'' @ B @ ( '\'times$\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom92) ).
thf(831,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'times$\'' @ B @ C ) )
= ( '\'times$\'' @ B @ ( '\'times$\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(167,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom376) ).
thf(1117,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(100,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ C ) )
<=> ( ( A = '\'zero$\'' )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom249) ).
thf(736,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ C ) )
=> ( ( A = '\'zero$\'' )
| ( B = C ) ) )
& ( ( ( A = '\'zero$\'' )
| ( B = C ) )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(265,axiom,
! [A: '\'N$\'',B: '\'N$\''] : ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'interchange_columns$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom37) ).
thf(1589,plain,
! [A: '\'N$\'',B: '\'N$\''] : ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'interchange_columns$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(10,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ ( '\'plus$d\'' @ B @ C ) )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ B ) @ ( '\'times$a\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom307) ).
thf(318,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ ( '\'plus$d\'' @ B @ C ) )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ B ) @ ( '\'times$a\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(86,axiom,
! [A: '\'A_n_vec_n_vec$\''] : ( '\'fun_app$\'' @ '\'reduced_row_echelon_form$\'' @ ( '\'gauss_Jordan$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom121) ).
thf(649,plain,
! [A: '\'A_n_vec_n_vec$\''] : ( '\'fun_app$\'' @ '\'reduced_row_echelon_form$\'' @ ( '\'gauss_Jordan$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(216,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ '\'zero$a\'' @ A )
= '\'zero$a\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom66) ).
thf(1376,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ '\'zero$a\'' @ A )
= '\'zero$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(124,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'zero$a\'' = A )
<=> ( A = '\'zero$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom89) ).
thf(863,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( ( '\'zero$a\'' = A )
=> ( A = '\'zero$a\'' ) )
& ( ( A = '\'zero$a\'' )
=> ( '\'zero$a\'' = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(18,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( A
= ( '\'plus$d\'' @ A @ B ) )
<=> ( B = '\'zero$c\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom402) ).
thf(362,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( A
= ( '\'plus$d\'' @ A @ B ) )
=> ( B = '\'zero$c\'' ) )
& ( ( B = '\'zero$c\'' )
=> ( A
= ( '\'plus$d\'' @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(39,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom375) ).
thf(451,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(50,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( '\'vec$a\'' @ A )
= ( '\'vec$a\'' @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom169) ).
thf(494,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( ( '\'vec$a\'' @ A )
= ( '\'vec$a\'' @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( '\'vec$a\'' @ A )
= ( '\'vec$a\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(209,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( B != '\'zero$\'' ) )
=> ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ D ) @ B ) )
<=> ( ( '\'times$\'' @ C @ B )
= ( '\'times$\'' @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom389) ).
thf(1339,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( B != '\'zero$\'' ) )
=> ( ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ D ) @ B ) )
=> ( ( '\'times$\'' @ C @ B )
= ( '\'times$\'' @ D @ A ) ) )
& ( ( ( '\'times$\'' @ C @ B )
= ( '\'times$\'' @ D @ A ) )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(78,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\''] :
( ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom87) ).
thf(621,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\''] :
( ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(54,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ '\'zero$c\'' )
= '\'zero$c\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom177) ).
thf(520,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ '\'zero$c\'' )
= '\'zero$c\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(256,axiom,
( ( '\'mat$\'' @ '\'zero$\'' )
= '\'zero$a\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom86) ).
thf(1557,plain,
( ( '\'mat$\'' @ '\'zero$\'' )
= '\'zero$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(62,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ A @ ( '\'transpose$\'' @ B ) )
= ( '\'matrix_vector_mult$\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom183) ).
thf(552,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ A @ ( '\'transpose$\'' @ B ) )
= ( '\'matrix_vector_mult$\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(91,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'orthogonal_matrix$\'' @ ( '\'transpose$\'' @ A ) )
<=> ( '\'fun_app$\'' @ '\'orthogonal_matrix$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom42) ).
thf(685,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( ( '\'fun_app$\'' @ '\'orthogonal_matrix$\'' @ ( '\'transpose$\'' @ A ) )
=> ( '\'fun_app$\'' @ '\'orthogonal_matrix$\'' @ A ) )
& ( ( '\'fun_app$\'' @ '\'orthogonal_matrix$\'' @ A )
=> ( '\'fun_app$\'' @ '\'orthogonal_matrix$\'' @ ( '\'transpose$\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(26,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ B )
= ( '\'times$a\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom99) ).
thf(399,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ B )
= ( '\'times$a\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(238,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A
= ( '\'times$\'' @ B @ A ) )
<=> ( ( A = '\'zero$\'' )
| ( B = '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom129) ).
thf(1474,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( A
= ( '\'times$\'' @ B @ A ) )
=> ( ( A = '\'zero$\'' )
| ( B = '\'one$\'' ) ) )
& ( ( ( A = '\'zero$\'' )
| ( B = '\'one$\'' ) )
=> ( A
= ( '\'times$\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(115,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( B
= ( '\'times$\'' @ C @ A ) ) )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom386) ).
thf(827,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( B
= ( '\'times$\'' @ C @ A ) ) )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(40,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ C ) @ ( '\'times$a\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom310) ).
thf(455,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ C ) @ ( '\'times$a\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(145,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\''] :
( ( '\'interchange_columns$\'' @ ( '\'transpose$\'' @ A ) @ B @ C )
= ( '\'transpose$\'' @ ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom127) ).
