%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP327_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:37:42 AM UTC 2026
% Result : Theorem 25.33s 7.73s
% Output : Refutation 27.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 713
% Syntax : Number of formulae : 1428 ( 677 unt; 0 typ; 0 def)
% Number of atoms : 3682 (2049 equ; 0 cnn)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 16215 ( 528 ~; 88 |; 880 &;13433 @)
% ( 163 <=>;1123 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 59 ( 58 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 288 ( 285 usr; 63 con; 0-4 aty)
% Number of variables : 3443 ( 0 ^;3327 !; 116 ?;3443 :)
% Comments :
%------------------------------------------------------------------------------
thf('A_m_vec_m_vec$_type',type,
'A_m_vec_m_vec$': $tType ).
thf('M_a_m_vec_bool_fun_fun$_type',type,
'M_a_m_vec_bool_fun_fun$': $tType ).
thf('A_n_vec_m_vec_n_vec$_type',type,
'A_n_vec_m_vec_n_vec$': $tType ).
thf('A_m_vec_bool_fun$_type',type,
'A_m_vec_bool_fun$': $tType ).
thf('M_a_n_vec_fun$_type',type,
'M_a_n_vec_fun$': $tType ).
thf('A_set_set$_type',type,
'A_set_set$': $tType ).
thf('M_a_m_vec_fun$_type',type,
'M_a_m_vec_fun$': $tType ).
thf('M$_type',type,
'M$': $tType ).
thf('A_n_vec_set$_type',type,
'A_n_vec_set$': $tType ).
thf('A_n_vec_a_fun$_type',type,
'A_n_vec_a_fun$': $tType ).
thf('A_m_vec_a_fun$_type',type,
'A_m_vec_a_fun$': $tType ).
thf('A_n_vec_a_n_vec_a_n_vec_fun_fun$_type',type,
'A_n_vec_a_n_vec_a_n_vec_fun_fun$': $tType ).
thf('N_a_n_vec_fun$_type',type,
'N_a_n_vec_fun$': $tType ).
thf('N_set$_type',type,
'N_set$': $tType ).
thf('A_n_vec_n_vec_m_vec$_type',type,
'A_n_vec_n_vec_m_vec$': $tType ).
thf('A_n_vec_n_vec$_type',type,
'A_n_vec_n_vec$': $tType ).
thf('N_a_n_vec_bool_fun_fun$_type',type,
'N_a_n_vec_bool_fun_fun$': $tType ).
thf('A_m_vec_set$_type',type,
'A_m_vec_set$': $tType ).
thf('M_a_fun$_type',type,
'M_a_fun$': $tType ).
thf('A_n_vec_a_n_vec_bool_fun_fun$_type',type,
'A_n_vec_a_n_vec_bool_fun_fun$': $tType ).
thf('A_n_vec_m_vec$_type',type,
'A_n_vec_m_vec$': $tType ).
thf('A_m_vec$_type',type,
'A_m_vec$': $tType ).
thf('M_a_n_vec_bool_fun_fun$_type',type,
'M_a_n_vec_bool_fun_fun$': $tType ).
thf('M_bool_fun$_type',type,
'M_bool_fun$': $tType ).
thf('N$_type',type,
'N$': $tType ).
thf('A_a_n_vec_a_n_vec_fun_fun$_type',type,
'A_a_n_vec_a_n_vec_fun_fun$': $tType ).
thf('A_n_vec_set_bool_fun$_type',type,
'A_n_vec_set_bool_fun$': $tType ).
thf('A_m_vec_n_vec_a_m_vec_n_vec_fun$_type',type,
'A_m_vec_n_vec_a_m_vec_n_vec_fun$': $tType ).
thf('A_n_vec_a_m_vec_fun$_type',type,
'A_n_vec_a_m_vec_fun$': $tType ).
thf('M_a_bool_fun_fun$_type',type,
'M_a_bool_fun_fun$': $tType ).
thf(tlbool_type,type,
tlbool: $tType ).
thf('N_a_bool_fun_fun$_type',type,
'N_a_bool_fun_fun$': $tType ).
thf('A_m_vec_n_vec_n_vec$_type',type,
'A_m_vec_n_vec_n_vec$': $tType ).
thf('A_bool_fun$_type',type,
'A_bool_fun$': $tType ).
thf('A_set$_type',type,
'A_set$': $tType ).
thf('N_a_fun$_type',type,
'N_a_fun$': $tType ).
thf('A_n_vec_set_set$_type',type,
'A_n_vec_set_set$': $tType ).
thf('A_m_vec_n_vec$_type',type,
'A_m_vec_n_vec$': $tType ).
thf('A$_type',type,
'A$': $tType ).
thf('A_a_m_vec_a_m_vec_fun_fun$_type',type,
'A_a_m_vec_a_m_vec_fun_fun$': $tType ).
thf('A_m_vec_a_m_vec_fun$_type',type,
'A_m_vec_a_m_vec_fun$': $tType ).
thf('N_a_m_vec_fun$_type',type,
'N_a_m_vec_fun$': $tType ).
thf('A_n_vec$_type',type,
'A_n_vec$': $tType ).
thf('A_a_a_fun_fun$_type',type,
'A_a_a_fun_fun$': $tType ).
thf('A_m_vec_n_vec_m_vec$_type',type,
'A_m_vec_n_vec_m_vec$': $tType ).
thf('A_n_vec_a_n_vec_fun$_type',type,
'A_n_vec_a_n_vec_fun$': $tType ).
thf('A_m_vec_m_vec_n_vec$_type',type,
'A_m_vec_m_vec_n_vec$': $tType ).
thf('A_m_vec_n_vec_set$_type',type,
'A_m_vec_n_vec_set$': $tType ).
thf('N_a_m_vec_n_vec_fun$_type',type,
'N_a_m_vec_n_vec_fun$': $tType ).
thf('A_a_fun$_type',type,
'A_a_fun$': $tType ).
thf('A_n_vec_n_vec_n_vec$_type',type,
'A_n_vec_n_vec_n_vec$': $tType ).
thf('A_n_vec_set_a_n_vec_set_fun$_type',type,
'A_n_vec_set_a_n_vec_set_fun$': $tType ).
thf('A_set_a_set_fun$_type',type,
'A_set_a_set_fun$': $tType ).
thf('A_a_m_vec_fun$_type',type,
'A_a_m_vec_fun$': $tType ).
thf('A_n_vec_bool_fun$_type',type,
'A_n_vec_bool_fun$': $tType ).
thf('N_a_m_vec_bool_fun_fun$_type',type,
'N_a_m_vec_bool_fun_fun$': $tType ).
thf('N_bool_fun$_type',type,
'N_bool_fun$': $tType ).
thf('M_a_m_vec_n_vec_fun$_type',type,
'M_a_m_vec_n_vec_fun$': $tType ).
thf('uwc$_decl',type,
'uwc$': 'A_a_m_vec_fun$' > 'A_n_vec_m_vec$' > 'M$' > 'N_a_m_vec_fun$' ).
thf('uxr$_decl',type,
'uxr$': 'A_n_vec_bool_fun$' ).
thf('least$_decl',type,
'least$': 'M_bool_fun$' > 'M$' ).
thf('one$d_decl',type,
'one$d': 'A_set$' ).
thf('interchange_columns_row$_decl',type,
'interchange_columns_row$': 'A_m_vec_n_vec$' > 'M$' > 'M$' > 'N_a_m_vec_fun$' ).
thf('fun_app$n_decl',type,
'fun_app$n': 'A_a_a_fun_fun$' > 'A$' > 'A_a_fun$' ).
thf('uxv$_decl',type,
'uxv$': 'A_n_vec$' > 'A_n_vec_set$' > 'A_n_vec_bool_fun$' ).
thf('uvy$_decl',type,
'uvy$': 'A_m_vec_m_vec$' > 'M$' > 'A$' > 'M$' > 'M_a_fun$' ).
thf('column$g_decl',type,
'column$g': 'N$' > 'A_n_vec_n_vec_m_vec$' > 'A_n_vec_m_vec$' ).
thf('map_matrix$b_decl',type,
'map_matrix$b': 'A_a_fun$' > 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
thf('uwa$_decl',type,
'uwa$': 'A_n_vec_n_vec$' > 'N$' > 'A$' > 'N$' > 'N_a_fun$' ).
thf('uvh$_decl',type,
'uvh$': 'A_m_vec$' > 'A_m_vec$' > 'M_a_fun$' ).
thf('uuk$_decl',type,
'uuk$': 'A_m_vec_set$' > 'A_m_vec_bool_fun$' ).
thf('fun_app$p_decl',type,
'fun_app$p': 'A_bool_fun$' > 'A$' > $o ).
thf('uvm$_decl',type,
'uvm$': 'M$' > 'A_m_vec_m_vec_n_vec$' > 'N_a_m_vec_fun$' ).
thf('uxc$_decl',type,
'uxc$': 'A_m_vec_m_vec$' > 'M$' > 'M_bool_fun$' ).
thf('fun_app$e_decl',type,
'fun_app$e': 'A_n_vec_bool_fun$' > 'A_n_vec$' > $o ).
thf('uxu$_decl',type,
'uxu$': 'A_n_vec$' > 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' ).
thf('zero$b_decl',type,
'zero$b': 'A_n_vec$' ).
thf('vec_nth$d_decl',type,
'vec_nth$d': 'A_n_vec_m_vec$' > 'M_a_n_vec_fun$' ).
thf('uup$_decl',type,
'uup$': 'A_n_vec_a_n_vec_fun$' ).
thf('map_matrix$c_decl',type,
'map_matrix$c': 'A_a_fun$' > 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
thf('dependent$b_decl',type,
'dependent$b': 'A_a_m_vec_a_m_vec_fun_fun$' > 'A_m_vec_set$' > $o ).
thf('bot$e_decl',type,
'bot$e': 'A_n_vec_bool_fun$' ).
thf('uue$_decl',type,
'uue$': 'A_a_fun$' ).
thf('times$k_decl',type,
'times$k': 'A_set_set$' > 'A_set_set$' > 'A_set_set$' ).
thf('uum$_decl',type,
'uum$': 'A_n_vec_set$' > 'A_n_vec_bool_fun$' ).
thf('member$a_decl',type,
'member$a': 'A_m_vec$' > 'A_m_vec_set$' > $o ).
thf('uvf$_decl',type,
'uvf$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).
thf('uuw$_decl',type,
'uuw$': 'M_bool_fun$' ).
thf('reduced_row_echelon_form$_decl',type,
'reduced_row_echelon_form$': 'A_m_vec_n_vec$' > $o ).
thf('interchange_rows_row$_decl',type,
'interchange_rows_row$': 'A_m_vec_n_vec$' > 'N$' > 'N$' > 'N_a_m_vec_fun$' ).
thf('fun_app$y_decl',type,
'fun_app$y': 'A_m_vec_a_fun$' > 'A_m_vec$' > 'A$' ).
thf('uxs$_decl',type,
'uxs$': 'A_n_vec_set$' > 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' ).
thf('fun_app$l_decl',type,
'fun_app$l': 'A_set_a_set_fun$' > 'A_set$' > 'A_set$' ).
thf('uvp$_decl',type,
'uvp$': 'N$' > 'A_n_vec_n_vec$' > 'N_a_fun$' ).
thf('uvt$_decl',type,
'uvt$': 'N_a_fun$' ).
thf('uvs$_decl',type,
'uvs$': 'M_a_fun$' ).
thf('bot$b_decl',type,
'bot$b': 'A_set$' ).
thf('collect$c_decl',type,
'collect$c': 'A_n_vec_bool_fun$' > 'A_n_vec_set$' ).
thf('bot$_decl',type,
'bot$': 'A_n_vec_set$' ).
thf('column$b_decl',type,
'column$b': 'N$' > 'A_n_vec_m_vec$' > 'A_m_vec$' ).
thf('one$c_decl',type,
'one$c': 'A_n_vec$' ).
thf('vec_nth$i_decl',type,
'vec_nth$i': 'A_m_vec_n_vec_m_vec$' > 'M$' > 'A_m_vec_n_vec$' ).
thf('minus$c_decl',type,
'minus$c': 'A_n_vec_a_n_vec_a_n_vec_fun_fun$' ).
thf('fun_app$t_decl',type,
'fun_app$t': 'M_a_m_vec_fun$' > 'M$' > 'A_m_vec$' ).
thf('uvo$_decl',type,
'uvo$': 'M$' > 'A_m_vec_m_vec$' > 'M_a_fun$' ).
thf('uyd$_decl',type,
'uyd$': 'N_set$' > 'N_bool_fun$' ).
thf('map_matrix$e_decl',type,
'map_matrix$e': 'A_n_vec_a_fun$' > 'A_n_vec_n_vec_m_vec$' > 'A_n_vec_m_vec$' ).
thf('zero$e_decl',type,
'zero$e': 'A_n_vec_m_vec$' ).
thf('uwq$_decl',type,
'uwq$': 'A_n_vec_a_fun$' > 'A_n_vec_m_vec_n_vec$' > 'N$' > 'M_a_fun$' ).
thf('zero$d_decl',type,
'zero$d': 'A_m_vec_m_vec$' ).
thf('uxm$_decl',type,
'uxm$': 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' ).
thf('uvd$_decl',type,
'uvd$': 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' > 'M_a_m_vec_fun$' ).
thf('one$h_decl',type,
'one$h': 'A_n_vec_n_vec$' ).
thf('member$e_decl',type,
'member$e': 'A_set$' > 'A_set_set$' > $o ).
thf('a$_decl',type,
'a$': 'A_m_vec_n_vec$' ).
thf('is_zero_row$_decl',type,
'is_zero_row$': 'N$' > 'A_m_vec_n_vec$' > $o ).
thf('uwm$_decl',type,
'uwm$': 'A_a_fun$' > 'A_m_vec_n_vec$' > 'N$' > 'M_a_fun$' ).
thf('uvl$_decl',type,
'uvl$': 'N$' > 'A_m_vec_n_vec_n_vec$' > 'N_a_m_vec_fun$' ).
thf('mult_row_row$b_decl',type,
'mult_row_row$b': 'A_m_vec_m_vec$' > 'M$' > 'A$' > 'M_a_m_vec_fun$' ).
thf('minus$e_decl',type,
'minus$e': 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' ).
thf('map_matrix$g_decl',type,
'map_matrix$g': 'A_n_vec_a_fun$' > 'A_n_vec_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
thf('insert$a_decl',type,
'insert$a': 'N$' > 'N_set$' > 'N_set$' ).
thf('vec_nth$c_decl',type,
'vec_nth$c': 'A_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).
thf('vec_nth$j_decl',type,
'vec_nth$j': 'A_n_vec_n_vec_m_vec$' > 'M$' > 'A_n_vec_n_vec$' ).
thf('less_eq$c_decl',type,
'less_eq$c': 'A_set$' > 'A_set$' > $o ).
thf('uvj$_decl',type,
'uvj$': 'N$' > 'M_bool_fun$' ).
thf('vec_lambda$e_decl',type,
'vec_lambda$e': 'N_a_n_vec_fun$' > 'A_n_vec_n_vec$' ).
thf('uuf$_decl',type,
'uuf$': 'A_n_vec_a_n_vec_bool_fun_fun$' ).
thf('less_eq$_decl',type,
'less_eq$': 'A_n_vec_set$' > 'A_n_vec_set_bool_fun$' ).
thf('uvv$_decl',type,
'uvv$': 'A_n_vec_m_vec$' > 'N$' > 'A$' > 'M$' > 'N_a_fun$' ).
thf('times$h_decl',type,
'times$h': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
thf('row$c_decl',type,
'row$c': 'N$' > 'A_n_vec_n_vec$' > 'A_n_vec$' ).
thf('uwg$_decl',type,
'uwg$': 'A_a_fun$' > 'A_m_vec_m_vec$' > 'M$' > 'M_a_fun$' ).
thf('insert$_decl',type,
'insert$': 'A_n_vec$' > 'A_n_vec_set_a_n_vec_set_fun$' ).
thf('the$_decl',type,
'the$': 'N_bool_fun$' > 'N$' ).
thf('times$a_decl',type,
'times$a': 'A_n_vec_a_n_vec_a_n_vec_fun_fun$' ).
thf('i$_decl',type,
'i$': 'N$' ).
thf('vec_lambda$_decl',type,
'vec_lambda$': 'M_a_fun$' > 'A_m_vec$' ).
thf('uxf$_decl',type,
'uxf$': 'A_m_vec_n_vec$' > 'A_n_vec_bool_fun$' ).
thf('fun_app$j_decl',type,
'fun_app$j': 'A_n_vec_a_n_vec_a_n_vec_fun_fun$' > 'A_n_vec$' > 'A_n_vec_a_n_vec_fun$' ).
thf('vec_nth$h_decl',type,
'vec_nth$h': 'A_n_vec_m_vec_n_vec$' > 'N$' > 'A_n_vec_m_vec$' ).
thf('minus$b_decl',type,
'minus$b': 'A_n_vec_set$' > 'A_n_vec_set_a_n_vec_set_fun$' ).
thf('uuh$_decl',type,
'uuh$': 'A_n_vec_a_n_vec_bool_fun_fun$' ).
thf('finite$_decl',type,
'finite$': 'A_n_vec_set_bool_fun$' ).
thf('vec_nth$e_decl',type,
'vec_nth$e': 'A_m_vec_m_vec$' > 'M_a_m_vec_fun$' ).
thf('vec_lambda$c_decl',type,
'vec_lambda$c': 'M_a_m_vec_fun$' > 'A_m_vec_m_vec$' ).
thf('vec_lambda$b_decl',type,
'vec_lambda$b': 'N_a_m_vec_fun$' > 'A_m_vec_n_vec$' ).
thf('map_matrix$i_decl',type,
'map_matrix$i': 'A_n_vec_a_fun$' > 'A_n_vec_m_vec_n_vec$' > 'A_m_vec_n_vec$' ).
thf('collect$_decl',type,
'collect$': 'A_bool_fun$' > 'A_set$' ).
thf('y$_decl',type,
'y$': 'N$' ).
thf('fun_app$r_decl',type,
'fun_app$r': 'N_a_n_vec_fun$' > 'N$' > 'A_n_vec$' ).
thf('vec_nth$b_decl',type,
'vec_nth$b': 'A_n_vec$' > 'N_a_fun$' ).
thf('uxe$_decl',type,
'uxe$': 'A_m_vec_n_vec$' > 'N$' > 'M_bool_fun$' ).
thf('one$_decl',type,
'one$': 'A$' ).
thf('least$a_decl',type,
'least$a': 'N_bool_fun$' > 'N$' ).
thf('mult_column_row$_decl',type,
'mult_column_row$': 'A_n_vec_m_vec$' > 'N$' > 'A$' > 'M_a_n_vec_fun$' ).
thf('times$f_decl',type,
'times$f': 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' > 'A_m_vec_m_vec$' ).
thf('uut$_decl',type,
'uut$': tlbool > 'A_n_vec$' > 'A_n_vec_a_n_vec_bool_fun_fun$' ).
thf('fun_app$ac_decl',type,
'fun_app$ac': 'N_a_n_vec_bool_fun_fun$' > 'N$' > 'A_n_vec_bool_fun$' ).
thf('row$b_decl',type,
'row$b': 'M$' > 'A_n_vec_m_vec$' > 'A_n_vec$' ).
thf('uxy$_decl',type,
'uxy$': 'A_n_vec_bool_fun$' > 'A_n_vec_a_n_vec_fun$' > 'A_n_vec_bool_fun$' ).
thf('one$e_decl',type,
'one$e': 'A_n_vec_set$' ).
thf('times$e_decl',type,
'times$e': 'A_a_a_fun_fun$' ).
thf('vec_nth$_decl',type,
'vec_nth$': 'A_m_vec$' > 'M_a_fun$' ).
thf('times$g_decl',type,
'times$g': 'A_n_vec_m_vec$' > 'A_n_vec_m_vec$' > 'A_n_vec_m_vec$' ).
thf('uyk$_decl',type,
'uyk$': 'A_n_vec_a_fun$' > 'A_n_vec_set$' > 'A_n_vec_bool_fun$' ).
thf('uws$_decl',type,
'uws$': 'N_a_m_vec_fun$' ).
thf('vec_nth$a_decl',type,
'vec_nth$a': 'A_m_vec_n_vec$' > 'N_a_m_vec_fun$' ).
thf('fun_app$g_decl',type,
'fun_app$g': 'A_n_vec_set_bool_fun$' > 'A_n_vec_set$' > $o ).
thf('fun_app$o_decl',type,
'fun_app$o': 'A_m_vec_bool_fun$' > 'A_m_vec$' > $o ).
thf('uxt$_decl',type,
'uxt$': 'A_n_vec_set$' > 'A_n_vec_a_n_vec_bool_fun_fun$' > 'A_n_vec_a_n_vec_bool_fun_fun$' ).
thf('fun_app$h_decl',type,
'fun_app$h': 'A_m_vec_n_vec_a_m_vec_n_vec_fun$' > 'A_m_vec_n_vec$' > 'A_m_vec_n_vec$' ).