thf(1000,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\''] :
( ( '\'interchange_columns$\'' @ ( '\'transpose$\'' @ A ) @ B @ C )
= ( '\'transpose$\'' @ ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(164,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ B @ ( '\'times$\'' @ C @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom277) ).
thf(1102,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'plus$h\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ A ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'plus$h\'' @ B @ ( '\'times$\'' @ C @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(233,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ ( '\'transpose$\'' @ A ) )
= ( '\'mat$\'' @ '\'one$\'' ) )
<=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom48) ).
thf(1445,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ ( '\'transpose$\'' @ A ) )
= ( '\'mat$\'' @ '\'one$\'' ) )
=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) ) )
& ( ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) )
=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ ( '\'transpose$\'' @ A ) )
= ( '\'mat$\'' @ '\'one$\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(248,axiom,
! [A: '\'A$\''] :
( ( '\'times$\'' @ '\'one$\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom118) ).
thf(1528,plain,
! [A: '\'A$\''] :
( ( '\'times$\'' @ '\'one$\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(142,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'vec$\'' @ A )
= ( '\'vec$\'' @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom172) ).
thf(986,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( ( '\'vec$\'' @ A )
= ( '\'vec$\'' @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( '\'vec$\'' @ A )
= ( '\'vec$\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(6,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ '\'zero$c\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom283) ).
thf(306,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ '\'zero$c\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(213,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ '\'zero$a\'' )
= '\'zero$a\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom65) ).
thf(1364,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ '\'zero$a\'' )
= '\'zero$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(192,axiom,
! [A: '\'N$\'',B: '\'A$\'',C: '\'N$\'',D: '\'A$\''] :
( ( ( '\'axis$a\'' @ A @ B )
= ( '\'axis$a\'' @ C @ D ) )
<=> ( ( ( B = D )
& ( A = C ) )
| ( ( B = '\'zero$\'' )
& ( D = '\'zero$\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom190) ).
thf(1250,plain,
! [A: '\'N$\'',B: '\'A$\'',C: '\'N$\'',D: '\'A$\''] :
( ( ( ( '\'axis$a\'' @ A @ B )
= ( '\'axis$a\'' @ C @ D ) )
=> ( ( ( B = D )
& ( A = C ) )
| ( ( B = '\'zero$\'' )
& ( D = '\'zero$\'' ) ) ) )
& ( ( ( ( B = D )
& ( A = C ) )
| ( ( B = '\'zero$\'' )
& ( D = '\'zero$\'' ) ) )
=> ( ( '\'axis$a\'' @ A @ B )
= ( '\'axis$a\'' @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(52,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\'',D: '\'A_n_vec$\''] :
( ( A
= ( '\'plus$d\'' @ B @ C ) )
=> ( ( '\'plus$d\'' @ A @ D )
= ( '\'plus$d\'' @ B @ ( '\'plus$d\'' @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom341) ).
thf(505,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\'',D: '\'A_n_vec$\''] :
( ( A
= ( '\'plus$d\'' @ B @ C ) )
=> ( ( '\'plus$d\'' @ A @ D )
= ( '\'plus$d\'' @ B @ ( '\'plus$d\'' @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(36,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( '\'vec$a\'' @ ( '\'plus$d\'' @ A @ B ) )
= ( '\'plus$g\'' @ ( '\'vec$a\'' @ A ) @ ( '\'vec$a\'' @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom332) ).
thf(438,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( '\'vec$a\'' @ ( '\'plus$d\'' @ A @ B ) )
= ( '\'plus$g\'' @ ( '\'vec$a\'' @ A ) @ ( '\'vec$a\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(276,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ ( '\'matrix_vector_mult$\'' @ B @ C ) )
= ( '\'matrix_vector_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom189) ).
thf(1626,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ ( '\'matrix_vector_mult$\'' @ B @ C ) )
= ( '\'matrix_vector_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(263,axiom,
! [A: '\'A$\''] :
( ( '\'times$\'' @ A @ '\'one$\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom114) ).
thf(1583,plain,
! [A: '\'A$\''] :
( ( '\'times$\'' @ A @ '\'one$\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(32,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ A @ '\'zero$c\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom399) ).
thf(426,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ A @ '\'zero$c\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(57,axiom,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ A @ '\'zero$\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom225) ).
thf(531,plain,
! [A: '\'A$\''] :
( ( '\'plus$h\'' @ A @ '\'zero$\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(102,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'plus$h\'' @ B @ C ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ B ) @ ( '\'times$\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom309) ).
thf(749,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'plus$h\'' @ B @ C ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ B ) @ ( '\'times$\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(41,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ '\'zero$c\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom295) ).
thf(458,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ '\'zero$c\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(254,axiom,
! [A: '\'A$\''] :
( ( '\'times$\'' @ A @ '\'one$\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom85) ).
thf(1551,plain,
! [A: '\'A$\''] :
( ( '\'times$\'' @ A @ '\'one$\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(157,axiom,
! [A: '\'A$\''] :
( ( '\'zero$\'' = A )
<=> ( A = '\'zero$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom88) ).
thf(1049,plain,
! [A: '\'A$\''] :
( ( ( '\'zero$\'' = A )
=> ( A = '\'zero$\'' ) )
& ( ( A = '\'zero$\'' )
=> ( '\'zero$\'' = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(106,axiom,
! [A: '\'A$\''] :
( ( '\'times$\'' @ A @ '\'zero$\'' )
= '\'zero$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom137) ).
thf(776,plain,
! [A: '\'A$\''] :
( ( '\'times$\'' @ A @ '\'zero$\'' )
= '\'zero$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(146,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ '\'zero$a\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom294) ).
thf(1003,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ '\'zero$a\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(3,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ C ) @ ( '\'times$a\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom304) ).
thf(295,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ ( '\'times$a\'' @ A @ C ) @ ( '\'times$a\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(95,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ ( '\'plus$g\'' @ A @ B ) @ C )
= ( '\'plus$g\'' @ A @ ( '\'plus$g\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom337) ).
thf(705,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ ( '\'plus$g\'' @ A @ B ) @ C )
= ( '\'plus$g\'' @ A @ ( '\'plus$g\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(258,axiom,
! [A: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mat$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom124) ).
thf(1566,plain,
! [A: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mat$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(282,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A
= ( '\'times$\'' @ A @ B ) )
<=> ( ( A = '\'zero$\'' )
| ( B = '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom131) ).
thf(1647,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( A
= ( '\'times$\'' @ A @ B ) )
=> ( ( A = '\'zero$\'' )
| ( B = '\'one$\'' ) ) )
& ( ( ( A = '\'zero$\'' )
| ( B = '\'one$\'' ) )
=> ( A
= ( '\'times$\'' @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(136,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ B @ A ) ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom257) ).
thf(954,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ B @ A ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(249,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom179) ).
thf(1531,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(92,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ C @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom217) ).
thf(690,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ C @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( '\'plus$g\'' @ A @ B )
= ( '\'plus$g\'' @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(245,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ ( '\'vector_matrix_mult$a\'' @ A @ B ) @ C )
= ( '\'vector_matrix_mult$a\'' @ A @ ( '\'matrix_matrix_mult$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom45) ).
thf(1516,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'vector_matrix_mult$a\'' @ ( '\'vector_matrix_mult$a\'' @ A @ B ) @ C )
= ( '\'vector_matrix_mult$a\'' @ A @ ( '\'matrix_matrix_mult$\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(186,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\'',D: '\'A_n_vec_n_vec$\''] :
( ( A
= ( '\'plus$g\'' @ B @ C ) )
=> ( ( '\'plus$g\'' @ D @ A )
= ( '\'plus$g\'' @ B @ ( '\'plus$g\'' @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom349) ).
thf(1230,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\'',D: '\'A_n_vec_n_vec$\''] :
( ( A
= ( '\'plus$g\'' @ B @ C ) )
=> ( ( '\'plus$g\'' @ D @ A )
= ( '\'plus$g\'' @ B @ ( '\'plus$g\'' @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(239,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= '\'one$\'' )
<=> ( ( B != '\'zero$\'' )
& ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom265) ).
thf(1484,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= '\'one$\'' )
=> ( ( B != '\'zero$\'' )
& ( A = B ) ) )
& ( ( ( B != '\'zero$\'' )
& ( A = B ) )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B )
= '\'one$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(109,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'Num$\''] :
( ( '\'times$\'' @ ( '\'plus$h\'' @ A @ B ) @ ( '\'numeral$b\'' @ C ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ ( '\'numeral$b\'' @ C ) ) @ ( '\'times$\'' @ B @ ( '\'numeral$b\'' @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom414) ).
thf(791,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'Num$\''] :
( ( '\'times$\'' @ ( '\'plus$h\'' @ A @ B ) @ ( '\'numeral$b\'' @ C ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ ( '\'numeral$b\'' @ C ) ) @ ( '\'times$\'' @ B @ ( '\'numeral$b\'' @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(37,axiom,
! [A: '\'A_n_vec_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$a\'' @ A @ '\'zero$a\'' )
= '\'zero$a\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom176) ).
thf(441,plain,
! [A: '\'A_n_vec_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$a\'' @ A @ '\'zero$a\'' )
= '\'zero$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(51,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ A @ ( '\'plus$d\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom353) ).
thf(502,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ ( '\'plus$d\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ A @ ( '\'plus$d\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(187,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ A @ '\'zero$a\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom226) ).
thf(1235,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'plus$g\'' @ A @ '\'zero$a\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(208,axiom,
! [A: tlbool] :
( ( A = tltrue )
| ( A = tlfalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_418) ).
thf(1336,plain,
! [A: tlbool] :
( ( A = tltrue )
| ( A = tlfalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(200,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( '\'transpose$\'' @ A )
= ( '\'transpose$\'' @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom39) ).
thf(1300,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( ( '\'transpose$\'' @ A )
= ( '\'transpose$\'' @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( '\'transpose$\'' @ A )
= ( '\'transpose$\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(234,axiom,
( ( '\'dbl_inc$b\'' @ '\'zero$\'' )
= '\'one$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom206) ).
thf(1452,plain,
( ( '\'dbl_inc$b\'' @ '\'zero$\'' )
= '\'one$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(279,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).
thf(1637,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(251,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
<=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) )
& ( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19) ).
thf(1536,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) )
& ( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) ) )
& ( ? [B: '\'A_n_vec_n_vec$\''] :
( ( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) )
& ( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(151,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'times$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom254) ).
thf(1023,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'times$\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(290,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
=> ( ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ A ) @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom25) ).
thf(1702,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
=> ( ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ A ) @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(211,axiom,
'\'fun_app$\'' @ '\'invertible$\'' @ '\'p$\'',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).
thf(1353,plain,
'\'fun_app$\'' @ '\'invertible$\'' @ '\'p$\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(23,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( A
= ( '\'plus$d\'' @ B @ A ) )
<=> ( B = '\'zero$c\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom236) ).