thf('uxi$_decl',type,
'uxi$': 'A_m_vec_n_vec$' > 'M$' > 'M$' > 'N_a_m_vec_fun$' ).
thf('fun_app$s_decl',type,
'fun_app$s': 'M_a_n_vec_fun$' > 'M$' > 'A_n_vec$' ).
thf(tltrue_decl,type,
tltrue: tlbool ).
thf('vector_scalar_mult$a_decl',type,
'vector_scalar_mult$a': 'A_a_m_vec_a_m_vec_fun_fun$' ).
thf('uuu$_decl',type,
'uuu$': tlbool > 'N$' > 'N$' > 'N_bool_fun$' ).
thf('uvg$_decl',type,
'uvg$': 'A_n_vec$' > 'A_n_vec$' > 'N_a_fun$' ).
thf('uwr$_decl',type,
'uwr$': 'A_n_vec_a_fun$' > 'A_n_vec_m_vec_n_vec$' > 'N_a_m_vec_fun$' ).
thf('map_matrix$h_decl',type,
'map_matrix$h': 'A_m_vec_a_fun$' > 'A_m_vec_m_vec_n_vec$' > 'A_m_vec_n_vec$' ).
thf('uxg$_decl',type,
'uxg$': 'A_m_vec_n_vec$' > 'M$' > 'A$' > 'N_a_m_vec_fun$' ).
thf('uwb$_decl',type,
'uwb$': 'A_m_vec_n_vec$' > 'N$' > 'A$' > 'N$' > 'M_a_fun$' ).
thf('uvn$_decl',type,
'uvn$': 'N$' > 'A_n_vec_m_vec$' > 'M_a_fun$' ).
thf('uxl$_decl',type,
'uxl$': 'A_m_vec_n_vec$' > 'A_m_vec_n_vec$' > 'N_a_m_vec_fun$' ).
thf('uus$_decl',type,
'uus$': 'A_a_fun$' ).
thf('reduced_row_echelon_form$c_decl',type,
'reduced_row_echelon_form$c': 'A_n_vec_m_vec$' > $o ).
thf('uwt$_decl',type,
'uwt$': 'N_a_fun$' ).
thf('zero$c_decl',type,
'zero$c': 'A_m_vec_n_vec$' ).
thf('uyj$_decl',type,
'uyj$': 'A_n_vec_set$' > 'A_n_vec_a_m_vec_fun$' > 'A_n_vec_bool_fun$' ).
thf('uyh$_decl',type,
'uyh$': 'A$' > 'A_n_vec$' > 'N_a_fun$' ).
thf('uxz$_decl',type,
'uxz$': 'A_n_vec$' > 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' ).
thf('one$b_decl',type,
'one$b': 'A_m_vec_n_vec$' ).
thf('less_eq$a_decl',type,
'less_eq$a': 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' > $o ).
thf('collect$a_decl',type,
'collect$a': 'A_m_vec_bool_fun$' > 'A_m_vec_set$' ).
thf('map_matrix$_decl',type,
'map_matrix$': 'A_a_fun$' > 'A_m_vec_n_vec$' > 'A_m_vec_n_vec$' ).
thf('column$a_decl',type,
'column$a': 'M$' > 'A_m_vec_m_vec$' > 'A_m_vec$' ).
thf('less$b_decl',type,
'less$b': 'A_n_vec_set$' > 'A_n_vec_set_bool_fun$' ).
thf('map_matrix$f_decl',type,
'map_matrix$f': 'A_m_vec_a_fun$' > 'A_m_vec_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
thf('uua$_decl',type,
'uua$': 'N_bool_fun$' ).
thf('dependent$_decl',type,
'dependent$': 'A_a_n_vec_a_n_vec_fun_fun$' > 'A_n_vec_set_bool_fun$' ).
thf('uwv$_decl',type,
'uwv$': 'A_m_vec_n_vec$' > 'M$' > 'M$' > 'N$' > 'M_a_fun$' ).
thf('uvk$_decl',type,
'uvk$': 'A_n_vec_bool_fun$' ).
thf('fun_app$f_decl',type,
'fun_app$f': 'A_n_vec_set_a_n_vec_set_fun$' > 'A_n_vec_set$' > 'A_n_vec_set$' ).
thf('times$d_decl',type,
'times$d': 'A_set$' > 'A_set_a_set_fun$' ).
thf('the_elem$a_decl',type,
'the_elem$a': 'A_n_vec_set$' > 'A_n_vec$' ).
thf('zero$f_decl',type,
'zero$f': 'A_n_vec_n_vec$' ).
thf('uu$_decl',type,
'uu$': 'N_bool_fun$' ).
thf('fun_app$ad_decl',type,
'fun_app$ad': 'N_a_bool_fun_fun$' > 'N$' > 'A_bool_fun$' ).
thf('column$_decl',type,
'column$': 'M$' > 'A_m_vec_n_vec$' > 'A_n_vec$' ).
thf('uye$_decl',type,
'uye$': 'A_n_vec_set$' > 'A_n_vec_bool_fun$' ).
thf('uyl$_decl',type,
'uyl$': 'A_n_vec_a_m_vec_fun$' > 'A_n_vec_set$' > 'A_n_vec_bool_fun$' ).
thf('uwn$_decl',type,
'uwn$': 'A_a_fun$' > 'A_m_vec_n_vec$' > 'N_a_m_vec_fun$' ).
thf('uug$_decl',type,
'uug$': 'N$' > 'N_bool_fun$' ).
thf('one$f_decl',type,
'one$f': 'A_m_vec_m_vec$' ).
thf('mult_column_row$a_decl',type,
'mult_column_row$a': 'A_n_vec_n_vec$' > 'N$' > 'A$' > 'N_a_n_vec_fun$' ).
thf('uwi$_decl',type,
'uwi$': 'A_a_fun$' > 'A_n_vec_m_vec$' > 'M$' > 'N_a_fun$' ).
thf('uwy$_decl',type,
'uwy$': 'A_n_vec_n_vec$' > 'N$' > 'N_bool_fun$' ).
thf('fun_app$m_decl',type,
'fun_app$m': 'A_a_fun$' > 'A$' > 'A$' ).
thf('fun_app$u_decl',type,
'fun_app$u': 'A_n_vec_a_m_vec_fun$' > 'A_n_vec$' > 'A_m_vec$' ).
thf('mult_column$_decl',type,
'mult_column$': 'A_m_vec_n_vec$' > 'M$' > 'A$' > 'A_m_vec_n_vec$' ).
thf('zero$k_decl',type,
'zero$k': 'M$' ).
thf('uwz$_decl',type,
'uwz$': 'A_n_vec_n_vec$' > 'A_n_vec_bool_fun$' ).
thf('member$c_decl',type,
'member$c': 'A$' > 'A_set$' > $o ).
thf('uwh$_decl',type,
'uwh$': 'A_a_fun$' > 'A_m_vec_m_vec$' > 'M_a_m_vec_fun$' ).
thf('uxk$_decl',type,
'uxk$': 'A_m_vec$' > 'A_m_vec$' > 'M_a_fun$' ).
thf('bot$a_decl',type,
'bot$a': 'N_set$' ).
thf('zero$j_decl',type,
'zero$j': 'N$' ).
thf('mult_row$_decl',type,
'mult_row$': 'A_m_vec_n_vec$' > 'N$' > 'A$' > 'A_m_vec_n_vec$' ).
thf('less_eq$b_decl',type,
'less_eq$b': 'M$' > 'M_bool_fun$' ).
thf('xa$_decl',type,
'xa$': 'A_n_vec$' ).
thf('mult_column_row$c_decl',type,
'mult_column_row$c': 'A_m_vec_n_vec$' > 'M$' > 'A$' > 'N_a_m_vec_fun$' ).
thf('uwu$_decl',type,
'uwu$': 'M_a_fun$' ).
thf('uvw$_decl',type,
'uvw$': 'A_n_vec_n_vec$' > 'N$' > 'A$' > 'N$' > 'N_a_fun$' ).
thf('uwp$_decl',type,
'uwp$': 'A_m_vec_a_fun$' > 'A_m_vec_m_vec_n_vec$' > 'N_a_m_vec_fun$' ).
thf('fun_app$af_decl',type,
'fun_app$af': 'N_a_m_vec_bool_fun_fun$' > 'N$' > 'A_m_vec_bool_fun$' ).
thf('uya$_decl',type,
'uya$': 'A_n_vec$' > 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' ).
thf('fun_app$ag_decl',type,
'fun_app$ag': 'A_a_n_vec_a_n_vec_fun_fun$' > 'A$' > 'A_n_vec_a_n_vec_fun$' ).
thf('uuy$_decl',type,
'uuy$': 'A_m_vec$' > 'A_m_vec_a_m_vec_fun$' ).
thf('fun_app$v_decl',type,
'fun_app$v': 'A_n_vec_a_fun$' > 'A_n_vec$' > 'A$' ).
thf('vector_scalar_mult$_decl',type,
'vector_scalar_mult$': 'A_a_n_vec_a_n_vec_fun_fun$' ).
thf('fun_app$q_decl',type,
'fun_app$q': 'A_n_vec_a_n_vec_bool_fun_fun$' > 'A_n_vec$' > 'A_n_vec_bool_fun$' ).
thf('uwk$_decl',type,
'uwk$': 'A_a_fun$' > 'A_n_vec_n_vec$' > 'N$' > 'N_a_fun$' ).
thf('uwl$_decl',type,
'uwl$': 'A_a_fun$' > 'A_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).
thf('uvq$_decl',type,
'uvq$': 'M$' > 'A_m_vec_n_vec$' > 'N_a_fun$' ).
thf('times$_decl',type,
'times$': 'A_m_vec_n_vec$' > 'A_m_vec_n_vec_a_m_vec_n_vec_fun$' ).
thf('uvx$_decl',type,
'uvx$': 'A_m_vec_n_vec$' > 'M$' > 'A$' > 'N$' > 'M_a_fun$' ).
thf('fun_app$z_decl',type,
'fun_app$z': 'A_a_m_vec_fun$' > 'A$' > 'A_m_vec$' ).
thf('fun_app$ab_decl',type,
'fun_app$ab': 'M_a_n_vec_bool_fun_fun$' > 'M$' > 'A_n_vec_bool_fun$' ).
thf('reduced_row_echelon_form$a_decl',type,
'reduced_row_echelon_form$a': 'A_n_vec_n_vec_n_vec$' > $o ).
thf('column$f_decl',type,
'column$f': 'N$' > 'A_n_vec_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
thf('columns$_decl',type,
'columns$': 'A_m_vec_n_vec$' > 'A_n_vec_set$' ).
thf('uwe$_decl',type,
'uwe$': 'A_a_m_vec_fun$' > 'A_n_vec_n_vec$' > 'N$' > 'N_a_m_vec_fun$' ).
thf('fun_app$a_decl',type,
'fun_app$a': 'M_a_fun$' > 'M$' > 'A$' ).
thf('mult_row_row$c_decl',type,
'mult_row_row$c': 'A_m_vec_n_vec$' > 'N$' > 'A$' > 'N_a_m_vec_fun$' ).
thf('minus$d_decl',type,
'minus$d': 'A_m_vec_n_vec$' > 'A_m_vec_n_vec$' > 'A_m_vec_n_vec$' ).
thf('mult_row_row$a_decl',type,
'mult_row_row$a': 'A_n_vec_n_vec$' > 'N$' > 'A$' > 'N_a_n_vec_fun$' ).
thf('reduced_row_echelon_form$b_decl',type,
'reduced_row_echelon_form$b': 'A_n_vec_n_vec_m_vec$' > $o ).
thf('is_singleton$_decl',type,
'is_singleton$': 'A_n_vec_set_bool_fun$' ).
thf('uww$_decl',type,
'uww$': 'A_m_vec_n_vec$' > 'N$' > 'N$' > 'N$' > 'M_a_fun$' ).
thf('uxd$_decl',type,
'uxd$': 'A_m_vec_m_vec$' > 'A_m_vec_bool_fun$' ).
thf('column$d_decl',type,
'column$d': 'N$' > 'A_m_vec_n_vec_n_vec$' > 'A_m_vec_n_vec$' ).
thf('reduced_row_echelon_form$e_decl',type,
'reduced_row_echelon_form$e': 'A_n_vec_n_vec$' > $o ).
thf('vec_nth$k_decl',type,
'vec_nth$k': 'A_n_vec_n_vec_n_vec$' > 'N$' > 'A_n_vec_n_vec$' ).
thf('uvi$_decl',type,
'uvi$': 'A_m_vec_n_vec$' > 'A_m_vec_n_vec$' > 'N_a_m_vec_fun$' ).
thf('b$_decl',type,
'b$': 'N$' ).
thf('interchange_rows$_decl',type,
'interchange_rows$': 'A_m_vec_n_vec$' > 'N$' > 'N$' > 'A_m_vec_n_vec$' ).
thf('map_matrix$a_decl',type,
'map_matrix$a': 'A_a_fun$' > 'A_n_vec_m_vec$' > 'A_n_vec_m_vec$' ).
thf('uxj$_decl',type,
'uxj$': 'A_n_vec$' > 'A_n_vec$' > 'N_a_fun$' ).
thf('dependent$a_decl',type,
'dependent$a': 'A_a_a_fun_fun$' > 'A_set$' > $o ).
thf('zero$_decl',type,
'zero$': 'A$' ).
thf('zero$g_decl',type,
'zero$g': 'A_n_vec_set$' ).
thf('column$e_decl',type,
'column$e': 'M$' > 'A_m_vec_m_vec_n_vec$' > 'A_m_vec_n_vec$' ).
thf('col_space$_decl',type,
'col_space$': 'A_m_vec_n_vec$' > 'A_n_vec_set$' ).
thf('column$c_decl',type,
'column$c': 'N$' > 'A_n_vec_n_vec$' > 'A_n_vec$' ).
thf(tlfalse_decl,type,
tlfalse: tlbool ).
thf('uve$_decl',type,
'uve$': 'A_n_vec_m_vec$' > 'A_n_vec_m_vec$' > 'M_a_n_vec_fun$' ).
thf('uuc$_decl',type,
'uuc$': 'A_n_vec_a_n_vec_fun$' ).
thf('fun_app$c_decl',type,
'fun_app$c': 'N_bool_fun$' > 'N$' > $o ).
thf('fun_app$d_decl',type,
'fun_app$d': 'N_a_fun$' > 'N$' > 'A$' ).
thf('one$a_decl',type,
'one$a': 'A_m_vec$' ).
thf('uyc$_decl',type,
'uyc$': 'A_n_vec_set$' > 'A_n_vec_a_fun$' > 'A_n_vec_a_fun$' > 'A_n_vec_bool_fun$' ).
thf('times$b_decl',type,
'times$b': 'A_m_vec$' > 'A_m_vec_a_m_vec_fun$' ).
thf('minus$_decl',type,
'minus$': 'A_m_vec$' > 'A_m_vec_a_m_vec_fun$' ).
thf('zero$i_decl',type,
'zero$i': 'A_set$' ).
thf('uwx$_decl',type,
'uwx$': 'A_m_vec_n_vec$' > 'A_m_vec_bool_fun$' ).
thf('minus$a_decl',type,
'minus$a': 'A$' > 'A_a_fun$' ).
thf('uxx$_decl',type,
'uxx$': 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' > 'A_n_vec_a_n_vec_a_n_vec_fun_fun$' > 'A_n_vec_bool_fun$' ).
thf('uuo$_decl',type,
'uuo$': 'A_m_vec_a_m_vec_fun$' ).
thf('fun_app$b_decl',type,
'fun_app$b': 'N_a_m_vec_fun$' > 'N$' > 'A_m_vec$' ).
thf('x$_decl',type,
'x$': 'A_n_vec$' ).
thf('uxw$_decl',type,
'uxw$': 'A_n_vec_set$' > 'A_n_vec_set$' > 'A_n_vec_bool_fun$' ).
thf('times$j_decl',type,
'times$j': 'A_m_vec_set$' > 'A_m_vec_set$' > 'A_m_vec_set$' ).
thf('insert$b_decl',type,
'insert$b': 'A$' > 'A_set$' > 'A_set$' ).
thf('uyb$_decl',type,
'uyb$': 'A_n_vec_set$' > 'A_n_vec_a_fun$' > 'A_n_vec_bool_fun$' ).
thf('uui$_decl',type,
'uui$': 'N$' > 'N_bool_fun$' ).
thf('row$_decl',type,
'row$': 'N$' > 'A_m_vec_n_vec$' > 'A_m_vec$' ).
thf('row$a_decl',type,
'row$a': 'M$' > 'A_m_vec_m_vec$' > 'A_m_vec$' ).
thf('less$a_decl',type,
'less$a': 'M$' > 'M_bool_fun$' ).
thf('fun_app$_decl',type,
'fun_app$': 'M_bool_fun$' > 'M$' > $o ).
thf('map_matrix$d_decl',type,
'map_matrix$d': 'A_m_vec_a_fun$' > 'A_m_vec_n_vec_m_vec$' > 'A_n_vec_m_vec$' ).
thf('fun_app$i_decl',type,
'fun_app$i': 'A_n_vec_a_n_vec_fun$' > 'A_n_vec$' > 'A_n_vec$' ).
thf('sum$_decl',type,
'sum$': 'A_n_vec_a_fun$' > 'A_n_vec_set$' > 'A$' ).
thf('uvu$_decl',type,
'uvu$': 'A_m_vec_m_vec$' > 'M$' > 'A$' > 'M$' > 'M_a_fun$' ).
thf('uwo$_decl',type,
'uwo$': 'A_m_vec_a_fun$' > 'A_m_vec_m_vec_n_vec$' > 'N$' > 'M_a_fun$' ).
thf('the_elem$_decl',type,
'the_elem$': 'N_set$' > 'N$' ).
thf('uym$_decl',type,
'uym$': 'A_m_vec_n_vec$' > 'N$' > 'N$' > 'N_a_m_vec_fun$' ).
thf('v$_decl',type,
'v$': 'A_n_vec$' ).
thf('vec_nth$f_decl',type,
'vec_nth$f': 'A_m_vec_n_vec_n_vec$' > 'N$' > 'A_m_vec_n_vec$' ).
thf('member$_decl',type,
'member$': 'A_n_vec$' > 'A_n_vec_set_bool_fun$' ).
thf('uvc$_decl',type,
'uvc$': 'A$' > 'A_a_fun$' ).
thf('uva$_decl',type,
'uva$': 'A_set$' > 'A_set_a_set_fun$' ).
thf('vec_lambda$d_decl',type,
'vec_lambda$d': 'M_a_n_vec_fun$' > 'A_n_vec_m_vec$' ).
thf('fun_app$aa_decl',type,
'fun_app$aa': 'M_a_m_vec_bool_fun_fun$' > 'M$' > 'A_m_vec_bool_fun$' ).
thf('mult_column_row$b_decl',type,
'mult_column_row$b': 'A_m_vec_m_vec$' > 'M$' > 'A$' > 'M_a_m_vec_fun$' ).
thf('uxa$_decl',type,
'uxa$': 'A_n_vec_m_vec$' > 'M$' > 'N_bool_fun$' ).
thf('uyf$_decl',type,
'uyf$': 'A$' > 'A_m_vec$' > 'M_a_fun$' ).
thf('sum$a_decl',type,
'sum$a': 'A_n_vec_a_m_vec_fun$' > 'A_n_vec_set$' > 'A_m_vec$' ).
thf('uxh$_decl',type,
'uxh$': 'A_m_vec_n_vec$' > 'N$' > 'A$' > 'N_a_m_vec_fun$' ).
thf('uxb$_decl',type,
'uxb$': 'A_n_vec_m_vec$' > 'A_m_vec_bool_fun$' ).
thf('uwj$_decl',type,
'uwj$': 'A_a_fun$' > 'A_n_vec_m_vec$' > 'M_a_n_vec_fun$' ).
thf('the$a_decl',type,
'the$a': 'A_n_vec_bool_fun$' > 'A_n_vec$' ).
thf('uyg$_decl',type,
'uyg$': 'A_m_vec$' > 'A_m_vec_n_vec$' > 'N_a_m_vec_fun$' ).
thf('times$c_decl',type,
'times$c': 'A_n_vec_set$' > 'A_n_vec_set_a_n_vec_set_fun$' ).
thf('fun_app$k_decl',type,
'fun_app$k': 'A_m_vec_a_m_vec_fun$' > 'A_m_vec$' > 'A_m_vec$' ).
thf('one$g_decl',type,
'one$g': 'A_n_vec_m_vec$' ).
thf('uvz$_decl',type,
'uvz$': 'A_n_vec_m_vec$' > 'M$' > 'A$' > 'M$' > 'N_a_fun$' ).
thf('finite$a_decl',type,
'finite$a': 'A_set$' > $o ).
thf('uud$_decl',type,
'uud$': 'A_m_vec_a_m_vec_fun$' ).
thf('uxn$_decl',type,
'uxn$': 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' > 'A_n_vec_bool_fun$' ).