thf(386,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( A
= ( '\'plus$d\'' @ B @ A ) )
=> ( B = '\'zero$c\'' ) )
& ( ( B = '\'zero$c\'' )
=> ( A
= ( '\'plus$d\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(67,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A
= ( '\'plus$h\'' @ B @ A ) )
<=> ( B = '\'zero$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom234) ).
thf(571,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( A
= ( '\'plus$h\'' @ B @ A ) )
=> ( B = '\'zero$\'' ) )
& ( ( B = '\'zero$\'' )
=> ( A
= ( '\'plus$h\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(226,axiom,
! [A: '\'N$\'',B: '\'N$\''] : ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom60) ).
thf(1421,plain,
! [A: '\'N$\'',B: '\'N$\''] : ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(203,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'times$\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ D ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ C ) ) @ ( '\'times$\'' @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom280) ).
thf(1321,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'times$\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ D ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ C ) ) @ ( '\'times$\'' @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(140,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom368) ).
thf(976,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(69,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom252) ).
thf(581,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(223,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) )
& ( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) )
=> ( ( '\'matrix_inv$\'' @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12) ).
thf(1412,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) )
& ( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) )
=> ( ( '\'matrix_inv$\'' @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(104,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( '\'plus$g\'' @ A @ B )
= B )
<=> ( A = '\'zero$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom229) ).
thf(759,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( ( '\'plus$g\'' @ A @ B )
= B )
=> ( A = '\'zero$a\'' ) )
& ( ( A = '\'zero$a\'' )
=> ( ( '\'plus$g\'' @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(128,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'plus$h\'' @ A @ ( '\'plus$h\'' @ B @ C ) )
= ( '\'plus$h\'' @ B @ ( '\'plus$h\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom374) ).
thf(891,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'plus$h\'' @ A @ ( '\'plus$h\'' @ B @ C ) )
= ( '\'plus$h\'' @ B @ ( '\'plus$h\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(148,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'times$\'' @ B @ C ) )
= ( '\'times$\'' @ ( '\'times$\'' @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).
thf(1010,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'times$\'' @ B @ C ) )
= ( '\'times$\'' @ ( '\'times$\'' @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(285,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ ( '\'similar_matrices$\'' @ A ) @ B )
<=> ? [C: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ C )
& ( B
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ C ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom30) ).
thf(1674,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( '\'fun_app$\'' @ ( '\'similar_matrices$\'' @ A ) @ B )
=> ? [C: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ C )
& ( B
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ C ) @ A ) @ C ) ) ) )
& ( ? [C: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ C )
& ( B
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ C ) @ A ) @ C ) ) )
=> ( '\'fun_app$\'' @ ( '\'similar_matrices$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(16,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ A @ ( '\'plus$d\'' @ B @ C ) )
= ( '\'plus$d\'' @ B @ ( '\'plus$d\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom371) ).
thf(351,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ A @ ( '\'plus$d\'' @ B @ C ) )
= ( '\'plus$d\'' @ B @ ( '\'plus$d\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(277,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'Nat$\''] :
? [C: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ C )
& ( ( '\'gauss_Jordan_upt_k$\'' @ A @ B )
= ( '\'matrix_matrix_mult$\'' @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).
thf(1629,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'Nat$\''] :
? [C: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ C )
& ( ( '\'gauss_Jordan_upt_k$\'' @ A @ B )
= ( '\'matrix_matrix_mult$\'' @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(80,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( '\'vec$\'' @ ( '\'plus$h\'' @ A @ B ) )
= ( '\'plus$d\'' @ ( '\'vec$\'' @ A ) @ ( '\'vec$\'' @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom331) ).
thf(632,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( '\'vec$\'' @ ( '\'plus$h\'' @ A @ B ) )
= ( '\'plus$d\'' @ ( '\'vec$\'' @ A ) @ ( '\'vec$\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(190,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'plus$h\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ A @ ( '\'plus$h\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom356) ).
thf(1244,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'plus$h\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ A @ ( '\'plus$h\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(31,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ A @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom213) ).
thf(418,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(108,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\'',D: '\'A_n_vec_n_vec$\''] :
( ( A
= ( '\'plus$g\'' @ B @ C ) )
=> ( ( '\'plus$g\'' @ A @ D )
= ( '\'plus$g\'' @ B @ ( '\'plus$g\'' @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom343) ).
thf(786,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\'',D: '\'A_n_vec_n_vec$\''] :
( ( A
= ( '\'plus$g\'' @ B @ C ) )
=> ( ( '\'plus$g\'' @ A @ D )
= ( '\'plus$g\'' @ B @ ( '\'plus$g\'' @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(66,axiom,
! [A: '\'A$\''] :
( ( '\'times$\'' @ '\'zero$\'' @ A )
= '\'zero$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom75) ).
thf(568,plain,
! [A: '\'A$\''] :
( ( '\'times$\'' @ '\'zero$\'' @ A )
= '\'zero$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(53,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ C @ B ) )
<=> ( ( A = C )
| ( B = '\'zero$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom72) ).
thf(510,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ C @ B ) )
=> ( ( A = C )
| ( B = '\'zero$\'' ) ) )
& ( ( ( A = C )
| ( B = '\'zero$\'' ) )
=> ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(88,axiom,
'\'zero$c\'' != '\'one$a\'',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom149) ).
thf(667,plain,
'\'zero$c\'' != '\'one$a\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(201,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'times$\'' @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom278) ).
thf(1308,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ B ) ) @ C )
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ ( '\'times$\'' @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(46,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( '\'times$a\'' @ A @ B )
!= '\'zero$c\'' )
=> ( ( A != '\'zero$c\'' )
& ( B != '\'zero$c\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom146) ).
thf(478,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\''] :
( ( ( '\'times$a\'' @ A @ B )
!= '\'zero$c\'' )
=> ( ( A != '\'zero$c\'' )
& ( B != '\'zero$c\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(272,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'orthogonal_matrix$\'' @ A )
<=> ( ( ( '\'matrix_matrix_mult$\'' @ ( '\'transpose$\'' @ A ) @ A )
= ( '\'mat$\'' @ '\'one$\'' ) )
& ( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'transpose$\'' @ A ) )
= ( '\'mat$\'' @ '\'one$\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom46) ).
thf(1607,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( ( '\'fun_app$\'' @ '\'orthogonal_matrix$\'' @ A )
=> ( ( ( '\'matrix_matrix_mult$\'' @ ( '\'transpose$\'' @ A ) @ A )
= ( '\'mat$\'' @ '\'one$\'' ) )
& ( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'transpose$\'' @ A ) )
= ( '\'mat$\'' @ '\'one$\'' ) ) ) )
& ( ( ( ( '\'matrix_matrix_mult$\'' @ ( '\'transpose$\'' @ A ) @ A )
= ( '\'mat$\'' @ '\'one$\'' ) )
& ( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'transpose$\'' @ A ) )
= ( '\'mat$\'' @ '\'one$\'' ) ) )
=> ( '\'fun_app$\'' @ '\'orthogonal_matrix$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(232,axiom,
'\'fun_app$\'' @ '\'orthogonal_matrix$\'' @ ( '\'mat$\'' @ '\'one$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom31) ).
thf(1444,plain,
'\'fun_app$\'' @ '\'orthogonal_matrix$\'' @ ( '\'mat$\'' @ '\'one$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(103,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( ( '\'transpose$\'' @ A )
= '\'zero$a\'' )
<=> ( A = '\'zero$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom67) ).
thf(752,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( ( ( '\'transpose$\'' @ A )
= '\'zero$a\'' )
=> ( A = '\'zero$a\'' ) )
& ( ( A = '\'zero$a\'' )
=> ( ( '\'transpose$\'' @ A )
= '\'zero$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(244,axiom,
! [A: '\'A$\'',B: '\'N$\''] :
( ( A != '\'zero$\'' )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mult_row$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom123) ).
thf(1512,plain,
! [A: '\'A$\'',B: '\'N$\''] :
( ( A != '\'zero$\'' )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'mult_row$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(34,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ A @ '\'zero$c\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom227) ).
thf(432,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'plus$d\'' @ A @ '\'zero$c\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(135,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom377) ).
thf(950,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'plus$h\'' @ A @ B )
= ( '\'plus$h\'' @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(220,axiom,
! [A: '\'N$\'',B: '\'N$\'',C: '\'A$\''] :
( ( A != B )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'column_add$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom32) ).
thf(1395,plain,
! [A: '\'N$\'',B: '\'N$\'',C: '\'A$\''] :
( ( A != B )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ ( '\'column_add$\'' @ ( '\'mat$\'' @ '\'one$\'' ) @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(267,axiom,
( ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ ( '\'matrix_matrix_mult$\'' @ '\'p$\'' @ '\'a$\'' ) )
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ ( '\'mat$\'' @ '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).
thf(1593,plain,
( ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ ( '\'matrix_matrix_mult$\'' @ '\'p$\'' @ '\'a$\'' ) )
= ( '\'matrix_matrix_mult$\'' @ ( '\'matrix_inv$\'' @ '\'p$\'' ) @ ( '\'mat$\'' @ '\'one$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(28,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ '\'one$a\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom77) ).
thf(405,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ '\'one$a\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ '\'one$a\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom82) ).
thf(373,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ '\'one$a\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ ( '\'times$a\'' @ B @ C ) )
= ( '\'times$a\'' @ B @ ( '\'times$a\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom95) ).
thf(315,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ A @ ( '\'times$a\'' @ B @ C ) )
= ( '\'times$a\'' @ B @ ( '\'times$a\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(196,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'one$a\'' = A )
<=> ( A = '\'one$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21) ).
thf(1280,plain,
! [A: '\'A_n_vec$\''] :
( ( ( '\'one$a\'' = A )
=> ( A = '\'one$a\'' ) )
& ( ( A = '\'one$a\'' )
=> ( '\'one$a\'' = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(283,axiom,
! [A: '\'A$\''] :
( ( '\'dbl_inc$b\'' @ A )
= ( '\'plus$h\'' @ ( '\'plus$h\'' @ A @ A ) @ '\'one$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom396) ).
thf(1657,plain,
! [A: '\'A$\''] :
( ( '\'dbl_inc$b\'' @ A )
= ( '\'plus$h\'' @ ( '\'plus$h\'' @ A @ A ) @ '\'one$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(112,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ A @ C ) )
<=> ( ( B = C )
| ( A = '\'zero$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom73) ).
thf(807,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ A @ C ) )
=> ( ( B = C )
| ( A = '\'zero$\'' ) ) )
& ( ( ( B = C )
| ( A = '\'zero$\'' ) )
=> ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(81,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'times$\'' @ A @ B ) @ C )
= ( '\'times$\'' @ A @ ( '\'times$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom106) ).