thf('uuz$_decl',type,
'uuz$': 'A_n_vec_a_n_vec_a_n_vec_fun_fun$' ).
thf('vec_nth$g_decl',type,
'vec_nth$g': 'A_m_vec_m_vec_n_vec$' > 'N$' > 'A_m_vec_m_vec$' ).
thf('fun_app$ah_decl',type,
'fun_app$ah': 'A_a_m_vec_a_m_vec_fun_fun$' > 'A$' > 'A_m_vec_a_m_vec_fun$' ).
thf('less$_decl',type,
'less$': 'N$' > 'N_bool_fun$' ).
thf('vec_lambda$a_decl',type,
'vec_lambda$a': 'N_a_fun$' > 'A_n_vec$' ).
thf('uuj$_decl',type,
'uuj$': 'A_set$' > 'A_bool_fun$' ).
thf('mult_row_row$_decl',type,
'mult_row_row$': 'A_n_vec_m_vec$' > 'M$' > 'A$' > 'M_a_n_vec_fun$' ).
thf('uyi$_decl',type,
'uyi$': 'A_n_vec_set$' > 'A_n_vec_a_fun$' > 'A_n_vec_bool_fun$' ).
thf('uuv$_decl',type,
'uuv$': 'M_bool_fun$' ).
thf('reduced_row_echelon_form$d_decl',type,
'reduced_row_echelon_form$d': 'A_m_vec_m_vec$' > $o ).
thf('uuq$_decl',type,
'uuq$': 'A_set_a_set_fun$' ).
thf('vector_scalar_mult$b_decl',type,
'vector_scalar_mult$b': 'A_m_vec$' > 'A_m_vec_n_vec$' > 'A_m_vec_n_vec$' ).
thf('fun_app$ae_decl',type,
'fun_app$ae': 'M_a_bool_fun_fun$' > 'M$' > 'A_bool_fun$' ).
thf('zero$a_decl',type,
'zero$a': 'A_m_vec$' ).
thf(37,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
<=> ( ( A != B )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom749) ).
thf(892,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( ( A != B )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) )
& ( ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
=> ( ( A != B )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(408,axiom,
! [A: 'A_n_vec_bool_fun$'] :
( ( 'bot$'
= ( A @ 'collect$c' ) )
<=> ! [B: 'A_n_vec$'] :
~ ( B @ ( A @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom491) ).
thf(2630,plain,
! [A: 'A_n_vec_bool_fun$'] :
( ( ! [B: 'A_n_vec$'] :
~ ( B @ ( A @ 'fun_app$e' ) )
=> ( 'bot$'
= ( A @ 'collect$c' ) ) )
& ( ( 'bot$'
= ( A @ 'collect$c' ) )
=> ! [B: 'A_n_vec$'] :
~ ( B @ ( A @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(176,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuh$' @ 'fun_app$q' ) @ 'collect$c' )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom490) ).
thf(1501,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuh$' @ 'fun_app$q' ) @ 'collect$c' )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(136,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom495) ).
thf(1337,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(645,axiom,
! [A: 'M$',B: 'A_n_vec_m_vec$'] :
( ( B @ ( A @ 'row$b' ) )
= ( A @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom384) ).
thf(3883,plain,
! [A: 'M$',B: 'A_n_vec_m_vec$'] :
( ( B @ ( A @ 'row$b' ) )
= ( A @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(598,axiom,
? [A: 'A_n_vec$'] :
( ( ( 'i$' @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( 'uvk$' @ 'collect$c' @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom370) ).
thf(3661,plain,
? [A: 'A_n_vec$'] :
( ( ( 'i$' @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( 'uvk$' @ 'collect$c' @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(599,axiom,
! [A: 'A_set$'] :
( ( A @ ( 'zero$' @ 'member$c' ) )
=> ( A @ ( 'times$e' @ 'dependent$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom693) ).
thf(3666,plain,
! [A: 'A_set$'] :
( ( A @ ( 'zero$' @ 'member$c' ) )
=> ( A @ ( 'times$e' @ 'dependent$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(508,axiom,
! [A: 'A_n_vec_bool_fun$'] :
( ( ( A @ 'collect$c' )
= 'bot$' )
<=> ! [B: 'A_n_vec$'] :
~ ( B @ ( A @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom492) ).
thf(3167,plain,
! [A: 'A_n_vec_bool_fun$'] :
( ( ! [B: 'A_n_vec$'] :
~ ( B @ ( A @ 'fun_app$e' ) )
=> ( ( A @ 'collect$c' )
= 'bot$' ) )
& ( ( ( A @ 'collect$c' )
= 'bot$' )
=> ! [B: 'A_n_vec$'] :
~ ( B @ ( A @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(455,axiom,
! [A: 'A_n_vec_a_m_vec_fun$'] :
( ( 'bot$' @ ( A @ 'sum$a' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom715) ).
thf(2921,plain,
! [A: 'A_n_vec_a_m_vec_fun$'] :
( ( 'bot$' @ ( A @ 'sum$a' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(369,axiom,
! [A: 'M_bool_fun$',B: 'M$'] :
( ( ( B @ ( A @ 'fun_app$' ) )
& ? [C: 'M$'] :
( ! [D: 'M$'] :
( ( ! [E: 'M$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D = C ) )
& ! [D: 'M$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) ) )
=> ( B @ ( A @ 'least$' @ 'less_eq$b' @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom637) ).
thf(2427,plain,
! [A: 'M_bool_fun$',B: 'M$'] :
( ( ( B @ ( A @ 'fun_app$' ) )
& ? [C: 'M$'] :
( ! [D: 'M$'] :
( ( ! [E: 'M$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D = C ) )
& ! [D: 'M$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) ) )
=> ( B @ ( A @ 'least$' @ 'less_eq$b' @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(392,axiom,
! [A: 'A_m_vec$',B: 'A$',C: 'A$'] :
( ( ( ( A @ ( B @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= ( A @ ( C @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) ) )
& ( A != 'zero$a' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom691) ).
thf(2544,plain,
! [A: 'A_m_vec$',B: 'A$',C: 'A$'] :
( ( ( ( A @ ( B @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= ( A @ ( C @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) ) )
& ( A != 'zero$a' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(102,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ~ ( A @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) )
=> ~ ( B @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom686) ).
thf(1179,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ~ ( A @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) )
=> ~ ( B @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(258,axiom,
! [A: 'A_m_vec$'] :
( ( A @ ( 'zero$a' @ 'times$b' @ 'fun_app$k' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom137) ).
thf(1950,plain,
! [A: 'A_m_vec$'] :
( ( A @ ( 'zero$a' @ 'times$b' @ 'fun_app$k' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(320,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_fun$',C: 'A_n_vec_a_fun$'] :
( ( ( C @ ( A @ 'uyb$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'uyb$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'uyc$' ) ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom606) ).
thf(2199,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_fun$',C: 'A_n_vec_a_fun$'] :
( ( ( C @ ( A @ 'uyb$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'uyb$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'uyc$' ) ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(481,axiom,
! [A: 'N$'] :
( ( A @ ( 'zero$c' @ 'vec_nth$a' @ 'fun_app$b' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom134) ).
thf(3021,plain,
! [A: 'N$'] :
( ( A @ ( 'zero$c' @ 'vec_nth$a' @ 'fun_app$b' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(204,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom568) ).
thf(1665,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(689,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_n_vec_m_vec$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$e' ) @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$j' ) @ 'vec_nth$c' @ 'fun_app$r' ) @ ( A @ 'fun_app$v' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom204) ).
thf(4094,plain,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_n_vec_m_vec$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$e' ) @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$j' ) @ 'vec_nth$c' @ 'fun_app$r' ) @ ( A @ 'fun_app$v' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(67,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) )
=> ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom599) ).
thf(1024,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) )
=> ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(167,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom569) ).
thf(1469,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(100,axiom,
! [A: 'A_n_vec$'] :
( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) )
<=> ( A = 'zero$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom682) ).
thf(1168,plain,
! [A: 'A_n_vec$'] :
( ( ( A = 'zero$b' )
=> ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) )
& ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) )
=> ( A = 'zero$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(487,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom308) ).
thf(3053,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(130,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom563) ).
thf(1315,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(400,axiom,
! [A: 'A$'] :
( ( 'zero$a' @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom659) ).
thf(2595,plain,
! [A: 'A$'] :
( ( 'zero$a' @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(384,axiom,
! [A: 'M_a_n_vec_fun$',B: 'M$'] :
( ( B @ ( A @ 'vec_lambda$d' @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( B @ ( A @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom356) ).
thf(2495,plain,
! [A: 'M_a_n_vec_fun$',B: 'M$'] :
( ( B @ ( A @ 'vec_lambda$d' @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( B @ ( A @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(485,axiom,
! [A: 'M$'] :
( ( A @ ( 'one$g' @ 'vec_nth$d' @ 'fun_app$s' ) )
= 'one$c' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom244) ).
thf(3040,plain,
! [A: 'M$'] :
( ( A @ ( 'one$g' @ 'vec_nth$d' @ 'fun_app$s' ) )
= 'one$c' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(152,axiom,
! [A: 'A_n_vec_set$'] : ( A @ ( A @ 'less_eq$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom609) ).
thf(1401,plain,
! [A: 'A_n_vec_set$'] : ( A @ ( A @ 'less_eq$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(661,axiom,
! [A: 'A_n_vec_m_vec$',B: 'N$',C: 'A$',D: 'M$',E: 'N$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$' ) ) @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$' ) ) @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom339) ).
thf(3959,plain,
! [A: 'A_n_vec_m_vec$',B: 'N$',C: 'A$',D: 'M$',E: 'N$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$' ) ) @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$' ) ) @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(651,axiom,
! [A: 'A$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uyh$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom58) ).
thf(3912,plain,
! [A: 'A$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uyh$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(92,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_m_vec_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( D @ ( C @ 'fun_app$u' ) )
= 'zero$a' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( B @ ( C @ 'sum$a' ) )
= ( A @ ( C @ 'sum$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom723) ).
thf(1142,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_m_vec_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( D @ ( C @ 'fun_app$u' ) )
= 'zero$a' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( B @ ( C @ 'sum$a' ) )
= ( A @ ( C @ 'sum$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(442,axiom,
! [A: 'M$'] :
( ( A @ ( 'one$a' @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom247) ).
thf(2854,plain,
! [A: 'M$'] :
( ( A @ ( 'one$a' @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(549,axiom,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$',D: 'N$',E: 'M$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$c' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$c' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom342) ).
thf(3382,plain,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$',D: 'N$',E: 'M$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$c' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$c' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(238,axiom,
! [A: 'M_bool_fun$',B: 'M$',C: 'M_bool_fun$'] :
( ( ! [D: 'M$'] :
( ( ! [E: 'M$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ! [D: 'M$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( B @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom639) ).
thf(1855,plain,
! [A: 'M_bool_fun$',B: 'M$',C: 'M_bool_fun$'] :
( ( ! [D: 'M$'] :
( ( ! [E: 'M$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ! [D: 'M$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( B @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(602,axiom,
! [A: 'A_m_vec$'] :
( ( A @ ( 'zero$' @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom672) ).
thf(3680,plain,
! [A: 'A_m_vec$'] :
( ( A @ ( 'zero$' @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(576,axiom,
( ( 'uua$' @ 'the$' )
= 'i$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom122) ).
thf(3534,plain,
( ( 'uua$' @ 'the$' )
= 'i$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(217,axiom,
! [A: 'A_m_vec_set$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'uuk$' @ 'fun_app$o' ) )
<=> ( A @ ( B @ 'member$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).
thf(1750,plain,
! [A: 'A_m_vec_set$',B: 'A_m_vec$'] :
( ( ( A @ ( B @ 'member$a' ) )
=> ( B @ ( A @ 'uuk$' @ 'fun_app$o' ) ) )
& ( ( B @ ( A @ 'uuk$' @ 'fun_app$o' ) )
=> ( A @ ( B @ 'member$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(510,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom296) ).
thf(3185,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(676,axiom,
! [A: 'A_set$'] :
( ~ ( A @ ( 'times$e' @ 'dependent$a' ) )
=> ( A @ 'finite$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom697) ).
thf(4037,plain,
! [A: 'A_set$'] :
( ~ ( A @ ( 'times$e' @ 'dependent$a' ) )
=> ( A @ 'finite$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(11,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$' ) ) )
= ( C @ ( B @ ( A @ 'uym$' ) ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom734) ).
thf(762,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$' ) ) )
= ( C @ ( B @ ( A @ 'uym$' ) ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(461,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( B @ ( C @ ( B @ ( A @ 'interchange_rows$' ) ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom736) ).
thf(2940,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( B @ ( C @ ( B @ ( A @ 'interchange_rows$' ) ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(154,axiom,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec_m_vec$'] :
( ( B @ ( A @ 'times$f' ) )
= ( B @ ( A @ 'uvd$' ) @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom349) ).
thf(1406,plain,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec_m_vec$'] :
( ( B @ ( A @ 'times$f' ) )
= ( B @ ( A @ 'uvd$' ) @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(299,axiom,
( 'uup$'
= ( 'one$c' @ ( 'times$a' @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom277) ).
thf(2104,plain,
( 'uup$'
= ( 'one$c' @ ( 'times$a' @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(414,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$' ) ) @ 'vec_nth$a' )
= ( C @ ( B @ ( A @ 'mult_row_row$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom480) ).
thf(2671,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$' ) ) @ 'vec_nth$a' )
= ( C @ ( B @ ( A @ 'mult_row_row$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(276,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'vector_scalar_mult$b' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom667) ).
thf(2014,plain,
! [A: 'A_m_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'vector_scalar_mult$b' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(297,axiom,
( 'v$'
= ( 'a$' @ ( 'uuv$' @ 'least$' @ 'column$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom329) ).
thf(2099,plain,
( 'v$'
= ( 'a$' @ ( 'uuv$' @ 'least$' @ 'column$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(339,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$'] :
( ( B @ 'collect$c' @ ( A @ 'member$' @ 'fun_app$g' ) )
<=> ( A @ ( B @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom222) ).
thf(2282,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$e' ) )
=> ( B @ 'collect$c' @ ( A @ 'member$' @ 'fun_app$g' ) ) )
& ( ( B @ 'collect$c' @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( A @ ( B @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(206,axiom,
! [A: 'A_n_vec_set$'] :
( ( 'bot$' @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom512) ).
thf(1671,plain,
! [A: 'A_n_vec_set$'] :
( ( 'bot$' @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(615,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'minus$' @ 'fun_app$k' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom457) ).
thf(3745,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'minus$' @ 'fun_app$k' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(402,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'uuz$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( A @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
thf(2607,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'uuz$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( A @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(218,axiom,
! [A: 'A_n_vec_set$'] : ( A @ ( A @ 'less_eq$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom530) ).
thf(1756,plain,
! [A: 'A_n_vec_set$'] : ( A @ ( A @ 'less_eq$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(454,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxl$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'minus$' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom35) ).
thf(2918,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxl$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'minus$' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(509,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec_a_n_vec_a_n_vec_fun_fun$',D: 'A_n_vec$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxx$' ) ) @ 'fun_app$e' ) )
<=> ? [E: 'A_n_vec$',F: 'A_n_vec$'] :
( ( F @ ( B @ 'fun_app$e' ) )
& ( E @ ( A @ 'fun_app$e' ) )
& ( D
= ( F @ ( E @ ( C @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom90) ).
thf(3175,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec_a_n_vec_a_n_vec_fun_fun$',D: 'A_n_vec$'] :
( ( ? [E: 'A_n_vec$',F: 'A_n_vec$'] :
( ( F @ ( B @ 'fun_app$e' ) )
& ( E @ ( A @ 'fun_app$e' ) )
& ( D
= ( F @ ( E @ ( C @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uxx$' ) ) @ 'fun_app$e' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uxx$' ) ) @ 'fun_app$e' ) )
=> ? [E: 'A_n_vec$',F: 'A_n_vec$'] :
( ( F @ ( B @ 'fun_app$e' ) )
& ( E @ ( A @ 'fun_app$e' ) )
& ( D
= ( F @ ( E @ ( C @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(23,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ~ ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
=> ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom745) ).
thf(814,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ~ ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
=> ( ( ( A = B )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(407,axiom,
! [A: 'A_m_vec$'] :
( ( A @ ( 'one$a' @ 'times$b' @ 'fun_app$k' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom260) ).
thf(2627,plain,
! [A: 'A_m_vec$'] :
( ( A @ ( 'one$a' @ 'times$b' @ 'fun_app$k' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(635,axiom,
! [A: 'A$',B: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' )
<=> ( ( B = 'zero$' )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom144) ).
thf(3826,plain,
! [A: 'A$',B: 'A$'] :
( ( ( ( B = 'zero$' )
| ( A = 'zero$' ) )
=> ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ) )
& ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' )
=> ( ( B = 'zero$' )
| ( A = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(220,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom618) ).
thf(1761,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(198,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwr$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( A @ 'uwq$' ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom60) ).
thf(1640,plain,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwr$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( A @ 'uwq$' ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(534,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_n_vec$',C: 'N$',D: 'N$'] :
( ( ( ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uxf$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom437) ).
thf(3313,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_n_vec$',C: 'N$',D: 'N$'] :
( ( ( ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uxf$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(310,axiom,
( 'uuc$'
= ( 'zero$b' @ ( 'times$a' @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom189) ).
thf(2146,plain,
( 'uuc$'
= ( 'zero$b' @ ( 'times$a' @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(163,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'times$c' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom478) ).
thf(1458,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'times$c' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(77,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A = B )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom533) ).
thf(1078,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A = B )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(227,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
<=> ( ( ~ ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
=> ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom600) ).
thf(1788,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( ( ( ~ ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
=> ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ) )
=> ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ( ~ ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
=> ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(516,axiom,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_column_row$c' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvx$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom399) ).
thf(3217,plain,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_column_row$c' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvx$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(629,axiom,
! [A: 'A_n_vec$'] :
( ( A @ 'vec_nth$b' @ 'vec_lambda$a' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom380) ).
thf(3794,plain,
! [A: 'A_n_vec$'] :
( ( A @ 'vec_nth$b' @ 'vec_lambda$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(192,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set_bool_fun$'] :
( ( ! [D: 'A_n_vec$',E: 'A_n_vec_set$'] :
( ( ( E @ ( C @ 'fun_app$g' ) )
& ~ ( E @ ( D @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( E @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
& ( E @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( E @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( C @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( A @ ( C @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom597) ).
thf(1608,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set_bool_fun$'] :
( ( ! [D: 'A_n_vec$',E: 'A_n_vec_set$'] :
( ( ( E @ ( C @ 'fun_app$g' ) )
& ~ ( E @ ( D @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( E @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
& ( E @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( E @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( C @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( A @ ( C @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(475,axiom,
! [A: 'A_set$',B: 'A_set$'] :
( ( B @ ( A @ 'uva$' @ 'fun_app$l' ) )
= ( A @ ( B @ 'times$d' @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12) ).
thf(3004,plain,
! [A: 'A_set$',B: 'A_set$'] :
( ( B @ ( A @ 'uva$' @ 'fun_app$l' ) )
= ( A @ ( B @ 'times$d' @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(281,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$'] :
( ( ( A @ ( B @ 'is_zero_row$' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ! [C: 'N$'] :
( ( C @ ( B @ 'less$' @ 'fun_app$c' ) )
=> ( A @ ( C @ 'is_zero_row$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom741) ).
thf(2035,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$'] :
( ( ( A @ ( B @ 'is_zero_row$' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ! [C: 'N$'] :
( ( C @ ( B @ 'less$' @ 'fun_app$c' ) )
=> ( A @ ( C @ 'is_zero_row$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(690,axiom,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'M$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvy$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvy$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom100) ).
thf(4097,plain,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'M$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvy$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvy$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(657,axiom,
! [A: 'A_n_vec_a_fun$'] :
( ( 'bot$' @ ( A @ 'sum$' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom714) ).
thf(3942,plain,
! [A: 'A_n_vec_a_fun$'] :
( ( 'bot$' @ ( A @ 'sum$' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(670,axiom,
! [A: 'A$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom668) ).
thf(4011,plain,
! [A: 'A$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(270,axiom,
'a$' @ 'reduced_row_echelon_form$',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom218) ).
thf(1999,plain,
'a$' @ 'reduced_row_echelon_form$',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(350,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( A = B )
<=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom165) ).
thf(2316,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(1,conjecture,
( ( 'i$' @ ( 'xa$' @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'uu$' @ 'the$' @ ( 'x$' @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture118) ).
thf(2,negated_conjecture,
( ( 'i$' @ ( 'xa$' @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'uu$' @ 'the$' @ ( 'x$' @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
!= 'zero$' ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(715,plain,
( ( 'i$' @ ( 'xa$' @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'uu$' @ 'the$' @ ( 'x$' @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
!= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(541,axiom,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'M$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$b' ) ) @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$b' ) ) @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom337) ).
thf(3338,plain,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'M$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$b' ) ) @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$b' ) ) @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(647,axiom,
! [A: 'A$',B: 'A$'] :
( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom305) ).