thf(635,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'times$\'' @ A @ B ) @ C )
= ( '\'times$\'' @ A @ ( '\'times$\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(210,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ ( '\'transpose$\'' @ A ) @ B )
= ( '\'mat$\'' @ '\'one$\'' ) )
<=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom38) ).
thf(1346,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ ( '\'transpose$\'' @ A ) @ B )
= ( '\'mat$\'' @ '\'one$\'' ) )
=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) )
& ( ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) )
=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ ( '\'transpose$\'' @ A ) @ B )
= ( '\'mat$\'' @ '\'one$\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(30,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ ( '\'times$a\'' @ A @ B ) @ C )
= ( '\'times$a\'' @ A @ ( '\'times$a\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom107) ).
thf(415,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ ( '\'times$a\'' @ A @ B ) @ C )
= ( '\'times$a\'' @ A @ ( '\'times$a\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(153,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\''] :
( ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ A @ B ) @ C )
= ( '\'transpose$\'' @ ( '\'interchange_columns$\'' @ ( '\'transpose$\'' @ A ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom126) ).
thf(1033,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'N$\'',C: '\'N$\''] :
( ( '\'fun_app$c\'' @ ( '\'interchange_rows$\'' @ A @ B ) @ C )
= ( '\'transpose$\'' @ ( '\'interchange_columns$\'' @ ( '\'transpose$\'' @ A ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(197,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ C ) @ ( '\'times$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom306) ).
thf(1288,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ ( '\'plus$h\'' @ A @ B ) @ C )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ C ) @ ( '\'times$\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(181,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom258) ).
thf(1197,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ ( '\'times$\'' @ A @ B ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(79,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( B
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A ) )
<=> ( ( '\'times$\'' @ B @ A )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom383) ).
thf(624,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A != '\'zero$\'' )
=> ( ( ( B
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A ) )
=> ( ( '\'times$\'' @ B @ A )
= C ) )
& ( ( ( '\'times$\'' @ B @ A )
= C )
=> ( B
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(97,axiom,
( ( '\'vec$\'' @ '\'zero$\'' )
= '\'zero$c\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom162) ).
thf(728,plain,
( ( '\'vec$\'' @ '\'zero$\'' )
= '\'zero$c\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(43,axiom,
! [A: '\'A_n_vec_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec_n_vec$\''] :
( ( A = B )
<=> ! [C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$a\'' @ A @ C )
= ( '\'matrix_vector_mult$a\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom186) ).
thf(464,plain,
! [A: '\'A_n_vec_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec_n_vec$\''] :
( ( ( A = B )
=> ! [C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$a\'' @ A @ C )
= ( '\'matrix_vector_mult$a\'' @ B @ C ) ) )
& ( ! [C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$a\'' @ A @ C )
= ( '\'matrix_vector_mult$a\'' @ B @ C ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(123,axiom,
! [A: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ '\'zero$\'' )
= '\'zero$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom246) ).
thf(860,plain,
! [A: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ '\'zero$\'' )
= '\'zero$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(56,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ '\'zero$c\'' )
= '\'zero$c\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom175) ).
thf(528,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ '\'zero$c\'' )
= '\'zero$c\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(84,axiom,
( ( '\'vec$a\'' @ '\'zero$c\'' )
= '\'zero$a\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom163) ).
thf(644,plain,
( ( '\'vec$a\'' @ '\'zero$c\'' )
= '\'zero$a\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(242,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ B )
& ( ( '\'gauss_Jordan$\'' @ A )
= ( '\'matrix_matrix_mult$\'' @ B @ A ) )
& ( '\'fun_app$\'' @ '\'reduced_row_echelon_form$\'' @ ( '\'gauss_Jordan$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom59) ).
thf(1500,plain,
! [A: '\'A_n_vec_n_vec$\''] :
? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ B )
& ( ( '\'gauss_Jordan$\'' @ A )
= ( '\'matrix_matrix_mult$\'' @ B @ A ) )
& ( '\'fun_app$\'' @ '\'reduced_row_echelon_form$\'' @ ( '\'gauss_Jordan$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(120,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'plus$h\'' @ B @ C ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ B ) @ ( '\'times$\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom303) ).
thf(850,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'times$\'' @ A @ ( '\'plus$h\'' @ B @ C ) )
= ( '\'plus$h\'' @ ( '\'times$\'' @ A @ B ) @ ( '\'times$\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(269,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'plus$g\'' @ B @ C ) )
= ( '\'plus$g\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) @ ( '\'matrix_matrix_mult$\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom322) ).
thf(1597,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ ( '\'plus$g\'' @ B @ C ) )
= ( '\'plus$g\'' @ ( '\'matrix_matrix_mult$\'' @ A @ B ) @ ( '\'matrix_matrix_mult$\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(125,axiom,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( B != '\'zero$\'' ) )
=> ( ( '\'times$\'' @ A @ B )
!= '\'zero$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom143) ).
thf(871,plain,
! [A: '\'A$\'',B: '\'A$\''] :
( ( ( A != '\'zero$\'' )
& ( B != '\'zero$\'' ) )
=> ( ( '\'times$\'' @ A @ B )
!= '\'zero$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(19,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom378) ).
thf(369,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(13,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ C @ B ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom216) ).
thf(332,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ C @ B ) )
=> ( A = C ) )
& ( ( A = C )
=> ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(169,axiom,
! [A: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ '\'zero$\'' )
= '\'zero$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom251) ).