thf(3895,plain,
! [A: 'A$',B: 'A$'] :
( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(356,axiom,
! [A: 'A_n_vec_set$'] :
( ( ! [B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( A @ ( B @ 'member$' @ 'fun_app$g' ) ) )
=> ( B = C ) )
& ( A != 'bot$' ) )
=> ( A @ ( 'is_singleton$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom730) ).
thf(2360,plain,
! [A: 'A_n_vec_set$'] :
( ( ! [B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( A @ ( B @ 'member$' @ 'fun_app$g' ) ) )
=> ( B = C ) )
& ( A != 'bot$' ) )
=> ( A @ ( 'is_singleton$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(540,axiom,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec$',C: 'M$',D: 'M$'] :
( ( ( ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxd$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$d' ) )
=> ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom436) ).
thf(3335,plain,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec$',C: 'M$',D: 'M$'] :
( ( ( ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxd$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$d' ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(543,axiom,
! [A: 'A$',B: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' )
=> ( ( B = 'zero$' )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom183) ).
thf(3350,plain,
! [A: 'A$',B: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' )
=> ( ( B = 'zero$' )
| ( A = 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(668,axiom,
! [A: 'N$'] :
( ( A @ ( 'uua$' @ 'fun_app$c' ) )
<=> ( ( A @ ( 'v$' @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
thf(3994,plain,
! [A: 'N$'] :
( ( ( ( A @ ( 'v$' @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
=> ( A @ ( 'uua$' @ 'fun_app$c' ) ) )
& ( ( A @ ( 'uua$' @ 'fun_app$c' ) )
=> ( ( A @ ( 'v$' @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(15,axiom,
! [A: 'A_n_vec_set$'] :
( ( A @ ( 'one$e' @ 'times$c' @ 'fun_app$f' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom240) ).
thf(782,plain,
! [A: 'A_n_vec_set$'] :
( ( A @ ( 'one$e' @ 'times$c' @ 'fun_app$f' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(278,axiom,
! [A: 'A_m_vec$'] :
( ( A @ ( A @ 'minus$' @ 'fun_app$k' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom449) ).
thf(2020,plain,
! [A: 'A_m_vec$'] :
( ( A @ ( A @ 'minus$' @ 'fun_app$k' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(623,axiom,
! [A: 'A$'] :
( ( 'one$' @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom235) ).
thf(3777,plain,
! [A: 'A$'] :
( ( 'one$' @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(200,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( C @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
<=> ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom571) ).
thf(1645,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
=> ( C @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( C @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
=> ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(142,axiom,
! [A: 'M$',B: 'A_m_vec_m_vec$'] :
( ( B @ ( A @ 'column$a' ) )
= ( B @ ( A @ 'uvo$' ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom390) ).
thf(1359,plain,
! [A: 'M$',B: 'A_m_vec_m_vec$'] :
( ( B @ ( A @ 'column$a' ) )
= ( B @ ( A @ 'uvo$' ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(648,axiom,
~ ( 'bot$b' @ ( 'one$' @ 'insert$b' ) @ ( 'times$e' @ 'dependent$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom700) ).
thf(3898,plain,
~ ( 'bot$b' @ ( 'one$' @ 'insert$b' ) @ ( 'times$e' @ 'dependent$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(644,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uxf$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom441) ).
thf(3880,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uxf$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(171,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ ( A @ 'times$c' @ 'fun_app$f' ) @ 'times$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( A @ 'times$c' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom298) ).
thf(1482,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ ( A @ 'times$c' @ 'fun_app$f' ) @ 'times$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( A @ 'times$c' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(89,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom622) ).
thf(1127,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(652,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'zero$' @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom673) ).
thf(3915,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'zero$' @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(532,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ 'minus$a' @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom473) ).
thf(3308,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ 'minus$a' @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(696,axiom,
! [A: 'A$'] :
( ( A @ ( A @ 'minus$a' @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom448) ).
thf(4124,plain,
! [A: 'A$'] :
( ( A @ ( A @ 'minus$a' @ 'fun_app$m' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(149,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom541) ).
thf(1386,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(526,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( ( ( 'zero$k' @ ( 'zero$j' @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( A @ ( 'zero$k' @ 'column$' ) )
= 'zero$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom424) ).
thf(3281,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( ( ( 'zero$k' @ ( 'zero$j' @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( A @ ( 'zero$k' @ 'column$' ) )
= 'zero$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(364,axiom,
( 'bot$'
= ( 'uxr$' @ 'collect$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom550) ).
thf(2400,plain,
( 'bot$'
= ( 'uxr$' @ 'collect$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(437,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ 'uui$' @ 'fun_app$c' ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21) ).
thf(2825,plain,
! [A: 'N$',B: 'N$'] :
( ( ( B = A )
=> ( B @ ( A @ 'uui$' @ 'fun_app$c' ) ) )
& ( ( B @ ( A @ 'uui$' @ 'fun_app$c' ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(264,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( ( B @ ( A @ 'times$b' @ 'fun_app$k' ) )
!= 'zero$a' )
=> ( ( B != 'zero$a' )
& ( A != 'zero$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom186) ).
thf(1967,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( ( B @ ( A @ 'times$b' @ 'fun_app$k' ) )
!= 'zero$a' )
=> ( ( B != 'zero$a' )
& ( A != 'zero$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(308,axiom,
'bot$' @ ( 'finite$' @ 'fun_app$g' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom560) ).
thf(2136,plain,
'bot$' @ ( 'finite$' @ 'fun_app$g' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(118,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec_a_n_vec_a_n_vec_fun_fun$'] :
( ( ( B @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
& ( A @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'uxx$' ) ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom579) ).
thf(1265,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec_a_n_vec_a_n_vec_fun_fun$'] :
( ( ( B @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
& ( A @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'uxx$' ) ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(605,axiom,
! [A: tlbool,B: 'N$',C: 'N$'] :
( ( ( A != tltrue )
=> ( C
= ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'the$' ) ) )
& ( ( A = tltrue )
=> ( B
= ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'the$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom325) ).
thf(3688,plain,
! [A: tlbool,B: 'N$',C: 'N$'] :
( ( ( A != tltrue )
=> ( C
= ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'the$' ) ) )
& ( ( A = tltrue )
=> ( B
= ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'the$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(445,axiom,
! [A: 'A_set$'] :
( ( 'zero$i' = A )
<=> ( A = 'zero$i' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom283) ).
thf(2869,plain,
! [A: 'A_set$'] :
( ( ( A = 'zero$i' )
=> ( 'zero$i' = A ) )
& ( ( 'zero$i' = A )
=> ( A = 'zero$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(522,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ 'minus$a' @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom469) ).
thf(3263,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ 'minus$a' @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(524,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom470) ).
thf(3275,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(702,axiom,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec$',C: 'M$',D: 'M$'] :
( ( ( C != D )
& ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxd$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$d' ) )
=> ( ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom432) ).
thf(4151,plain,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec$',C: 'M$',D: 'M$'] :
( ( ( C != D )
& ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxd$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$d' ) )
=> ( ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(16,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A != B )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom735) ).
thf(785,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A != B )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(592,axiom,
! [A: 'A$',B: 'A_m_vec$'] :
( ( ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' )
<=> ( ( B = 'zero$a' )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom674) ).
thf(3617,plain,
! [A: 'A$',B: 'A_m_vec$'] :
( ( ( ( B = 'zero$a' )
| ( A = 'zero$' ) )
=> ( ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' ) )
& ( ( ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' )
=> ( ( B = 'zero$a' )
| ( A = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(503,axiom,
! [A: 'N$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'row$' ) )
= ( A @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom386) ).
thf(3148,plain,
! [A: 'N$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'row$' ) )
= ( A @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(698,axiom,
! [A: 'A_n_vec$',B: 'N_a_fun$'] :
( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'fun_app$d' ) ) )
<=> ( ( B @ 'vec_lambda$a' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom374) ).
thf(4130,plain,
! [A: 'A_n_vec$',B: 'N_a_fun$'] :
( ( ( ( B @ 'vec_lambda$a' )
= A )
=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'fun_app$d' ) ) ) )
& ( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'fun_app$d' ) ) )
=> ( ( B @ 'vec_lambda$a' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(544,axiom,
! [A: 'N$'] :
( ( A @ 'uui$' @ 'the$' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom196) ).
thf(3353,plain,
! [A: 'N$'] :
( ( A @ 'uui$' @ 'the$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(486,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ 'uxf$' @ 'fun_app$e' ) )
<=> ? [C: 'N$'] :
( ( ( A @ ( C @ 'row$' ) )
!= 'zero$a' )
& ( B
= ( A @ ( C @ ( A @ 'uxe$' ) @ 'least$' @ 'column$' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom23) ).
thf(3043,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_n_vec$'] :
( ( ? [C: 'N$'] :
( ( ( A @ ( C @ 'row$' ) )
!= 'zero$a' )
& ( B
= ( A @ ( C @ ( A @ 'uxe$' ) @ 'least$' @ 'column$' ) ) ) )
=> ( B @ ( A @ 'uxf$' @ 'fun_app$e' ) ) )
& ( ( B @ ( A @ 'uxf$' @ 'fun_app$e' ) )
=> ? [C: 'N$'] :
( ( ( A @ ( C @ 'row$' ) )
!= 'zero$a' )
& ( B
= ( A @ ( C @ ( A @ 'uxe$' ) @ 'least$' @ 'column$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(49,axiom,
! [A: 'A_n_vec_m_vec$'] :
( ( A @ 'vec_nth$d' @ 'vec_lambda$d' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom378) ).
thf(949,plain,
! [A: 'A_n_vec_m_vec$'] :
( ( A @ 'vec_nth$d' @ 'vec_lambda$d' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(419,axiom,
! [A: 'A_set$'] :
( ( A @ ( 'one$d' @ 'times$d' @ 'fun_app$l' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom262) ).
thf(2703,plain,
! [A: 'A_set$'] :
( ( A @ ( 'one$d' @ 'times$d' @ 'fun_app$l' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(633,axiom,
! [A: 'A$'] :
( ( A @ ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom242) ).
thf(3820,plain,
! [A: 'A$'] :
( ( A @ ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(195,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( C @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'insert$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom539) ).
thf(1628,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( C @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'insert$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(519,axiom,
! [A: 'A_m_vec$'] :
( ( A @ 'uuy$' )
= ( A @ 'times$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom344) ).
thf(3248,plain,
! [A: 'A_m_vec$'] :
( ( A @ 'uuy$' )
= ( A @ 'times$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(155,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( ( ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
=> $false )
& ( ( A = B )
=> $false )
& ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom546) ).
thf(1409,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
~ ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( A != B )
& ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(338,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_fun$',D: 'A_n_vec$'] :
( ( ( A @ ( C @ ( B @ 'uyi$' ) @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( ( ~ ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( C @ 'sum$' ) )
= ( B @ ( C @ 'sum$' ) ) ) )
& ( ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( C @ 'sum$' ) )
= ( D @ ( C @ 'fun_app$v' ) @ ( B @ ( C @ 'sum$' ) @ 'minus$a' @ 'fun_app$m' ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom712) ).
thf(2274,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_fun$',D: 'A_n_vec$'] :
( ( ( A @ ( C @ ( B @ 'uyi$' ) @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( ( ~ ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( C @ 'sum$' ) )
= ( B @ ( C @ 'sum$' ) ) ) )
& ( ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( C @ 'sum$' ) )
= ( D @ ( C @ 'fun_app$v' ) @ ( B @ ( C @ 'sum$' ) @ 'minus$a' @ 'fun_app$m' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(42,axiom,
! [A: 'A_n_vec_set_bool_fun$',B: 'A_n_vec_set$'] :
( ( ! [C: 'A_n_vec_set$'] :
( ( ! [D: 'A_n_vec$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'fun_app$g' ) ) )
& ( B @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( C != 'bot$' )
& ( C @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'fun_app$g' ) ) )
& ( ~ ( B @ ( 'finite$' @ 'fun_app$g' ) )
=> ( B @ ( A @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( A @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom605) ).
thf(917,plain,
! [A: 'A_n_vec_set_bool_fun$',B: 'A_n_vec_set$'] :
( ( ! [C: 'A_n_vec_set$'] :
( ( ! [D: 'A_n_vec$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'fun_app$g' ) ) )
& ( B @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( C != 'bot$' )
& ( C @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'fun_app$g' ) ) )
& ( ~ ( B @ ( 'finite$' @ 'fun_app$g' ) )
=> ( B @ ( A @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( A @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(566,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'reduced_row_echelon_form$' )
=> ! [B: 'N$'] :
( ~ ( A @ ( B @ 'is_zero_row$' ) )
=> ! [C: 'N$'] :
( ( B != C )
=> ( ( B @ ( A @ 'uxe$' ) @ 'least$' @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom705) ).
thf(3485,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'reduced_row_echelon_form$' )
=> ! [B: 'N$'] :
( ~ ( A @ ( B @ 'is_zero_row$' ) )
=> ! [C: 'N$'] :
( ( B != C )
=> ( ( B @ ( A @ 'uxe$' ) @ 'least$' @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(317,axiom,
! [A: 'A$',B: 'A$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom694) ).
thf(2185,plain,
! [A: 'A$',B: 'A$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(189,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom627) ).
thf(1577,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(451,axiom,
! [A: 'N$'] :
( ( 'zero$j' = A )
<=> ( A = 'zero$j' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom284) ).
thf(2897,plain,
! [A: 'N$'] :
( ( ( A = 'zero$j' )
=> ( 'zero$j' = A ) )
& ( ( 'zero$j' = A )
=> ( A = 'zero$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(44,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom593) ).
thf(934,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= ( C @ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(38,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ ( 'one$b' @ 'times$' @ 'fun_app$h' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom236) ).
thf(902,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ ( 'one$b' @ 'times$' @ 'fun_app$h' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(31,axiom,
! [A: 'A_n_vec_set$'] :
( ( 'one$e' = A )
<=> ( A = 'one$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom256) ).
thf(853,plain,
! [A: 'A_n_vec_set$'] :
( ( ( A = 'one$e' )
=> ( 'one$e' = A ) )
& ( ( 'one$e' = A )
=> ( A = 'one$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(443,axiom,
! [A: 'A$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( B @ ( A @ 'uyh$' ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom703) ).
thf(2857,plain,
! [A: 'A$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( B @ ( A @ 'uyh$' ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(170,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ ( A @ 'times$c' @ 'fun_app$f' ) @ 'times$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( A @ 'times$c' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom292) ).
thf(1479,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ ( A @ 'times$c' @ 'fun_app$f' ) @ 'times$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( A @ 'times$c' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(493,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uup$' @ 'fun_app$i' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).
thf(3084,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uup$' @ 'fun_app$i' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(389,axiom,
! [A: 'M$'] :
( ( A @ ( 'uvs$' @ 'fun_app$a' ) )
= 'one$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom116) ).
thf(2520,plain,
! [A: 'M$'] :
( ( A @ ( 'uvs$' @ 'fun_app$a' ) )
= 'one$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(608,axiom,
! [A: 'A$',B: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' )
<=> ( ( B = 'zero$' )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom143) ).
thf(3708,plain,
! [A: 'A$',B: 'A$'] :
( ( ( ( B = 'zero$' )
| ( A = 'zero$' ) )
=> ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ) )
& ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' )
=> ( ( B = 'zero$' )
| ( A = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(143,axiom,
( 'zero$g'
= ( 'bot$' @ ( 'zero$b' @ 'insert$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom464) ).
thf(1362,plain,
( 'zero$g'
= ( 'bot$' @ ( 'zero$b' @ 'insert$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(244,axiom,
! [A: 'M_a_m_vec_fun$',B: 'M$'] :
( ( B @ ( A @ 'vec_lambda$c' @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( B @ ( A @ 'fun_app$t' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom355) ).
thf(1875,plain,
! [A: 'M_a_m_vec_fun$',B: 'M$'] :
( ( B @ ( A @ 'vec_lambda$c' @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( B @ ( A @ 'fun_app$t' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(363,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'M$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom428) ).
thf(2388,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'M$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(237,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
<=> ! [C: 'A_n_vec$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom534) ).
thf(1847,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ! [C: 'A_n_vec$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ! [C: 'A_n_vec$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(627,axiom,
! [A: 'A$'] :
( ( A @ ( 'uue$' @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom113) ).
thf(3788,plain,
! [A: 'A$'] :
( ( A @ ( 'uue$' @ 'fun_app$m' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(637,axiom,
! [A: 'A$',B: 'A_set$',C: 'A_set$'] :
( ( ! [D: 'A$',E: 'A$'] :
( ( ( C @ ( E @ 'member$c' ) )
& ( B @ ( D @ 'member$c' ) )
& ( A
= ( E @ ( D @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) )
=> $false )
& ( C @ ( B @ 'times$d' @ 'fun_app$l' ) @ ( A @ 'member$c' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom317) ).
thf(3840,plain,
! [A: 'A$',B: 'A_set$',C: 'A_set$'] :
~ ( ! [D: 'A$',E: 'A$'] :
~ ( ( C @ ( E @ 'member$c' ) )
& ( B @ ( D @ 'member$c' ) )
& ( A
= ( E @ ( D @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) )
& ( C @ ( B @ 'times$d' @ 'fun_app$l' ) @ ( A @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(248,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$'] :
( ( ~ ( A @ ( B @ 'is_zero_row$' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( B @ ( A @ 'uxe$' ) @ 'least$' @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom707) ).
thf(1892,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$'] :
( ( ~ ( A @ ( B @ 'is_zero_row$' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( B @ ( A @ 'uxe$' ) @ 'least$' @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(712,axiom,
! [A: 'A$',B: 'A_n_vec$'] :
( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' )
<=> ( ( B = 'zero$b' )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom671) ).
thf(4194,plain,
! [A: 'A$',B: 'A_n_vec$'] :
( ( ( ( B = 'zero$b' )
| ( A = 'zero$' ) )
=> ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' ) )
& ( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' )
=> ( ( B = 'zero$b' )
| ( A = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(286,axiom,
! [A: 'A_n_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_row_row$' ) ) @ 'fun_app$s' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvz$' ) ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom401) ).
thf(2049,plain,
! [A: 'A_n_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_row_row$' ) ) @ 'fun_app$s' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvz$' ) ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(345,axiom,
! [A: 'A_set$'] :
( ( A @ ( 'uuq$' @ 'fun_app$l' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom105) ).
thf(2301,plain,
! [A: 'A_set$'] :
( ( A @ ( 'uuq$' @ 'fun_app$l' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(230,axiom,
! [A: tlbool,B: 'A_m_vec_n_vec$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'zero$c' @ 'times$' @ 'fun_app$h' ) )
= 'zero$c' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'zero$c' @ 'times$' @ 'fun_app$h' ) )
= B ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'one$b' @ 'times$' @ 'fun_app$h' ) )
= 'zero$c' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'one$b' @ 'times$' @ 'fun_app$h' ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom330) ).
thf(1815,plain,
! [A: tlbool,B: 'A_m_vec_n_vec$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'zero$c' @ 'times$' @ 'fun_app$h' ) )
= 'zero$c' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'zero$c' @ 'times$' @ 'fun_app$h' ) )
= B ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'one$b' @ 'times$' @ 'fun_app$h' ) )
= 'zero$c' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'one$b' @ 'times$' @ 'fun_app$h' ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(537,axiom,
'b$' = 'i$',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom121) ).
thf(3322,plain,
'b$' = 'i$',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(125,axiom,
! [A: 'A_n_vec$'] : ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( 'is_singleton$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom729) ).
thf(1302,plain,
! [A: 'A_n_vec$'] : ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( 'is_singleton$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(513,axiom,
! [A: 'A_m_vec$'] :
( ( 'zero$a' @ ( A @ 'times$b' @ 'fun_app$k' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom141) ).
thf(3199,plain,
! [A: 'A_m_vec$'] :
( ( 'zero$a' @ ( A @ 'times$b' @ 'fun_app$k' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(294,axiom,
! [A: 'A$',B: 'A_m_vec$'] :
( ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= ( B @ ( A @ 'uyf$' ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom701) ).
thf(2090,plain,
! [A: 'A$',B: 'A_m_vec$'] :
( ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= ( B @ ( A @ 'uyf$' ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(529,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwy$' ) @ 'fun_app$c' ) )
<=> ( ( C @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom68) ).
thf(3295,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( ( ( C @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
=> ( C @ ( B @ ( A @ 'uwy$' ) @ 'fun_app$c' ) ) )
& ( ( C @ ( B @ ( A @ 'uwy$' ) @ 'fun_app$c' ) )
=> ( ( C @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(83,axiom,
! [A: 'A_n_vec$'] : ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom507) ).
thf(1109,plain,
! [A: 'A_n_vec$'] : ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(335,axiom,
! [A: 'A_m_vec$'] :
( ( A @ ( 'uud$' @ 'fun_app$k' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom109) ).
thf(2259,plain,
! [A: 'A_m_vec$'] :
( ( A @ ( 'uud$' @ 'fun_app$k' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(411,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'M$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uww$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uww$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uww$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom95) ).
thf(2650,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'M$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uww$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uww$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uww$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(208,axiom,
! [A: 'A_m_vec$'] :
( ( A @ 'vec_nth$' @ 'vec_lambda$' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom381) ).
thf(1677,plain,
! [A: 'A_m_vec$'] :
( ( A @ 'vec_nth$' @ 'vec_lambda$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(291,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( ( A @ 'vec_nth$a' )
= ( B @ 'vec_nth$a' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom177) ).
thf(2073,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( ( A = B )
=> ( ( A @ 'vec_nth$a' )
= ( B @ 'vec_nth$a' ) ) )
& ( ( ( A @ 'vec_nth$a' )
= ( B @ 'vec_nth$a' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(713,axiom,
! [A: 'A$',B: 'A$'] :
( ( A
= ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
<=> ( ( B = 'one$' )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom249) ).
thf(4205,plain,
! [A: 'A$',B: 'A$'] :
( ( ( ( B = 'one$' )
| ( A = 'zero$' ) )
=> ( A
= ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) )
& ( ( A
= ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
=> ( ( B = 'one$' )
| ( A = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(157,axiom,
! [A: 'A_n_vec_n_vec$'] :
( ( A @ 'vec_nth$c' @ 'vec_lambda$e' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom379) ).
thf(1415,plain,
! [A: 'A_n_vec_n_vec$'] :
( ( A @ 'vec_nth$c' @ 'vec_lambda$e' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(158,axiom,
( 'one$a'
= ( 'uvs$' @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom394) ).
thf(1418,plain,
( 'one$a'
= ( 'uvs$' @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(562,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_fun$',C: 'A_n_vec_a_fun$',D: 'A_n_vec$'] :
( ( D @ ( C @ ( B @ ( A @ 'uyc$' ) ) @ 'fun_app$e' ) )
<=> ( ( ( D @ ( C @ 'fun_app$v' ) @ ( D @ ( B @ 'fun_app$v' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
!= 'one$' )
& ( A @ ( D @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom77) ).
thf(3453,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_fun$',C: 'A_n_vec_a_fun$',D: 'A_n_vec$'] :
( ( ( ( ( D @ ( C @ 'fun_app$v' ) @ ( D @ ( B @ 'fun_app$v' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
!= 'one$' )
& ( A @ ( D @ 'member$' @ 'fun_app$g' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uyc$' ) ) @ 'fun_app$e' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uyc$' ) ) @ 'fun_app$e' ) )
=> ( ( ( D @ ( C @ 'fun_app$v' ) @ ( D @ ( B @ 'fun_app$v' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
!= 'one$' )
& ( A @ ( D @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(135,axiom,
! [A: 'A_n_vec_set$'] :
( ( A @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom510) ).
thf(1334,plain,
! [A: 'A_n_vec_set$'] :
( ( A @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(564,axiom,
! [A: 'N$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvp$' ) @ 'fun_app$d' ) )
= ( A @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).
thf(3473,plain,
! [A: 'N$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvp$' ) @ 'fun_app$d' ) )
= ( A @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(447,axiom,
! [A: 'A_n_vec_set$'] : ( A @ ( 'bot$' @ 'less_eq$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom634) ).
thf(2880,plain,
! [A: 'A_n_vec_set$'] : ( A @ ( 'bot$' @ 'less_eq$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(26,axiom,
! [A: 'A_n_vec_set$'] :
( ( 'zero$g' = A )
<=> ( A = 'zero$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom281) ).
thf(834,plain,
! [A: 'A_n_vec_set$'] :
( ( ( A = 'zero$g' )
=> ( 'zero$g' = A ) )
& ( ( 'zero$g' = A )
=> ( A = 'zero$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(557,axiom,
! [A: 'A$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) )
& ( A != 'zero$' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom690) ).
thf(3438,plain,
! [A: 'A$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) )
& ( A != 'zero$' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(680,axiom,
( 'uue$'
= ( 'zero$' @ ( 'times$e' @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom191) ).
thf(4050,plain,
( 'uue$'
= ( 'zero$' @ ( 'times$e' @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(94,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'insert$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom484) ).
thf(1151,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'insert$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(45,axiom,
! [A: 'A_m_vec_m_vec$'] :
( ( A @ 'vec_nth$e' @ 'vec_lambda$c' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom361) ).
thf(937,plain,
! [A: 'A_m_vec_m_vec$'] :
( ( A @ 'vec_nth$e' @ 'vec_lambda$c' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(341,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec_set$',C: 'A_m_vec$',D: 'A_m_vec_set$'] :
( ( ( D @ ( C @ 'member$a' ) )
& ( B @ ( A @ 'member$a' ) ) )
=> ( D @ ( B @ 'times$j' ) @ ( C @ ( A @ 'times$b' @ 'fun_app$k' ) @ 'member$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom210) ).
thf(2291,plain,
! [A: 'A_m_vec$',B: 'A_m_vec_set$',C: 'A_m_vec$',D: 'A_m_vec_set$'] :
( ( ( D @ ( C @ 'member$a' ) )
& ( B @ ( A @ 'member$a' ) ) )
=> ( D @ ( B @ 'times$j' ) @ ( C @ ( A @ 'times$b' @ 'fun_app$k' ) @ 'member$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(148,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ~ ( A @ ( 'finite$' @ 'fun_app$g' ) )
=> ~ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom603) ).
thf(1383,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ~ ( A @ ( 'finite$' @ 'fun_app$g' ) )
=> ~ ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(621,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom152) ).
thf(3771,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(24,axiom,
! [A: 'A_n_vec$'] :
( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'the_elem$a' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom649) ).
thf(821,plain,
! [A: 'A_n_vec$'] :
( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'the_elem$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(277,axiom,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwo$' ) ) @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$g' ) @ 'vec_nth$e' @ 'fun_app$t' ) @ ( A @ 'fun_app$y' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom79) ).
thf(2017,plain,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwo$' ) ) @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$g' ) @ 'vec_nth$e' @ 'fun_app$t' ) @ ( A @ 'fun_app$y' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(39,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
<=> ( ~ ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom747) ).
thf(905,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( ~ ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) )
& ( ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
=> ( ~ ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(55,axiom,
! [A: 'A_n_vec_set$'] :
( ~ ( A @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) )
=> ( A @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom689) ).
thf(981,plain,
! [A: 'A_n_vec_set$'] :
( ~ ( A @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) )
=> ( A @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(289,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'uwx$' @ 'fun_app$o' ) )
<=> ? [C: 'N$'] :
( ( ( A @ ( C @ 'row$' ) )
!= 'zero$a' )
& ( B
= ( A @ ( C @ 'row$' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom27) ).
thf(2058,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec$'] :
( ( ? [C: 'N$'] :
( ( ( A @ ( C @ 'row$' ) )
!= 'zero$a' )
& ( B
= ( A @ ( C @ 'row$' ) ) ) )
=> ( B @ ( A @ 'uwx$' @ 'fun_app$o' ) ) )
& ( ( B @ ( A @ 'uwx$' @ 'fun_app$o' ) )
=> ? [C: 'N$'] :
( ( ( A @ ( C @ 'row$' ) )
!= 'zero$a' )
& ( B
= ( A @ ( C @ 'row$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(146,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'vector_scalar_mult$b' ) )
= ( B @ ( A @ 'uyg$' ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom702) ).
thf(1377,plain,
! [A: 'A_m_vec$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'vector_scalar_mult$b' ) )
= ( B @ ( A @ 'uyg$' ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(604,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom126) ).
thf(3685,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(368,axiom,
! [A: 'A_a_fun$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwn$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( A @ 'uwm$' ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom62) ).
thf(2424,plain,
! [A: 'A_a_fun$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwn$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( A @ 'uwm$' ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(309,axiom,
! [A: 'A_n_vec_m_vec$',B: 'A_n_vec_m_vec$'] :
( ( A = B )
<=> ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom161) ).
thf(2137,plain,
! [A: 'A_n_vec_m_vec$',B: 'A_n_vec_m_vec$'] :
( ( ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(139,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$',D: 'A_n_vec_set$'] :
( ( ( D @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( D @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom576) ).
thf(1351,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$',D: 'A_n_vec_set$'] :
( ( ( D @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( D @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(539,axiom,
! [A: 'N$'] :
( ( A @ ( 'uu$' @ 'fun_app$c' ) )
<=> ( ( A @ ( 'xa$' @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
thf(3327,plain,
! [A: 'N$'] :
( ( ( ( A @ ( 'xa$' @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
=> ( A @ ( 'uu$' @ 'fun_app$c' ) ) )
& ( ( A @ ( 'uu$' @ 'fun_app$c' ) )
=> ( ( A @ ( 'xa$' @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(105,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_bool_fun$'] : ( A @ ( B @ ( A @ 'uxs$' ) @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom551) ).
thf(1201,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_bool_fun$'] : ( A @ ( B @ ( A @ 'uxs$' ) @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(435,axiom,
! [A: 'A_m_vec$'] :
( ( 'zero$a' = A )
<=> ( A = 'zero$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).
thf(2804,plain,
! [A: 'A_m_vec$'] :
( ( ( A = 'zero$a' )
=> ( 'zero$a' = A ) )
& ( ( 'zero$a' = A )
=> ( A = 'zero$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(581,axiom,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$c' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$c' ) ) )
=> ( ( A @ 'the$' )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom198) ).
thf(3559,plain,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$c' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$c' ) ) )
=> ( ( A @ 'the$' )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(399,axiom,
! [A: 'A_n_vec$'] :
( ( 'one$c' = A )
<=> ( A = 'one$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom255) ).
thf(2586,plain,
! [A: 'A_n_vec$'] :
( ( ( A = 'one$c' )
=> ( 'one$c' = A ) )
& ( ( 'one$c' = A )
=> ( A = 'one$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(265,axiom,
! [A: 'A_m_vec_n_vec$'] : ( A @ 'columns$' @ ( 'finite$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom711) ).
thf(1975,plain,
! [A: 'A_m_vec_n_vec$'] : ( A @ 'columns$' @ ( 'finite$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(438,axiom,
! [A: 'A_m_vec_set$'] :
( ( A @ 'uuk$' @ 'collect$a' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom224) ).
thf(2833,plain,
! [A: 'A_m_vec_set$'] :
( ( A @ 'uuk$' @ 'collect$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(613,axiom,
! [A: 'A$'] :
( ( A @ ( 'zero$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom145) ).
thf(3739,plain,
! [A: 'A$'] :
( ( A @ ( 'zero$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(162,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
<=> ( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
| ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom585) ).
thf(1447,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( ( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
| ( A = 'bot$' ) )
=> ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
| ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(51,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( C @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) )
= ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom516) ).
thf(956,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( C @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) )
= ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(631,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( A = B )
<=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom163) ).
thf(3808,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(390,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_m_vec_fun$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uyj$' ) @ 'fun_app$e' ) )
<=> ( ( ( C @ ( B @ 'fun_app$u' ) )
!= 'zero$a' )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom42) ).
thf(2523,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_m_vec_fun$',C: 'A_n_vec$'] :
( ( ( ( ( C @ ( B @ 'fun_app$u' ) )
!= 'zero$a' )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'uyj$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uyj$' ) @ 'fun_app$e' ) )
=> ( ( ( C @ ( B @ 'fun_app$u' ) )
!= 'zero$a' )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(515,axiom,
! [A: 'N_a_m_vec_bool_fun_fun$'] :
( ! [B: 'N$'] :
? [C: 'A_m_vec$'] : ( C @ ( B @ ( A @ 'fun_app$af' ) @ 'fun_app$o' ) )
<=> ? [B: 'A_m_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'fun_app$af' ) @ 'fun_app$o' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom171) ).
thf(3211,plain,
! [A: 'N_a_m_vec_bool_fun_fun$'] :
( ( ? [B: 'A_m_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'fun_app$af' ) @ 'fun_app$o' ) )
=> ! [B: 'N$'] :
? [C: 'A_m_vec$'] : ( C @ ( B @ ( A @ 'fun_app$af' ) @ 'fun_app$o' ) ) )
& ( ! [B: 'N$'] :
? [C: 'A_m_vec$'] : ( C @ ( B @ ( A @ 'fun_app$af' ) @ 'fun_app$o' ) )
=> ? [B: 'A_m_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'fun_app$af' ) @ 'fun_app$o' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(312,axiom,
( 'uud$'
= ( 'zero$a' @ 'times$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom190) ).
thf(2154,plain,
( 'uud$'
= ( 'zero$a' @ 'times$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(201,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] : ( A @ ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom575) ).
thf(1651,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] : ( A @ ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(107,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_bool_fun$'] :
( ( ! [C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ( D @ ( B @ 'fun_app$g' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( D @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( D @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( B @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( A @ ( B @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom589) ).
thf(1206,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_bool_fun$'] :
( ( ! [C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ( D @ ( B @ 'fun_app$g' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( D @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( D @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( B @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( A @ ( B @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(530,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvg$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom33) ).
thf(3303,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvg$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(127,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( A @ 'times$c' @ 'fun_app$f' ) )
= ( C @ ( A @ 'times$c' @ 'fun_app$f' ) @ ( B @ 'times$c' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom310) ).
thf(1306,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( A @ 'times$c' @ 'fun_app$f' ) )
= ( C @ ( A @ 'times$c' @ 'fun_app$f' ) @ ( B @ 'times$c' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(303,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'A_m_vec$'] :
( ( C @ ( B @ ( A @ 'times$b' @ 'fun_app$k' ) @ 'times$b' @ 'fun_app$k' ) )
= ( C @ ( B @ 'times$b' @ 'fun_app$k' ) @ ( A @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom295) ).
thf(2118,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'A_m_vec$'] :
( ( C @ ( B @ ( A @ 'times$b' @ 'fun_app$k' ) @ 'times$b' @ 'fun_app$k' ) )
= ( C @ ( B @ 'times$b' @ 'fun_app$k' ) @ ( A @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(424,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( ( A @ 'vec_nth$' )
= ( B @ 'vec_nth$' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom176) ).
thf(2737,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( ( A = B )
=> ( ( A @ 'vec_nth$' )
= ( B @ 'vec_nth$' ) ) )
& ( ( ( A @ 'vec_nth$' )
= ( B @ 'vec_nth$' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(410,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> $false )
& ( A = B ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom535) ).
thf(2641,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
~ ( ~ ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(484,axiom,
! [A: tlbool] :
( ( A = tlfalse )
| ( A = tltrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_754) ).
thf(3037,plain,
! [A: tlbool] :
( ( A = tlfalse )
| ( A = tltrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(504,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'A_m_vec$'] :
( ( C @ ( B @ 'times$b' @ 'fun_app$k' ) @ ( A @ 'times$b' @ 'fun_app$k' ) )
= ( C @ ( A @ 'times$b' @ 'fun_app$k' ) @ ( B @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom307) ).
thf(3151,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'A_m_vec$'] :
( ( C @ ( B @ 'times$b' @ 'fun_app$k' ) @ ( A @ 'times$b' @ 'fun_app$k' ) )
= ( C @ ( A @ 'times$b' @ 'fun_app$k' ) @ ( B @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(275,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwl$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ ( A @ 'uwk$' ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom63) ).
thf(2011,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwl$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ ( A @ 'uwk$' ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(561,axiom,
! [A: 'A$'] :
( ( A @ ( A @ 'minus$a' @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom454) ).
thf(3450,plain,
! [A: 'A$'] :
( ( A @ ( A @ 'minus$a' @ 'fun_app$m' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(572,axiom,
! [A: 'A_a_fun$',B: 'A_m_vec_m_vec$',C: 'M$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$c' ) @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom202) ).
thf(3503,plain,
! [A: 'A_a_fun$',B: 'A_m_vec_m_vec$',C: 'M$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$c' ) @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(714,axiom,
! [A: 'A$',B: 'A$'] :
( ( ( B != 'zero$' )
& ( A != 'zero$' ) )
=> ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom182) ).
thf(4216,plain,
! [A: 'A$',B: 'A$'] :
( ( ( B != 'zero$' )
& ( A != 'zero$' ) )
=> ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
!= 'zero$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(587,axiom,
! [A: 'A$'] :
( ( 'one$' @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom270) ).
thf(3591,plain,
! [A: 'A$'] :
( ( 'one$' @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(213,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ~ ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> ( ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( D @ ( C @ 'insert$' @ 'fun_app$f' ) ) )
<=> ( ( ( A != C )
=> ? [E: 'A_n_vec_set$'] :
( ~ ( E @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( D
= ( E @ ( A @ 'insert$' @ 'fun_app$f' ) ) )
& ~ ( E @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( B
= ( E @ ( C @ 'insert$' @ 'fun_app$f' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom540) ).
thf(1708,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ~ ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> ( ( ( ( ( A != C )
=> ? [E: 'A_n_vec_set$'] :
( ~ ( E @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( D
= ( E @ ( A @ 'insert$' @ 'fun_app$f' ) ) )
& ~ ( E @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( B
= ( E @ ( C @ 'insert$' @ 'fun_app$f' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) )
=> ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( D @ ( C @ 'insert$' @ 'fun_app$f' ) ) ) )
& ( ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( D @ ( C @ 'insert$' @ 'fun_app$f' ) ) )
=> ( ( ( A != C )
=> ? [E: 'A_n_vec_set$'] :
( ~ ( E @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( D
= ( E @ ( A @ 'insert$' @ 'fun_app$f' ) ) )
& ~ ( E @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( B
= ( E @ ( C @ 'insert$' @ 'fun_app$f' ) ) ) ) )
& ( ( A = C )
=> ( B = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(295,axiom,
! [A: 'M$'] :
( ( A @ ( 'zero$e' @ 'vec_nth$d' @ 'fun_app$s' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom130) ).
thf(2093,plain,
! [A: 'M$'] :
( ( A @ ( 'zero$e' @ 'vec_nth$d' @ 'fun_app$s' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(343,axiom,
! [A: 'M_bool_fun$',B: 'M$'] :
( ( B @ ( A @ 'fun_app$' ) )
=> ( B @ ( A @ 'least$' @ 'less_eq$b' @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom645) ).
thf(2296,plain,
! [A: 'M_bool_fun$',B: 'M$'] :
( ( B @ ( A @ 'fun_app$' ) )
=> ( B @ ( A @ 'least$' @ 'less_eq$b' @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(347,axiom,
! [A: 'A_a_fun$',B: 'A_m_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uwh$' ) @ 'fun_app$t' ) )
= ( C @ ( B @ ( A @ 'uwg$' ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom65) ).
thf(2307,plain,
! [A: 'A_a_fun$',B: 'A_m_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uwh$' ) @ 'fun_app$t' ) )
= ( C @ ( B @ ( A @ 'uwg$' ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(292,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C @ ( B @ 'fun_app$e' ) ) )
=> ( B @ 'collect$c' @ ( A @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom529) ).
thf(2083,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C @ ( B @ 'fun_app$e' ) ) )
=> ( B @ 'collect$c' @ ( A @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(674,axiom,
! [A: 'A_m_vec_m_vec$'] :
( ( ( ( 'zero$k' @ ( 'zero$k' @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' )
& ( A @ 'reduced_row_echelon_form$d' ) )
=> ( ( A @ ( 'zero$k' @ 'column$a' ) )
= 'zero$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom423) ).
thf(4031,plain,
! [A: 'A_m_vec_m_vec$'] :
( ( ( ( 'zero$k' @ ( 'zero$k' @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' )
& ( A @ 'reduced_row_echelon_form$d' ) )
=> ( ( A @ ( 'zero$k' @ 'column$a' ) )
= 'zero$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(405,axiom,
! [A: 'A_m_vec$'] :
( ( 'zero$a' @ ( A @ 'minus$' @ 'fun_app$k' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom453) ).
thf(2621,plain,
! [A: 'A_m_vec$'] :
( ( 'zero$a' @ ( A @ 'minus$' @ 'fun_app$k' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(241,axiom,
( ( 'one$a' @ ( 'one$a' @ 'minus$' @ 'fun_app$k' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom489) ).
thf(1868,plain,
( ( 'one$a' @ ( 'one$a' @ 'minus$' @ 'fun_app$k' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(361,axiom,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'times$f' ) @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ ( C @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom123) ).
thf(2382,plain,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'times$f' ) @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ ( C @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(580,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_fun$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uyi$' ) @ 'fun_app$e' ) )
<=> ( ( ( C @ ( B @ 'fun_app$v' ) )
!= 'zero$' )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom43) ).
thf(3550,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_fun$',C: 'A_n_vec$'] :
( ( ( ( ( C @ ( B @ 'fun_app$v' ) )
!= 'zero$' )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'uyi$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uyi$' ) @ 'fun_app$e' ) )
=> ( ( ( C @ ( B @ 'fun_app$v' ) )
!= 'zero$' )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(707,axiom,
! [A: 'N_bool_fun$'] :
( ? [B: 'N$'] :
( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$c' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$c' ) ) )
=> ( A @ 'the$' @ ( A @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom321) ).