thf(1129,plain,
! [A: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'divide$\'' @ A ) @ '\'zero$\'' )
= '\'zero$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(243,axiom,
! [A: '\'A_n_vec_n_vec$\''] :
( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
<=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).
thf(1505,plain,
! [A: '\'A_n_vec_n_vec$\''] :
( ( ( '\'fun_app$\'' @ '\'invertible$\'' @ A )
=> ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) ) )
& ( ? [B: '\'A_n_vec_n_vec$\''] :
( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) )
=> ( '\'fun_app$\'' @ '\'invertible$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(221,axiom,
! [A: '\'A$\''] :
( ( '\'times$\'' @ '\'one$\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).
thf(1399,plain,
! [A: '\'A$\''] :
( ( '\'times$\'' @ '\'one$\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(17,axiom,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ A @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom357) ).
thf(354,plain,
! [A: '\'A_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ A @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( '\'plus$d\'' @ A @ B )
= ( '\'plus$d\'' @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ '\'zero$c\'' @ A )
= '\'zero$c\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom133) ).
thf(309,plain,
! [A: '\'A_n_vec$\''] :
( ( '\'times$a\'' @ '\'zero$c\'' @ A )
= '\'zero$c\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(49,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ ( '\'plus$d\'' @ B @ C ) )
= ( '\'plus$d\'' @ ( '\'matrix_vector_mult$\'' @ A @ B ) @ ( '\'matrix_vector_mult$\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom321) ).
thf(491,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ A @ ( '\'plus$d\'' @ B @ C ) )
= ( '\'plus$d\'' @ ( '\'matrix_vector_mult$\'' @ A @ B ) @ ( '\'matrix_vector_mult$\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(183,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ ( '\'plus$g\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ ( '\'matrix_vector_mult$\'' @ A @ C ) @ ( '\'matrix_vector_mult$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom330) ).
thf(1204,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\'',C: '\'A_n_vec$\''] :
( ( '\'matrix_vector_mult$\'' @ ( '\'plus$g\'' @ A @ B ) @ C )
= ( '\'plus$d\'' @ ( '\'matrix_vector_mult$\'' @ A @ C ) @ ( '\'matrix_vector_mult$\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(96,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( A
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) )
<=> ( ( ( C != '\'zero$\'' )
=> ( ( '\'times$\'' @ A @ C )
= B ) )
& ( ( C != '\'zero$\'' )
=> ( A = '\'zero$\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom387) ).
thf(708,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( A
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) )
=> ( ( ( C != '\'zero$\'' )
=> ( ( '\'times$\'' @ A @ C )
= B ) )
& ( ( C = '\'zero$\'' )
=> ( A = '\'zero$\'' ) ) ) )
& ( ( ( ( C != '\'zero$\'' )
=> ( ( '\'times$\'' @ A @ C )
= B ) )
& ( ( C = '\'zero$\'' )
=> ( A = '\'zero$\'' ) ) )
=> ( A
= ( '\'fun_app$d\'' @ ( '\'divide$\'' @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(214,axiom,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) )
<=> ( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).
thf(1367,plain,
! [A: '\'A_n_vec_n_vec$\'',B: '\'A_n_vec_n_vec$\''] :
( ( ( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) )
=> ( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) ) )
& ( ( ( '\'matrix_matrix_mult$\'' @ B @ A )
= ( '\'mat$\'' @ '\'one$\'' ) )
=> ( ( '\'matrix_matrix_mult$\'' @ A @ B )
= ( '\'mat$\'' @ '\'one$\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(134,axiom,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ C @ B ) )
<=> ( ( B = '\'zero$\'' )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom140) ).
thf(940,plain,
! [A: '\'A$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ C @ B ) )
=> ( ( B = '\'zero$\'' )
| ( A = C ) ) )
& ( ( ( B = '\'zero$\'' )
| ( A = C ) )
=> ( ( '\'times$\'' @ A @ B )
= ( '\'times$\'' @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(1712,plain,
$false,
inference(e,[status(thm)],[1036,1586,1190,1454,1633,1559,909,555,1554,408,523,730,1068,994,1569,1591,379,1692,677,1426,472,1327,698,1640,340,1354,670,1497,1705,1441,1386,301,565,1623,651,973,1046,1660,1330,587,917,1132,1545,1379,1247,1572,1013,1494,817,902,638,853,1415,475,321,376,1418,646,1682,485,834,1151,937,1581,966,766,293,396,1433,1201,1600,1521,312,1604,1708,1311,534,1057,1163,894,1519,1580,1174,598,820,429,1238,746,1091,1423,847,435,1296,461,1291,324,1106,1402,578,1270,1534,615,1121,1064,1227,1006,857,874,1143,488,1182,1700,1644,1039,1155,1461,537,1016,1207,590,837,997,1099,701,1382,1266,1429,779,1324,393,1114,1333,343,1241,541,1170,1616,794,888,558,1071,1026,1167,1135,618,1698,1548,1595,444,1374,733,601,1278,298,584,402,1620,958,545,641,611,804,1464,979,831,1117,736,1589,318,649,1376,863,362,451,494,1339,621,520,1557,552,685,399,1474,827,455,1000,1102,1445,1528,986,306,1364,1250,505,438,1626,1583,426,531,749,458,1551,1049,776,1003,295,705,1566,1647,954,1531,690,1516,1230,1484,791,441,502,1235,1336,1300,1452,1637,1536,1023,1702,1353,386,571,1421,1321,976,581,1412,759,891,1010,1674,351,1629,632,1244,418,786,568,510,667,1308,478,1607,1444,752,1512,432,950,1395,1593,405,373,315,1280,1657,807,635,1346,415,1033,1288,1197,624,728,464,860,528,644,1500,850,1597,871,369,332,1129,1505,1399,354,309,491,1204,708,1367,940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP341_1 : TPTP v8.1.2. Released v8.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:37:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.88/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.87/1.14 % [INFO] Parsing done (297ms).