thf(4172,plain,
! [A: 'N_bool_fun$'] :
( ? [B: 'N$'] :
( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$c' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$c' ) ) )
=> ( A @ 'the$' @ ( A @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(271,axiom,
! [A: 'A_set$'] :
( ( 'one$d' @ ( A @ 'times$d' @ 'fun_app$l' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom268) ).
thf(2000,plain,
! [A: 'A_set$'] :
( ( 'one$d' @ ( A @ 'times$d' @ 'fun_app$l' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(251,axiom,
! [A: 'A_m_vec$',B: 'M_a_fun$'] :
( ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'fun_app$a' ) ) )
<=> ( ( B @ 'vec_lambda$' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom375) ).
thf(1900,plain,
! [A: 'A_m_vec$',B: 'M_a_fun$'] :
( ( ( ( B @ 'vec_lambda$' )
= A )
=> ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'fun_app$a' ) ) ) )
& ( ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'fun_app$a' ) ) )
=> ( ( B @ 'vec_lambda$' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(81,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) )
= ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) ) ) )
& ( ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) )
= ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom578) ).
thf(1091,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) )
= ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) ) ) )
& ( ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) )
= ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(332,axiom,
! [A: 'A_n_vec_set$'] :
( ! [B: 'A_n_vec$'] :
( ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
=> $false )
=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom523) ).
thf(2249,plain,
! [A: 'A_n_vec_set$'] :
( ! [B: 'A_n_vec$'] :
~ ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
=> ( A = 'bot$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(50,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
!= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom565) ).
thf(952,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
!= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(32,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
<=> ( ~ ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom752) ).
thf(862,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( ~ ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) )
& ( ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
=> ( ~ ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(307,axiom,
! [A: 'N$'] :
( ( A @ ( 'one$h' @ 'vec_nth$c' @ 'fun_app$r' ) )
= 'one$c' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom245) ).
thf(2133,plain,
! [A: 'N$'] :
( ( A @ ( 'one$h' @ 'vec_nth$c' @ 'fun_app$r' ) )
= 'one$c' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(459,axiom,
'a$' @ 'col_space$' @ ( 'uvk$' @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom443) ).
thf(2937,plain,
'a$' @ 'col_space$' @ ( 'uvk$' @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(505,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uxn$' ) @ 'fun_app$e' ) )
<=> ( ( C @ ( B @ 'fun_app$e' ) )
& ( C @ ( A @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom55) ).
thf(3154,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( ( ( C @ ( B @ 'fun_app$e' ) )
& ( C @ ( A @ 'fun_app$e' ) ) )
=> ( C @ ( B @ ( A @ 'uxn$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uxn$' ) @ 'fun_app$e' ) )
=> ( ( C @ ( B @ 'fun_app$e' ) )
& ( C @ ( A @ 'fun_app$e' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(17,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_m_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$i' ) )
= ( B @ ( A @ 'uwr$' ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom411) ).
thf(788,plain,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_m_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$i' ) )
= ( B @ ( A @ 'uwr$' ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(471,axiom,
! [A: 'M_a_n_vec_bool_fun_fun$'] :
( ! [B: 'M$'] :
? [C: 'A_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$ab' ) @ 'fun_app$e' ) )
<=> ? [B: 'A_n_vec_m_vec$'] :
! [C: 'M$'] : ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ ( C @ ( A @ 'fun_app$ab' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom167) ).
thf(2986,plain,
! [A: 'M_a_n_vec_bool_fun_fun$'] :
( ( ? [B: 'A_n_vec_m_vec$'] :
! [C: 'M$'] : ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ ( C @ ( A @ 'fun_app$ab' ) @ 'fun_app$e' ) )
=> ! [B: 'M$'] :
? [C: 'A_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$ab' ) @ 'fun_app$e' ) ) )
& ( ! [B: 'M$'] :
? [C: 'A_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$ab' ) @ 'fun_app$e' ) )
=> ? [B: 'A_n_vec_m_vec$'] :
! [C: 'M$'] : ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ ( C @ ( A @ 'fun_app$ab' ) @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(705,axiom,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxd$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$d' ) )
=> ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom440) ).
thf(4160,plain,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxd$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$d' ) )
=> ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(138,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_m_vec_fun$',C: 'A_n_vec$'] :
( ( B @ ( A @ 'uyj$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
=> ( ( ~ ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'sum$a' ) )
= ( A @ ( B @ 'sum$a' ) ) ) )
& ( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'sum$a' ) )
= ( C @ ( B @ 'fun_app$u' ) @ ( A @ ( B @ 'sum$a' ) @ 'minus$' @ 'fun_app$k' ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom727) ).
thf(1343,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_m_vec_fun$',C: 'A_n_vec$'] :
( ( B @ ( A @ 'uyj$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
=> ( ( ~ ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'sum$a' ) )
= ( A @ ( B @ 'sum$a' ) ) ) )
& ( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'sum$a' ) )
= ( C @ ( B @ 'fun_app$u' ) @ ( A @ ( B @ 'sum$a' ) @ 'minus$' @ 'fun_app$k' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(395,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( A = B )
<=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom162) ).
thf(2560,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(614,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_m_vec$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwi$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom83) ).
thf(3742,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_m_vec$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwi$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(688,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec$',C: 'N$',D: 'N$'] :
( ( ( C != D )
& ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uwz$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$e' ) )
=> ( ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom430) ).
thf(4091,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec$',C: 'N$',D: 'N$'] :
( ( ( C != D )
& ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uwz$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$e' ) )
=> ( ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(659,axiom,
! [A: 'A$',B: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
!= 'zero$' )
=> ( ( B != 'zero$' )
& ( A != 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom187) ).
thf(3948,plain,
! [A: 'A$',B: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
!= 'zero$' )
=> ( ( B != 'zero$' )
& ( A != 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(371,axiom,
! [A: 'M_bool_fun$',B: 'M_bool_fun$'] :
( ( ! [C: 'M$'] :
( ( ! [D: 'M$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
& ? [C: 'M$'] : ( C @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( B @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom644) ).
thf(2445,plain,
! [A: 'M_bool_fun$',B: 'M_bool_fun$'] :
( ( ! [C: 'M$'] :
( ( ! [D: 'M$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
& ? [C: 'M$'] : ( C @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( B @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(700,axiom,
! [A: 'M$'] :
( ( A @ ( 'uuv$' @ 'fun_app$' ) )
<=> ( ( A @ ( 'b$' @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(4140,plain,
! [A: 'M$'] :
( ( ( ( A @ ( 'b$' @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
=> ( A @ ( 'uuv$' @ 'fun_app$' ) ) )
& ( ( A @ ( 'uuv$' @ 'fun_app$' ) )
=> ( ( A @ ( 'b$' @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(711,axiom,
! [A: 'A$',B: 'A_set$',C: 'A$',D: 'A_set$'] :
( ( ( D @ ( C @ 'member$c' ) )
& ( B @ ( A @ 'member$c' ) ) )
=> ( D @ ( B @ 'times$d' @ 'fun_app$l' ) @ ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'member$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom214) ).
thf(4192,plain,
! [A: 'A$',B: 'A_set$',C: 'A$',D: 'A_set$'] :
( ( ( D @ ( C @ 'member$c' ) )
& ( B @ ( A @ 'member$c' ) ) )
=> ( D @ ( B @ 'times$d' @ 'fun_app$l' ) @ ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(495,axiom,
! [A: 'A_n_vec_set$'] :
( ~ ( A @ ( 'finite$' @ 'fun_app$g' ) )
=> ( A != 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom559) ).
thf(3090,plain,
! [A: 'A_n_vec_set$'] :
( ~ ( A @ ( 'finite$' @ 'fun_app$g' ) )
=> ( A != 'bot$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(123,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ ( 'zero$c' @ 'times$' @ 'fun_app$h' ) )
= 'zero$c' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom135) ).
thf(1296,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ ( 'zero$c' @ 'times$' @ 'fun_app$h' ) )
= 'zero$c' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(290,axiom,
! [A: 'M_bool_fun$',B: 'M$',C: 'M_bool_fun$'] :
( ( ! [D: 'M$'] :
( ( ! [E: 'M$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom643) ).
thf(2068,plain,
! [A: 'M_bool_fun$',B: 'M$',C: 'M_bool_fun$'] :
( ( ! [D: 'M$'] :
( ( ! [E: 'M$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(233,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( 'zero$c' @ ( A @ 'times$' @ 'fun_app$h' ) )
= 'zero$c' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom139) ).
thf(1836,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( 'zero$c' @ ( A @ 'times$' @ 'fun_app$h' ) )
= 'zero$c' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(323,axiom,
! [A: 'A_m_vec$'] :
( ( A @ ( 'one$a' @ 'times$b' @ 'fun_app$k' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom237) ).
thf(2211,plain,
! [A: 'A_m_vec$'] :
( ( A @ ( 'one$a' @ 'times$b' @ 'fun_app$k' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(610,axiom,
( ( 'i$' @ ( 'v$' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom192) ).
thf(3727,plain,
( ( 'i$' @ ( 'v$' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(54,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> ( ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( C @ ( A @ 'insert$' @ 'fun_app$f' ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom542) ).
thf(974,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> ( ( ( B = C )
=> ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( C @ ( A @ 'insert$' @ 'fun_app$f' ) ) ) )
& ( ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( C @ ( A @ 'insert$' @ 'fun_app$f' ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(429,axiom,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec_m_vec$'] :
( ( ( A @ 'vec_nth$e' )
= ( B @ 'vec_nth$e' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom172) ).
thf(2769,plain,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec_m_vec$'] :
( ( ( A = B )
=> ( ( A @ 'vec_nth$e' )
= ( B @ 'vec_nth$e' ) ) )
& ( ( ( A @ 'vec_nth$e' )
= ( B @ 'vec_nth$e' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(512,axiom,
( ! [A: 'N$'] :
( ( ( ( 'a$' @ ( A @ 'row$' ) )
!= 'zero$a' )
& ( 'v$'
= ( 'a$' @ ( A @ 'uvj$' @ 'least$' @ 'column$' ) ) ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom367) ).
thf(3191,plain,
~ ! [A: 'N$'] :
~ ( ( ( 'a$' @ ( A @ 'row$' ) )
!= 'zero$a' )
& ( 'v$'
= ( 'a$' @ ( A @ 'uvj$' @ 'least$' @ 'column$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(377,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( C @ ( B @ ( A @ 'interchange_rows$' ) ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom737) ).
thf(2464,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( C @ ( B @ ( A @ 'interchange_rows$' ) ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(29,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'the$a' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom193) ).
thf(847,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'the$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(427,axiom,
! [A: 'A_n_vec_m_vec$',B: 'M_a_n_vec_fun$'] :
( ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( C @ ( B @ 'fun_app$s' ) ) )
<=> ( ( B @ 'vec_lambda$d' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom372) ).
thf(2758,plain,
! [A: 'A_n_vec_m_vec$',B: 'M_a_n_vec_fun$'] :
( ( ( ( B @ 'vec_lambda$d' )
= A )
=> ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( C @ ( B @ 'fun_app$s' ) ) ) )
& ( ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( C @ ( B @ 'fun_app$s' ) ) )
=> ( ( B @ 'vec_lambda$d' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(349,axiom,
! [A: 'A_set$'] :
( ( 'one$d' @ ( A @ 'times$d' @ 'fun_app$l' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom233) ).
thf(2313,plain,
! [A: 'A_set$'] :
( ( 'one$d' @ ( A @ 'times$d' @ 'fun_app$l' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(383,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'reduced_row_echelon_form$' )
=> ! [B: 'N$'] :
( ~ ( A @ ( B @ 'is_zero_row$' ) )
=> ( ( B @ ( A @ 'uxe$' ) @ 'least$' @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom652) ).
thf(2492,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'reduced_row_echelon_form$' )
=> ! [B: 'N$'] :
( ~ ( A @ ( B @ 'is_zero_row$' ) )
=> ( ( B @ ( A @ 'uxe$' ) @ 'least$' @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(393,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ! [D: 'A_n_vec$',E: 'A_n_vec$'] :
( ( ( C @ ( E @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
& ( A
= ( E @ ( D @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) )
=> $false )
& ( C @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom316) ).
thf(2547,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
~ ( ! [D: 'A_n_vec$',E: 'A_n_vec$'] :
~ ( ( C @ ( E @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
& ( A
= ( E @ ( D @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ) )
& ( C @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(353,axiom,
! [A: 'A_n_vec_m_vec$',B: 'A_n_vec_m_vec$'] :
( ( ( A @ 'vec_nth$d' )
= ( B @ 'vec_nth$d' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom173) ).
thf(2344,plain,
! [A: 'A_n_vec_m_vec$',B: 'A_n_vec_m_vec$'] :
( ( ( A = B )
=> ( ( A @ 'vec_nth$d' )
= ( B @ 'vec_nth$d' ) ) )
& ( ( ( A @ 'vec_nth$d' )
= ( B @ 'vec_nth$d' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(301,axiom,
! [A: 'A_n_vec$'] :
( ( 'zero$b' @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom140) ).
thf(2112,plain,
! [A: 'A_n_vec$'] :
( ( 'zero$b' @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(686,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uxe$' ) @ 'fun_app$' ) )
<=> ( ( C @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom70) ).
thf(4080,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'M$'] :
( ( ( ( C @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
=> ( C @ ( B @ ( A @ 'uxe$' ) @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'uxe$' ) @ 'fun_app$' ) )
=> ( ( C @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(656,axiom,
! [A: 'A$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) )
<=> ( ( A = 'zero$' )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom654) ).
thf(3931,plain,
! [A: 'A$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( ( ( A = 'zero$' )
| ( B = C ) )
=> ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) ) )
& ( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) )
=> ( ( A = 'zero$' )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(215,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'times$' @ 'fun_app$h' ) )
= ( B @ ( A @ 'uvi$' ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom354) ).
thf(1740,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'times$' @ 'fun_app$h' ) )
= ( B @ ( A @ 'uvi$' ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(662,axiom,
! [A: 'A$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uyf$' ) @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom59) ).
thf(3968,plain,
! [A: 'A$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uyf$' ) @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(302,axiom,
! [A: 'N$'] :
( ( A @ ( 'zero$f' @ 'vec_nth$c' @ 'fun_app$r' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom131) ).
thf(2115,plain,
! [A: 'N$'] :
( ( A @ ( 'zero$f' @ 'vec_nth$c' @ 'fun_app$r' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(463,axiom,
! [A: 'A$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom698) ).
thf(2946,plain,
! [A: 'A$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(434,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'one$c' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom261) ).
thf(2801,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'one$c' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(84,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'A_m_vec_n_vec$'] :
( ( C @ ( B @ ( A @ 'times$' @ 'fun_app$h' ) @ 'times$' @ 'fun_app$h' ) )
= ( C @ ( B @ 'times$' @ 'fun_app$h' ) @ ( A @ 'times$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom294) ).
thf(1111,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'A_m_vec_n_vec$'] :
( ( C @ ( B @ ( A @ 'times$' @ 'fun_app$h' ) @ 'times$' @ 'fun_app$h' ) )
= ( C @ ( B @ 'times$' @ 'fun_app$h' ) @ ( A @ 'times$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(679,axiom,
~ ( 'bot$b' @ ( 'one$' @ 'insert$b' ) @ ( 'zero$' @ 'member$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom466) ).
thf(4048,plain,
~ ( 'bot$b' @ ( 'one$' @ 'insert$b' ) @ ( 'zero$' @ 'member$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(387,axiom,
( 'zero$b'
= ( 'uwt$' @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom413) ).
thf(2509,plain,
( 'zero$b'
= ( 'uwt$' @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(245,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'uuy$' @ 'fun_app$k' ) )
= ( A @ ( B @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).
thf(1878,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'uuy$' @ 'fun_app$k' ) )
= ( A @ ( B @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(33,axiom,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_m_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$h' ) )
= ( B @ ( A @ 'uwp$' ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom410) ).
thf(869,plain,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_m_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$h' ) )
= ( B @ ( A @ 'uwp$' ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(409,axiom,
! [A: 'A_n_vec$'] :
( ( 'one$c' @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom232) ).
thf(2638,plain,
! [A: 'A_n_vec$'] :
( ( 'one$c' @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(385,axiom,
! [A: 'M$'] :
( ( 'zero$k' = A )
<=> ( A = 'zero$k' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom285) ).
thf(2498,plain,
! [A: 'M$'] :
( ( ( A = 'zero$k' )
=> ( 'zero$k' = A ) )
& ( ( 'zero$k' = A )
=> ( A = 'zero$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(591,axiom,
( 'xa$'
= ( 'a$' @ ( 'uuw$' @ 'least$' @ 'column$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom334) ).
thf(3615,plain,
( 'xa$'
= ( 'a$' @ ( 'uuw$' @ 'least$' @ 'column$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(183,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) )
<=> ( B @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom509) ).
thf(1541,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$g' ) )
=> ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) )
& ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) )
=> ( B @ ( 'finite$' @ 'fun_app$g' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(65,axiom,
! [A: 'A_n_vec_set$'] : ( A @ ( A @ 'less_eq$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom608) ).
thf(1017,plain,
! [A: 'A_n_vec_set$'] : ( A @ ( A @ 'less_eq$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(259,axiom,
( 'bot$'
= ( 'bot$e' @ 'collect$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom610) ).
thf(1953,plain,
( 'bot$'
= ( 'bot$e' @ 'collect$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(229,axiom,
! [A: 'A_n_vec_set_bool_fun$',B: 'A_n_vec_set$'] :
( ( ! [C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ( D @ ( A @ 'fun_app$g' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( D @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( D @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( A @ 'fun_app$g' ) )
& ! [C: 'A_n_vec_set$'] :
( ~ ( C @ ( 'finite$' @ 'fun_app$g' ) )
=> ( C @ ( A @ 'fun_app$g' ) ) ) )
=> ( B @ ( A @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom587) ).
thf(1804,plain,
! [A: 'A_n_vec_set_bool_fun$',B: 'A_n_vec_set$'] :
( ( ! [C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ( D @ ( A @ 'fun_app$g' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( D @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( D @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( A @ 'fun_app$g' ) )
& ! [C: 'A_n_vec_set$'] :
( ~ ( C @ ( 'finite$' @ 'fun_app$g' ) )
=> ( C @ ( A @ 'fun_app$g' ) ) ) )
=> ( B @ ( A @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(640,axiom,
! [A: 'M$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvq$' ) @ 'fun_app$d' ) )
= ( A @ ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom52) ).
thf(3862,plain,
! [A: 'M$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvq$' ) @ 'fun_app$d' ) )
= ( A @ ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(397,axiom,
'uvk$' @ 'collect$c' @ ( 'v$' @ 'member$' @ 'fun_app$g' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom369) ).
thf(2577,plain,
'uvk$' @ 'collect$c' @ ( 'v$' @ 'member$' @ 'fun_app$g' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(73,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom623) ).
thf(1064,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(417,axiom,
! [A: 'N_a_n_vec_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$e' @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( B @ ( A @ 'fun_app$r' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom357) ).
thf(2692,plain,
! [A: 'N_a_n_vec_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$e' @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( B @ ( A @ 'fun_app$r' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(175,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uym$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uww$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom86) ).
thf(1498,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uym$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uww$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(474,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvf$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom29) ).
thf(3001,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvf$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(58,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( B @ ( C @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) )
= ( B @ ( C @ 'minus$b' @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom515) ).
thf(989,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( B @ ( C @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) )
= ( B @ ( C @ 'minus$b' @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(494,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'times$b' @ 'fun_app$k' ) )
= ( A @ ( B @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom301) ).
thf(3087,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'times$b' @ 'fun_app$k' ) )
= ( A @ ( B @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(480,axiom,
! [A: 'M$',B: 'A_m_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uvo$' ) @ 'fun_app$a' ) )
= ( A @ ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom53) ).
thf(3018,plain,
! [A: 'M$',B: 'A_m_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uvo$' ) @ 'fun_app$a' ) )
= ( A @ ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(188,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) )
<=> ( ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom498) ).
thf(1567,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( ( ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
| ( A = B ) )
=> ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) )
& ( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(263,axiom,
! [A: 'M$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'column$' ) )
= ( B @ ( A @ 'uvq$' ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom392) ).
thf(1964,plain,
! [A: 'M$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'column$' ) )
= ( B @ ( A @ 'uvq$' ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(9,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec$'] :
( ( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$e' ) ) )
=> ( ( A @ 'the$a' )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom197) ).
thf(753,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec$'] :
( ( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$e' ) ) )
=> ( ( A @ 'the$a' )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(496,axiom,
! [A: tlbool,B: 'A_n_vec$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'zero$b' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= 'zero$b' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'zero$b' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= B ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'one$c' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= 'zero$b' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'one$c' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom331) ).
thf(3094,plain,
! [A: tlbool,B: 'A_n_vec$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'zero$b' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= 'zero$b' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'zero$b' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= B ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'one$c' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= 'zero$b' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'one$c' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(601,axiom,
! [A: 'A_n_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvz$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvz$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( B @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom98) ).
thf(3671,plain,
! [A: 'A_n_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvz$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvz$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( B @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(247,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uxr$' @ 'fun_app$e' ) )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom117) ).
thf(1889,plain,
! [A: 'A_n_vec$'] :
~ ( A @ ( 'uxr$' @ 'fun_app$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(469,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( A = 'bot$' )
=> ~ ( A @ ( B @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom524) ).
thf(2978,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( A = 'bot$' )
=> ~ ( A @ ( B @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(431,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uyg$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom57) ).
thf(2781,plain,
! [A: 'A_m_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uyg$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(97,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ~ ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ~ ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom577) ).
thf(1160,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ~ ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ~ ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(533,axiom,
( 'zero$i'
= ( 'bot$b' @ ( 'zero$' @ 'insert$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom462) ).
thf(3311,plain,
( 'zero$i'
= ( 'bot$b' @ ( 'zero$' @ 'insert$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(78,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$' ) ) )
= ( C @ ( B @ ( A @ 'uxh$' ) ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom445) ).
thf(1082,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$' ) ) )
= ( C @ ( B @ ( A @ 'uxh$' ) ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(279,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'A_m_vec$'] :
( ( C @ ( B @ ( A @ 'times$b' @ 'fun_app$k' ) @ 'times$b' @ 'fun_app$k' ) )
= ( C @ ( B @ 'times$b' @ 'fun_app$k' ) @ ( A @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom289) ).
thf(2023,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'A_m_vec$'] :
( ( C @ ( B @ ( A @ 'times$b' @ 'fun_app$k' ) @ 'times$b' @ 'fun_app$k' ) )
= ( C @ ( B @ 'times$b' @ 'fun_app$k' ) @ ( A @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(558,axiom,
! [A: 'A_n_vec$'] :
( ( A @ 'vec_nth$b' @ 'vec_lambda$a' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom364) ).
thf(3441,plain,
! [A: 'A_n_vec$'] :
( ( A @ 'vec_nth$b' @ 'vec_lambda$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(477,axiom,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_column$' ) ) @ 'vec_nth$a' )
= ( C @ ( B @ ( A @ 'mult_column_row$c' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom482) ).
thf(3010,plain,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_column$' ) ) @ 'vec_nth$a' )
= ( C @ ( B @ ( A @ 'mult_column_row$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(374,axiom,
! [A: 'A_n_vec_m_vec$',B: 'A_n_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'times$g' ) @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ ( C @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom124) ).
thf(2455,plain,
! [A: 'A_n_vec_m_vec$',B: 'A_n_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'times$g' ) @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ ( C @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(319,axiom,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_column_row$b' ) ) @ 'fun_app$t' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvu$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom396) ).
thf(2196,plain,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_column_row$b' ) ) @ 'fun_app$t' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvu$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(235,axiom,
( 'one$d'
= ( 'bot$b' @ ( 'one$' @ 'insert$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom460) ).
thf(1842,plain,
( 'one$d'
= ( 'bot$b' @ ( 'one$' @ 'insert$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(211,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) )
<=> ( C @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom483) ).
thf(1700,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( ( C @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) )
=> ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) )
& ( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) )
=> ( C @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(404,axiom,
! [A: 'A_m_vec_m_vec$',B: 'M_a_m_vec_fun$'] :
( ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( C @ ( B @ 'fun_app$t' ) ) )
<=> ( ( B @ 'vec_lambda$c' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom371) ).
thf(2613,plain,
! [A: 'A_m_vec_m_vec$',B: 'M_a_m_vec_fun$'] :
( ( ( ( B @ 'vec_lambda$c' )
= A )
=> ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( C @ ( B @ 'fun_app$t' ) ) ) )
& ( ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( C @ ( B @ 'fun_app$t' ) ) )
=> ( ( B @ 'vec_lambda$c' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(596,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
& ( A != 'zero$' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom181) ).
thf(3656,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
& ( A != 'zero$' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(346,axiom,
tltrue != tlfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_755) ).
thf(2304,plain,
tltrue != tlfalse,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(439,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$i' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$h' ) @ 'vec_nth$d' @ 'fun_app$s' ) @ ( A @ 'fun_app$v' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom208) ).
thf(2836,plain,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$i' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$h' ) @ 'vec_nth$d' @ 'fun_app$s' ) @ ( A @ 'fun_app$v' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(401,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uya$' ) @ 'fun_app$e' ) )
<=> ( ( C @ ( B @ 'fun_app$e' ) )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom41) ).
thf(2598,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( ( ( C @ ( B @ 'fun_app$e' ) )
& ( C = A ) )
=> ( C @ ( B @ ( A @ 'uya$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uya$' ) @ 'fun_app$e' ) )
=> ( ( C @ ( B @ 'fun_app$e' ) )
& ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(111,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$'] :
( ( ~ ( A @ ( B @ 'fun_app$e' ) )
=> ( ( B @ ( A @ 'uya$' ) @ 'collect$c' )
= 'bot$' ) )
& ( ( A @ ( B @ 'fun_app$e' ) )
=> ( ( B @ ( A @ 'uya$' ) @ 'collect$c' )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom582) ).
thf(1231,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$'] :
( ( ~ ( A @ ( B @ 'fun_app$e' ) )
=> ( ( B @ ( A @ 'uya$' ) @ 'collect$c' )
= 'bot$' ) )
& ( ( A @ ( B @ 'fun_app$e' ) )
=> ( ( B @ ( A @ 'uya$' ) @ 'collect$c' )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(205,axiom,
! [A: 'A_set$'] :
( ( A @ 'uuj$' @ 'collect$' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom223) ).
thf(1668,plain,
! [A: 'A_set$'] :
( ( A @ 'uuj$' @ 'collect$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(273,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( ( ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) )
& ( A @ 'uwx$' @ 'collect$a' @ ( A @ ( B @ 'row$' ) @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom427) ).
thf(2006,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( ( ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) )
& ( A @ 'uwx$' @ 'collect$a' @ ( A @ ( B @ 'row$' ) @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(436,axiom,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'M$',D: 'N$',E: 'M$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( B @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom429) ).
thf(2813,plain,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'M$',D: 'N$',E: 'M$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( B @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(593,axiom,
! [A: 'N_bool_fun$',B: 'N$',C: 'N_bool_fun$'] :
( ( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$c' ) )
=> ( D @ ( C @ 'fun_app$c' ) ) )
& ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$c' ) )
=> ( D = B ) )
& ( B @ ( A @ 'fun_app$c' ) ) )
=> ( A @ 'the$' @ ( C @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom323) ).
thf(3628,plain,
! [A: 'N_bool_fun$',B: 'N$',C: 'N_bool_fun$'] :
( ( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$c' ) )
=> ( D @ ( C @ 'fun_app$c' ) ) )
& ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$c' ) )
=> ( D = B ) )
& ( B @ ( A @ 'fun_app$c' ) ) )
=> ( A @ 'the$' @ ( C @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(553,axiom,
! [A: 'A_a_fun$',B: 'A_m_vec_m_vec$',C: 'M$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwg$' ) ) @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom85) ).
thf(3409,plain,
! [A: 'A_a_fun$',B: 'A_m_vec_m_vec$',C: 'M$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwg$' ) ) @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(426,axiom,
! [A: 'A_n_vec_set$'] : ( A @ ( 'bot$' @ 'less_eq$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom505) ).
thf(2756,plain,
! [A: 'A_n_vec_set$'] : ( A @ ( 'bot$' @ 'less_eq$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(359,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom537) ).
thf(2370,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(466,axiom,
! [A: 'A_set$'] :
( ( A @ ( 'one$d' @ 'times$d' @ 'fun_app$l' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom239) ).
thf(2968,plain,
! [A: 'A_set$'] :
( ( A @ ( 'one$d' @ 'times$d' @ 'fun_app$l' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(133,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= 'bot$' )
<=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom485) ).
thf(1324,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= 'bot$' ) )
& ( ( ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= 'bot$' )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(85,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
| ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom586) ).
thf(1114,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
| ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(372,axiom,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_row_row$b' ) ) @ 'fun_app$t' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvy$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom400) ).
thf(2450,plain,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_row_row$b' ) ) @ 'fun_app$t' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvy$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(82,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( C @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
<=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom486) ).
thf(1099,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( B = A ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( C @ ( B @ 'insert$' @ 'fun_app$f' ) ) ) )
& ( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( C @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(257,axiom,
! [A: 'A_set$',B: 'A_set$'] :
( ( B @ ( A @ 'times$d' @ 'fun_app$l' ) )
= ( A @ ( B @ 'times$d' @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom303) ).
thf(1947,plain,
! [A: 'A_set$',B: 'A_set$'] :
( ( B @ ( A @ 'times$d' @ 'fun_app$l' ) )
= ( A @ ( B @ 'times$d' @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(694,axiom,
'uvk$' @ 'collect$c' @ ( 'xa$' @ 'member$' @ 'fun_app$g' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom416) ).
thf(4120,plain,
'uvk$' @ 'collect$c' @ ( 'xa$' @ 'member$' @ 'fun_app$g' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(428,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'one$' @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom658) ).
thf(2766,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'one$' @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(287,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'minus$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'minus$' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom458) ).
thf(2052,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'minus$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'minus$' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(191,axiom,
! [A: 'A_m_vec$'] :
( ( 'one$a' = A )
<=> ( A = 'one$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom254) ).
thf(1599,plain,
! [A: 'A_m_vec$'] :
( ( ( A = 'one$a' )
=> ( 'one$a' = A ) )
& ( ( 'one$a' = A )
=> ( A = 'one$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(115,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A = B )
=> ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom532) ).
thf(1246,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A = B )
=> ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(497,axiom,
! [A: tlbool,B: 'A_n_vec$',C: 'A_n_vec$',D: 'A_n_vec$'] :
( ( D @ ( C @ ( B @ ( A @ 'uut$' ) @ 'fun_app$q' ) @ 'fun_app$e' ) )
<=> ( ( ( ( A = tltrue )
<=> $false )
=> ( D = C ) )
& ( ( ( A = tltrue )
<=> $true )
=> ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom74) ).
thf(3109,plain,
! [A: tlbool,B: 'A_n_vec$',C: 'A_n_vec$',D: 'A_n_vec$'] :
( ( ( ( ( A != tltrue )
=> ( D = C ) )
& ( ( A = tltrue )
=> ( D = B ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uut$' ) @ 'fun_app$q' ) @ 'fun_app$e' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uut$' ) @ 'fun_app$q' ) @ 'fun_app$e' ) )
=> ( ( ( A != tltrue )
=> ( D = C ) )
& ( ( A = tltrue )
=> ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(14,axiom,
! [A: 'N$'] :
( ( A @ ( 'one$b' @ 'vec_nth$a' @ 'fun_app$b' ) )
= 'one$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom248) ).
thf(779,plain,
! [A: 'N$'] :
( ( A @ ( 'one$b' @ 'vec_nth$a' @ 'fun_app$b' ) )
= 'one$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(706,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$a' ) ) @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$a' ) ) @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom340) ).
thf(4163,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$a' ) ) @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$a' ) ) @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(565,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uyk$' ) @ 'fun_app$e' ) )
<=> ( ( ( C @ ( A @ 'fun_app$v' ) )
!= 'zero$' )
& ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom46) ).
thf(3476,plain,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ( ( ( C @ ( A @ 'fun_app$v' ) )
!= 'zero$' )
& ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'uyk$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uyk$' ) @ 'fun_app$e' ) )
=> ( ( ( C @ ( A @ 'fun_app$v' ) )
!= 'zero$' )
& ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(131,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] : ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom545) ).
thf(1318,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] : ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(113,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom594) ).
thf(1241,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(284,axiom,
~ ( 'bot$' @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom679) ).
thf(2043,plain,
~ ( 'bot$' @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(639,axiom,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$c' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$c' ) ) )
=> ( A @ 'the$' @ ( A @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom319) ).
thf(3856,plain,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$c' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$c' ) ) )
=> ( A @ 'the$' @ ( A @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(357,axiom,
'bot$b' @ ( 'one$' @ 'insert$b' ) @ 'finite$a',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom465) ).
thf(2368,plain,
'bot$b' @ ( 'one$' @ 'insert$b' ) @ 'finite$a',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(193,axiom,
! [A: 'A_set$'] :
( ( 'one$d' = A )
<=> ( A = 'one$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom257) ).
thf(1616,plain,
! [A: 'A_set$'] :
( ( ( A = 'one$d' )
=> ( 'one$d' = A ) )
& ( ( 'one$d' = A )
=> ( A = 'one$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(412,axiom,
! [A: 'A_n_vec$',B: 'A$',C: 'A$'] :
( ( ( ( A @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( A @ ( C @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) )
& ( A != 'zero$b' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom692) ).
thf(2662,plain,
! [A: 'A_n_vec$',B: 'A$',C: 'A$'] :
( ( ( ( A @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( A @ ( C @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) )
& ( A != 'zero$b' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(269,axiom,
! [A: 'A_n_vec_m_vec$',B: 'A_n_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uve$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ ( C @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom30) ).
thf(1996,plain,
! [A: 'A_n_vec_m_vec$',B: 'A_n_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uve$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ ( C @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(214,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( B @ ( A @ 'uye$' @ 'fun_app$e' ) )
<=> ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).
thf(1732,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
=> ( B @ ( A @ 'uye$' @ 'fun_app$e' ) ) )
& ( ( B @ ( A @ 'uye$' @ 'fun_app$e' ) )
=> ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(453,axiom,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec_m_vec$'] :
( ( A = B )
<=> ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom160) ).
thf(2909,plain,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec_m_vec$'] :
( ( ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(701,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( A @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
& ( A != 'zero$' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom180) ).
thf(4148,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( A @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
& ( A != 'zero$' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(650,axiom,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$',D: 'N$',E: 'M$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvx$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvx$' ) ) ) @ 'fun_app$a' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom93) ).
thf(3903,plain,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$',D: 'N$',E: 'M$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvx$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvx$' ) ) ) @ 'fun_app$a' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(322,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvi$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom31) ).
thf(2208,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvi$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(20,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( 'one$b' @ ( A @ 'times$' @ 'fun_app$h' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom265) ).
thf(805,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( 'one$b' @ ( A @ 'times$' @ 'fun_app$h' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec$'] :
( ( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$e' ) ) )
=> ( A @ 'the$a' @ ( A @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom318) ).
thf(765,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec$'] :
( ( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$e' ) ) )
=> ( A @ 'the$a' @ ( A @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(531,axiom,
( ( 'one$' @ ( 'one$' @ 'minus$a' @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom488) ).
thf(3306,plain,
( ( 'one$' @ ( 'one$' @ 'minus$a' @ 'fun_app$m' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(166,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) )
= ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom500) ).
thf(1466,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) )
= ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(365,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
<=> ( C @ ( B @ 'fun_app$e' ) ) )
=> ( ( A @ 'collect$c' )
= ( B @ 'collect$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom229) ).
thf(2402,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ! [C: 'A_n_vec$'] :
( ( ( C @ ( B @ 'fun_app$e' ) )
=> ( C @ ( A @ 'fun_app$e' ) ) )
& ( ( C @ ( A @ 'fun_app$e' ) )
=> ( C @ ( B @ 'fun_app$e' ) ) ) )
=> ( ( A @ 'collect$c' )
= ( B @ 'collect$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(68,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_m_vec_fun$',D: 'A_n_vec$'] :
( ( ( A @ ( C @ ( B @ 'uyj$' ) @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( ( ~ ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( C @ 'sum$a' ) )
= ( B @ ( C @ 'sum$a' ) ) ) )
& ( ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( C @ 'sum$a' ) )
= ( D @ ( C @ 'fun_app$u' ) @ ( B @ ( C @ 'sum$a' ) @ 'minus$' @ 'fun_app$k' ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom713) ).
thf(1026,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_m_vec_fun$',D: 'A_n_vec$'] :
( ( ( A @ ( C @ ( B @ 'uyj$' ) @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( ( ~ ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( C @ 'sum$a' ) )
= ( B @ ( C @ 'sum$a' ) ) ) )
& ( ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( C @ 'sum$a' ) )
= ( D @ ( C @ 'fun_app$u' ) @ ( B @ ( C @ 'sum$a' ) @ 'minus$' @ 'fun_app$k' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(249,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'uyk$' ) @ 'collect$c' @ ( A @ 'sum$' ) )
= ( B @ ( A @ 'sum$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom716) ).
thf(1895,plain,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'uyk$' ) @ 'collect$c' @ ( A @ 'sum$' ) )
= ( B @ ( A @ 'sum$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(209,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( ( B @ ( A @ 'times$' @ 'fun_app$h' ) )
!= 'zero$c' )
=> ( ( B != 'zero$c' )
& ( A != 'zero$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom184) ).
thf(1680,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( ( B @ ( A @ 'times$' @ 'fun_app$h' ) )
!= 'zero$c' )
=> ( ( B != 'zero$c' )
& ( A != 'zero$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(261,axiom,
! [A: 'A$'] :
( ( 'zero$b' @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom660) ).
thf(1959,plain,
! [A: 'A$'] :
( ( 'zero$b' @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(25,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ~ ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
<=> ( ( A = B )
| ~ ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom744) ).
thf(824,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( ( A = B )
| ~ ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ~ ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) )
& ( ~ ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
=> ( ( A = B )
| ~ ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(568,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom153) ).
thf(3491,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(491,axiom,
! [A: 'A_n_vec_n_vec_n_vec$'] :
( ( ( ( A @ ( 'zero$j' @ 'column$f' ) )
!= 'zero$f' )
& ( A @ 'reduced_row_echelon_form$a' ) )
=> ( ( 'zero$j' @ ( 'zero$j' @ ( A @ 'vec_nth$k' ) @ 'vec_nth$c' @ 'fun_app$r' ) )
= 'one$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom417) ).
thf(3079,plain,
! [A: 'A_n_vec_n_vec_n_vec$'] :
( ( ( ( A @ ( 'zero$j' @ 'column$f' ) )
!= 'zero$f' )
& ( A @ 'reduced_row_echelon_form$a' ) )
=> ( ( 'zero$j' @ ( 'zero$j' @ ( A @ 'vec_nth$k' ) @ 'vec_nth$c' @ 'fun_app$r' ) )
= 'one$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(665,axiom,
! [A: 'A$'] :
( ( A @ 'uvc$' )
= ( A @ ( 'times$e' @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom348) ).
thf(3985,plain,
! [A: 'A$'] :
( ( A @ 'uvc$' )
= ( A @ ( 'times$e' @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(7,axiom,
! [A: 'A_n_vec_set$'] :
( ( 'one$e' @ ( A @ 'times$c' @ 'fun_app$f' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom234) ).
thf(745,plain,
! [A: 'A_n_vec_set$'] :
( ( 'one$e' @ ( A @ 'times$c' @ 'fun_app$f' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(575,axiom,
! [A: 'A$',B: 'A$'] :
( ( A
= ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
<=> ( ( B = 'one$' )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom251) ).
thf(3523,plain,
! [A: 'A$',B: 'A$'] :
( ( ( ( B = 'one$' )
| ( A = 'zero$' ) )
=> ( A
= ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) )
& ( ( A
= ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
=> ( ( B = 'one$' )
| ( A = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(672,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( B @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
<=> ( ( A = C )
| ( B = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom151) ).
thf(4017,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( ( A = C )
| ( B = 'zero$' ) )
=> ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( B @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) )
& ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( B @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
=> ( ( A = C )
| ( B = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(450,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( B @ ( A @ 'uxj$' ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom475) ).
thf(2894,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( B @ ( A @ 'uxj$' ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(196,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$g' ) )
=> ( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) )
<=> ( B @ ( 'finite$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom513) ).
thf(1631,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$g' ) )
=> ( ( ( B @ ( 'finite$' @ 'fun_app$g' ) )
=> ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) )
& ( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) )
=> ( B @ ( 'finite$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(304,axiom,
! [A: 'A_m_vec$'] :
( ( A @ ( 'uuo$' @ 'fun_app$k' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom103) ).
thf(2121,plain,
! [A: 'A_m_vec$'] :
( ( A @ ( 'uuo$' @ 'fun_app$k' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(327,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( B @ ( A @ 'uvg$' ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom352) ).
thf(2235,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( B @ ( A @ 'uvg$' ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(221,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom611) ).
thf(1764,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ( ( B = A )
=> ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(366,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ( B @ 'collect$c' @ ( A @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ) )
<=> ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C @ ( B @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom526) ).
thf(2413,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C @ ( B @ 'fun_app$e' ) ) )
=> ( B @ 'collect$c' @ ( A @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( B @ 'collect$c' @ ( A @ 'collect$c' @ 'less_eq$' @ 'fun_app$g' ) )
=> ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C @ ( B @ 'fun_app$e' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(333,axiom,
! [A: 'A_m_vec$'] :
( ( 'zero$a' @ ( A @ 'minus$' @ 'fun_app$k' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom451) ).
thf(2253,plain,
! [A: 'A_m_vec$'] :
( ( 'zero$a' @ ( A @ 'minus$' @ 'fun_app$k' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(643,axiom,
! [A: 'A_n_vec_m_vec$',B: 'N$',C: 'A$',D: 'M$',E: 'N$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvv$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvv$' ) ) ) @ 'fun_app$d' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom92) ).