% 1.87/1.15 % [INFO] Running in sequential loop mode.
% 2.59/1.36 % [INFO] eprover registered as external prover.
% 2.59/1.36 % [INFO] cvc4 registered as external prover.
% 2.59/1.37 % [INFO] Scanning for conjecture ...
% 2.99/1.47 % [INFO] Found a conjecture and 418 axioms. Running axiom selection ...
% 3.26/1.57 % [INFO] Axiom selection finished. Selected 290 axioms (removed 128 axioms).
% 3.90/1.72 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.90/1.73 % [INFO] Type checking passed.
% 3.90/1.74 % [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 ...
% 6.43/2.48 % [INFO] [Domain constraints] Detected constraint on tlbool
% 6.43/2.48 % [INFO] [Domain constraints] dom(tlbool) ⊆ {tltrue,tlfalse}
% 9.53/3.13 % External prover 'e' found a proof!
% 9.53/3.13 % [INFO] Killing All external provers ...
% 9.53/3.13 % Time passed: 2618ms (effective reasoning time: 1976ms)
% 9.53/3.13 % 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)>
% 9.53/3.14 % Axioms used in derivation (290): axiom32, axiom260, axiom280, axiom127, axiom315, axiom28, axiom76, axiom273, axiom61, axiom230, axiom6, axiom295, axiom396, axiom25, axiom14, axiom214, axiom322, axiom307, axiom142, axiom169, axiom65, axiom36, axiom203, axiom131, axiom10, axiom386, axiom337, axiom119, axiom344, axiom138, axiom191, axiom17, axiom401, axiom257, axiom397, axiom172, axiom266, axiom147, axiom341, axiom329, axiom376, axiom42, axiom239, axiom300, axiom350, axiom195, axiom162, axiom358, axiom161, axiom123, axiom246, axiom383, axiom134, axiom33, axiom150, axiom87, axiom11, axiom130, axiom235, axiom98, axiom304, axiom225, axiom365, axiom39, axiom330, axiom251, axiom64, axiom27, axiom179, axiom283, axiom126, axiom289, axiom236, axiom59, axiom247, axiom48, axiom217, axiom343, axiom411, axiom294, axiom115, formula_418, axiom228, axiom94, axiom5, axiom121, axiom321, axiom35, axiom24, axiom278, axiom272, axiom60, axiom56, axiom137, axiom206, axiom13, axiom143, axiom359, axiom416, axiom387, axiom90, axiom16, axiom400, axiom258, axiom75, axiom385, axiom332, axiom9, axiom303, axiom185, axiom133, axiom80, axiom371, axiom146, axiom355, axiom202, axiom252, axiom360, axiom263, axiom415, axiom254, axiom82, formula_419, axiom45, axiom229, axiom174, axiom398, axiom382, axiom243, axiom319, axiom347, axiom67, axiom213, axiom72, axiom232, axiom310, axiom122, axiom91, axiom267, axiom163, axiom89, axiom38, axiom377, axiom218, axiom86, axiom111, axiom120, axiom297, axiom279, axiom12, axiom390, axiom37, axiom331, axiom205, axiom193, axiom152, axiom190, axiom41, axiom149, axiom189, axiom375, axiom394, axiom23, axiom227, axiom93, axiom216, axiom320, axiom30, axiom313, axiom118, axiom275, axiom63, axiom19, axiom102, axiom8, axiom259, axiom74, axiom276, axiom85, axiom233, axiom186, axiom367, axiom378, axiom57, axiom374, axiom153, axiom71, axiom282, axiom271, axiom287, axiom4, axiom255, axiom106, axiom15, axiom129, axiom114, axiom244, axiom136, axiom414, axiom170, axiom181, axiom262, axiom335, axiom268, axiom293, axiom175, axiom237, axiom26, axiom356, axiom298, axiom46, axiom248, axiom110, axiom125, axiom49, axiom18, axiom338, axiom379, axiom88, axiom92, axiom389, axiom226, axiom399, axiom66, axiom215, axiom296, axiom141, axiom357, axiom274, axiom269, axiom7, axiom81, axiom103, axiom231, axiom306, axiom253, axiom368, axiom29, axiom361, axiom99, axiom128, axiom264, axiom20, axiom349, axiom249, axiom183, axiom301, axiom380, axiom177, axiom31, axiom159, axiom402, axiom384, axiom73, axiom107, axiom171, axiom40, axiom265, axiom47, axiom270, axiom176, axiom187, axiom245, axiom288, axiom69, axiom277, axiom373, axiom144, axiom312, axiom95, axiom238, axiom281, axiom124, axiom261, axiom77, axiom256, axiom388, axiom160, axiom43, axiom309, axiom62, axiom21, axiom140, axiom139, axiom250, axiom58, axiom234, axiom362, axiom194, axiom353
% 9.53/3.14 % No. of inferences in proof: 584
% 9.53/3.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2618 ms resp. 1976 ms w/o parsing
% 10.02/3.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.02/3.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------