thf(3871,plain,
! [A: 'A_n_vec_m_vec$',B: 'N$',C: 'A$',D: 'M$',E: 'N$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvv$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvv$' ) ) ) @ 'fun_app$d' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(536,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_n_vec$',C: 'N$',D: 'N$'] :
( ( ( C != D )
& ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uxf$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom433) ).
thf(3319,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_n_vec$',C: 'N$',D: 'N$'] :
( ( ( C != D )
& ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uxf$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(518,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
!= 'zero$b' )
=> ( ( B != 'zero$b' )
& ( A != 'zero$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom185) ).
thf(3240,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
!= 'zero$b' )
=> ( ( B != 'zero$b' )
& ( A != 'zero$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(318,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
<=> ! [C: 'A_n_vec$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom531) ).
thf(2188,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ! [C: 'A_n_vec$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ! [C: 'A_n_vec$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(658,axiom,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$f' ) @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$f' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$y' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).
thf(3945,plain,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$f' ) @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$f' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$y' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(35,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec$',C: 'A_n_vec_bool_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( D @ ( A @ 'fun_app$e' ) )
=> ( D @ ( C @ 'fun_app$e' ) ) )
& ! [D: 'A_n_vec$'] :
( ( D @ ( A @ 'fun_app$e' ) )
=> ( D = B ) )
& ( B @ ( A @ 'fun_app$e' ) ) )
=> ( A @ 'the$a' @ ( C @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom322) ).
thf(875,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec$',C: 'A_n_vec_bool_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( D @ ( A @ 'fun_app$e' ) )
=> ( D @ ( C @ 'fun_app$e' ) ) )
& ! [D: 'A_n_vec$'] :
( ( D @ ( A @ 'fun_app$e' ) )
=> ( D = B ) )
& ( B @ ( A @ 'fun_app$e' ) ) )
=> ( A @ 'the$a' @ ( C @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(649,axiom,
! [A: 'A$'] :
( ( 'zero$' @ ( A @ 'minus$a' @ 'fun_app$m' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom452) ).
thf(3900,plain,
! [A: 'A$'] :
( ( 'zero$' @ ( A @ 'minus$a' @ 'fun_app$m' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(153,axiom,
! [A: 'A_a_fun$',B: 'A_m_vec_m_vec$'] :
( ( B @ ( A @ 'map_matrix$c' ) )
= ( B @ ( A @ 'uwh$' ) @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom406) ).
thf(1403,plain,
! [A: 'A_a_fun$',B: 'A_m_vec_m_vec$'] :
( ( B @ ( A @ 'map_matrix$c' ) )
= ( B @ ( A @ 'uwh$' ) @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(590,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
<=> ( ( A = 'zero$' )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom147) ).
thf(3604,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( ( A = 'zero$' )
| ( B = C ) )
=> ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) )
& ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
=> ( ( A = 'zero$' )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(642,axiom,
! [A: 'A$',B: 'A$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom678) ).
thf(3868,plain,
! [A: 'A$',B: 'A$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(465,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( A = B )
<=> ( ( B @ ( A @ 'minus$' @ 'fun_app$k' ) )
= 'zero$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom468) ).
thf(2959,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( ( ( B @ ( A @ 'minus$' @ 'fun_app$k' ) )
= 'zero$a' )
=> ( A = B ) )
& ( ( A = B )
=> ( ( B @ ( A @ 'minus$' @ 'fun_app$k' ) )
= 'zero$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(577,axiom,
! [A: 'A$'] :
( ( 'zero$' @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom146) ).
thf(3536,plain,
! [A: 'A$'] :
( ( 'zero$' @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(95,axiom,
! [A: 'A_n_vec_set$'] :
( ( A @ 'uum$' @ 'collect$c' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom226) ).
thf(1154,plain,
! [A: 'A_n_vec_set$'] :
( ( A @ 'uum$' @ 'collect$c' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(579,axiom,
! [A: 'A_a_fun$',B: 'A_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwm$' ) ) @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom84) ).
thf(3547,plain,
! [A: 'A_a_fun$',B: 'A_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwm$' ) ) @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(232,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'uxv$' ) @ 'collect$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom555) ).
thf(1833,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'uxv$' ) @ 'collect$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(620,axiom,
! [A: 'N$'] :
( ( A @ ( 'uvt$' @ 'fun_app$d' ) )
= 'one$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom115) ).
thf(3768,plain,
! [A: 'N$'] :
( ( A @ ( 'uvt$' @ 'fun_app$d' ) )
= 'one$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(253,axiom,
! [A: tlbool,B: 'A_m_vec$',C: 'A_m_vec$',D: 'M$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( C @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( C @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( C @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom158) ).
thf(1916,plain,
! [A: tlbool,B: 'A_m_vec$',C: 'A_m_vec$',D: 'M$'] :
( ( ( A != tltrue )
=> ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) )
& ( ( A = tltrue )
=> ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( C @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(594,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'M$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwb$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwb$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom99) ).
thf(3636,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'M$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwb$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwb$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(460,axiom,
! [A: 'A_m_vec_set$'] :
( ( A @ ( 'zero$a' @ 'member$a' ) )
=> ( A @ ( 'vector_scalar_mult$a' @ 'dependent$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom695) ).
thf(2938,plain,
! [A: 'A_m_vec_set$'] :
( ( A @ ( 'zero$a' @ 'member$a' ) )
=> ( A @ ( 'vector_scalar_mult$a' @ 'dependent$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(225,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom502) ).
thf(1784,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(150,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_m_vec_fun$',D: 'A_n_vec_a_m_vec_fun$'] :
( ( ! [E: 'A_n_vec$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$u' ) )
= ( E @ ( D @ 'fun_app$u' ) ) ) )
& ! [E: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$u' ) )
= 'zero$a' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( B @ ( C @ 'sum$a' ) )
= ( A @ ( D @ 'sum$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom719) ).
thf(1389,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_m_vec_fun$',D: 'A_n_vec_a_m_vec_fun$'] :
( ( ! [E: 'A_n_vec$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$u' ) )
= ( E @ ( D @ 'fun_app$u' ) ) ) )
& ! [E: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$u' ) )
= 'zero$a' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( B @ ( C @ 'sum$a' ) )
= ( A @ ( D @ 'sum$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(685,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxj$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom36) ).
thf(4077,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxj$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(27,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less$b' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less$b' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom750) ).
thf(843,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less$b' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less$b' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(88,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
=> ? [C: 'A_n_vec$'] : ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( C @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom738) ).
thf(1125,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
=> ? [C: 'A_n_vec$'] : ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( C @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(523,axiom,
! [A: 'A_n_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$' ) ) @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$' ) ) @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( B @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom335) ).
thf(3266,plain,
! [A: 'A_n_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$' ) ) @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$' ) ) @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( B @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(415,axiom,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'uxd$' @ 'fun_app$o' ) )
<=> ? [C: 'M$'] :
( ( ( A @ ( C @ 'row$a' ) )
!= 'zero$a' )
& ( B
= ( A @ ( C @ ( A @ 'uxc$' ) @ 'least$' @ 'column$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom24) ).
thf(2674,plain,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec$'] :
( ( ? [C: 'M$'] :
( ( ( A @ ( C @ 'row$a' ) )
!= 'zero$a' )
& ( B
= ( A @ ( C @ ( A @ 'uxc$' ) @ 'least$' @ 'column$a' ) ) ) )
=> ( B @ ( A @ 'uxd$' @ 'fun_app$o' ) ) )
& ( ( B @ ( A @ 'uxd$' @ 'fun_app$o' ) )
=> ? [C: 'M$'] :
( ( ( A @ ( C @ 'row$a' ) )
!= 'zero$a' )
& ( B
= ( A @ ( C @ ( A @ 'uxc$' ) @ 'least$' @ 'column$a' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(418,axiom,
! [A: 'N$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'is_zero_row$' ) )
<=> ( ( B @ ( A @ 'row$' ) )
= 'zero$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom699) ).
thf(2695,plain,
! [A: 'N$',B: 'A_m_vec_n_vec$'] :
( ( ( ( B @ ( A @ 'row$' ) )
= 'zero$a' )
=> ( B @ ( A @ 'is_zero_row$' ) ) )
& ( ( B @ ( A @ 'is_zero_row$' ) )
=> ( ( B @ ( A @ 'row$' ) )
= 'zero$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(173,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$b' ) )
= ( B @ ( A @ 'uwl$' ) @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom408) ).
thf(1488,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$b' ) )
= ( B @ ( A @ 'uwl$' ) @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(226,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) )
=> ( B @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom708) ).
thf(1786,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) )
=> ( B @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(709,axiom,
! [A: 'M$'] :
( ( A @ ( 'zero$a' @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom133) ).
thf(4186,plain,
! [A: 'M$'] :
( ( A @ ( 'zero$a' @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(342,axiom,
! [A: 'M$',B: 'A_m_vec_m_vec$'] :
( ( B @ ( A @ 'row$a' ) )
= ( A @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom383) ).
thf(2293,plain,
! [A: 'M$',B: 'A_m_vec_m_vec$'] :
( ( B @ ( A @ 'row$a' ) )
= ( A @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(145,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ 'uum$' @ ( A @ 'uum$' @ 'less_eq$a' ) )
<=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom646) ).
thf(1371,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( B @ 'uum$' @ ( A @ 'uum$' @ 'less_eq$a' ) ) )
& ( ( B @ 'uum$' @ ( A @ 'uum$' @ 'less_eq$a' ) )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(129,axiom,
! [A: 'A_m_vec$'] :
( ( A @ 'vec_nth$' @ 'vec_lambda$' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom365) ).
thf(1312,plain,
! [A: 'A_m_vec$'] :
( ( A @ 'vec_nth$' @ 'vec_lambda$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(240,axiom,
! [A: 'N$'] :
( ( A @ ( 'uws$' @ 'fun_app$b' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom110) ).
thf(1865,plain,
! [A: 'N$'] :
( ( A @ ( 'uws$' @ 'fun_app$b' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(72,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_bool_fun$'] :
( ( ! [C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ( D @ ( B @ 'fun_app$g' ) )
& ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( D @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( D @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) ) )
& ( A @ ( B @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( 'bot$' @ ( B @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom601) ).
thf(1058,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_bool_fun$'] :
( ( ! [C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ( D @ ( B @ 'fun_app$g' ) )
& ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( D @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( D @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) ) )
& ( A @ ( B @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( 'bot$' @ ( B @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(134,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$',D: 'A_n_vec_set$',E: 'A_n_vec$'] :
( ( ( C @ ( A @ 'times$c' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) )
& ( D @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( D @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom479) ).
thf(1332,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$',D: 'A_n_vec_set$',E: 'A_n_vec$'] :
( ( ( C @ ( A @ 'times$c' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) )
& ( D @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( D @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(420,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ! [C: 'A_n_vec$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom496) ).
thf(2706,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ! [C: 'A_n_vec$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(583,axiom,
! [A: 'A$',B: 'A_n_vec$'] :
( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' )
<=> ( ( B = 'zero$b' )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom675) ).
thf(3568,plain,
! [A: 'A$',B: 'A_n_vec$'] :
( ( ( ( B = 'zero$b' )
| ( A = 'zero$' ) )
=> ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' ) )
& ( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' )
=> ( ( B = 'zero$b' )
| ( A = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(617,axiom,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_n_vec_m_vec$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$d' ) @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$i' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$y' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom203) ).
thf(3751,plain,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_n_vec_m_vec$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$d' ) @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$i' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$y' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(697,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'zero$' @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom677) ).
thf(4127,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'zero$' @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(588,axiom,
( ! [A: 'A_n_vec$'] :
( ( ( ( 'i$' @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( 'uvk$' @ 'collect$c' @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom415) ).
thf(3594,plain,
~ ! [A: 'A_n_vec$'] :
~ ( ( ( 'i$' @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( 'uvk$' @ 'collect$c' @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(112,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( B @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom561) ).
thf(1239,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( B @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(625,axiom,
! [A: 'A_m_vec$'] :
( ( A @ ( 'zero$' @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom676) ).
thf(3783,plain,
! [A: 'A_m_vec$'] :
( ( A @ ( 'zero$' @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(288,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( A @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom302) ).
thf(2055,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( A @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(314,axiom,
! [A: 'M_bool_fun$'] :
( ? [B: 'M$'] :
( ! [C: 'M$'] :
( ( ! [D: 'M$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) )
=> ( C = B ) )
& ! [C: 'M$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom635) ).
thf(2166,plain,
! [A: 'M_bool_fun$'] :
( ? [B: 'M$'] :
( ! [C: 'M$'] :
( ( ! [D: 'M$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) )
=> ( C = B ) )
& ! [C: 'M$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(584,axiom,
'a$' @ 'columns$' @ ( 'x$' @ 'member$' @ 'fun_app$g' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom215) ).
thf(3579,plain,
'a$' @ 'columns$' @ ( 'x$' @ 'member$' @ 'fun_app$g' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(141,axiom,
! [A: 'A_n_vec_m_vec$',B: 'A_n_vec_m_vec$'] :
( ( B @ ( A @ 'times$g' ) )
= ( B @ ( A @ 'uve$' ) @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom350) ).
thf(1356,plain,
! [A: 'A_n_vec_m_vec$',B: 'A_n_vec_m_vec$'] :
( ( B @ ( A @ 'times$g' ) )
= ( B @ ( A @ 'uve$' ) @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(311,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_n_vec_bool_fun_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ? [E: 'A_n_vec$'] :
( ( E @ ( D @ ( C @ 'fun_app$q' ) @ 'fun_app$e' ) )
& ( B @ ( E @ 'member$' @ 'fun_app$g' ) ) ) )
& ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ~ ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ? [D: 'A_n_vec$'] :
( ~ ( D @ ( C @ ( A @ 'uxt$' ) @ 'fun_app$q' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom552) ).
thf(2148,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_n_vec_bool_fun_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ? [E: 'A_n_vec$'] :
( ( E @ ( D @ ( C @ 'fun_app$q' ) @ 'fun_app$e' ) )
& ( B @ ( E @ 'member$' @ 'fun_app$g' ) ) ) )
& ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ~ ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ? [D: 'A_n_vec$'] :
( ~ ( D @ ( C @ ( A @ 'uxt$' ) @ 'fun_app$q' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$g' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(609,axiom,
( ! [A: 'N$'] :
( ( ( ( 'a$' @ ( A @ 'row$' ) )
!= 'zero$a' )
& ( 'xa$'
= ( 'a$' @ ( A @ 'uvj$' @ 'least$' @ 'column$' ) ) ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom368) ).
thf(3719,plain,
~ ! [A: 'N$'] :
~ ( ( ( 'a$' @ ( A @ 'row$' ) )
!= 'zero$a' )
& ( 'xa$'
= ( 'a$' @ ( A @ 'uvj$' @ 'least$' @ 'column$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(86,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ? [C: 'A_n_vec_set$'] :
( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( B
= ( C @ ( A @ 'insert$' @ 'fun_app$f' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom538) ).
thf(1117,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ? [C: 'A_n_vec_set$'] :
( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( B
= ( C @ ( A @ 'insert$' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(63,axiom,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwp$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( A @ 'uwo$' ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom61) ).
thf(1011,plain,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwp$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( A @ 'uwo$' ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(452,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_row_row$a' ) ) @ 'fun_app$r' ) )
= ( D @ ( C @ ( B @ ( A @ 'uwa$' ) ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom402) ).
thf(2906,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_row_row$a' ) ) @ 'fun_app$r' ) )
= ( D @ ( C @ ( B @ ( A @ 'uwa$' ) ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(440,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uxw$' ) @ 'fun_app$e' ) )
<=> ( ~ ( B @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom47) ).
thf(2839,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ( ~ ( B @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'uxw$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uxw$' ) @ 'fun_app$e' ) )
=> ( ~ ( B @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(571,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_m_vec$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$a' ) @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom200) ).
thf(3500,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_m_vec$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$a' ) @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(87,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom592) ).
thf(1122,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(489,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( ( A @ 'vec_nth$c' )
= ( B @ 'vec_nth$c' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom174) ).
thf(3066,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( ( A = B )
=> ( ( A @ 'vec_nth$c' )
= ( B @ 'vec_nth$c' ) ) )
& ( ( ( A @ 'vec_nth$c' )
= ( B @ 'vec_nth$c' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(121,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( ! [C: 'A_n_vec_set$'] :
( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( B
= ( C @ ( A @ 'insert$' @ 'fun_app$f' ) ) ) )
=> $false )
& ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom543) ).
thf(1282,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
~ ( ! [C: 'A_n_vec_set$'] :
~ ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( B
= ( C @ ( A @ 'insert$' @ 'fun_app$f' ) ) ) )
& ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(380,axiom,
! [A: 'A_set$',B: 'A$'] :
( ( B @ ( A @ 'uuj$' @ 'fun_app$p' ) )
<=> ( A @ ( B @ 'member$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).
thf(2478,plain,
! [A: 'A_set$',B: 'A$'] :
( ( ( A @ ( B @ 'member$c' ) )
=> ( B @ ( A @ 'uuj$' @ 'fun_app$p' ) ) )
& ( ( B @ ( A @ 'uuj$' @ 'fun_app$p' ) )
=> ( A @ ( B @ 'member$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(520,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$a' ) ) @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$a' ) ) @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom336) ).
thf(3251,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$a' ) ) @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$a' ) ) @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( E @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(324,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uxu$' ) @ 'fun_app$e' ) )
<=> ( ( C != A )
=> ( C @ ( B @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom56) ).
thf(2214,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( ( ( C != A )
=> ( C @ ( B @ 'fun_app$e' ) ) )
=> ( C @ ( B @ ( A @ 'uxu$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uxu$' ) @ 'fun_app$e' ) )
=> ( ( C != A )
=> ( C @ ( B @ 'fun_app$e' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(406,axiom,
! [A: 'A_m_vec$'] :
( ( 'one$a' @ ( A @ 'times$b' @ 'fun_app$k' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom266) ).
thf(2624,plain,
! [A: 'A_m_vec$'] :
( ( 'one$a' @ ( A @ 'times$b' @ 'fun_app$k' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(603,axiom,
! [A: 'A_set$',B: 'A_set$'] :
( ( ( A @ ( B @ 'less_eq$c' ) )
& ~ ( A @ ( 'times$e' @ 'dependent$a' ) ) )
=> ~ ( B @ ( 'times$e' @ 'dependent$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom684) ).
thf(3683,plain,
! [A: 'A_set$',B: 'A_set$'] :
( ( ( A @ ( B @ 'less_eq$c' ) )
& ~ ( A @ ( 'times$e' @ 'dependent$a' ) ) )
=> ~ ( B @ ( 'times$e' @ 'dependent$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(179,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_a_n_vec_set_fun$',C: 'A_n_vec_set$',D: 'A_n_vec_set$'] :
( ( ! [E: 'A_n_vec_set$',F: 'A_n_vec_set$'] :
( ( F @ ( E @ 'less_eq$' @ 'fun_app$g' ) )
=> ( F @ ( B @ 'fun_app$f' ) @ ( E @ ( B @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( D @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( C @ ( B @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( D @ ( B @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom616) ).
thf(1524,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_a_n_vec_set_fun$',C: 'A_n_vec_set$',D: 'A_n_vec_set$'] :
( ( ! [E: 'A_n_vec_set$',F: 'A_n_vec_set$'] :
( ( F @ ( E @ 'less_eq$' @ 'fun_app$g' ) )
=> ( F @ ( B @ 'fun_app$f' ) @ ( E @ ( B @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( D @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( C @ ( B @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( D @ ( B @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(574,axiom,
! [A: 'M$'] :
( ( A @ ( 'uuw$' @ 'fun_app$' ) )
<=> ( ( A @ ( 'y$' @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom0) ).
thf(3515,plain,
! [A: 'M$'] :
( ( ( ( A @ ( 'y$' @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
=> ( A @ ( 'uuw$' @ 'fun_app$' ) ) )
& ( ( A @ ( 'uuw$' @ 'fun_app$' ) )
=> ( ( A @ ( 'y$' @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(190,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_m_vec_fun$',D: 'A_n_vec_a_m_vec_fun$'] :
( ( ! [E: 'A_n_vec$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( D @ 'fun_app$u' ) )
= ( E @ ( C @ 'fun_app$u' ) ) ) )
& ! [E: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$u' ) )
= 'zero$a' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( A @ ( D @ 'sum$a' ) )
= ( B @ ( C @ 'sum$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom721) ).
thf(1589,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_m_vec_fun$',D: 'A_n_vec_a_m_vec_fun$'] :
( ( ! [E: 'A_n_vec$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( D @ 'fun_app$u' ) )
= ( E @ ( C @ 'fun_app$u' ) ) ) )
& ! [E: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$u' ) )
= 'zero$a' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( A @ ( D @ 'sum$a' ) )
= ( B @ ( C @ 'sum$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(60,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set_a_n_vec_set_fun$',D: 'A_n_vec_set$'] :
( ( ! [E: 'A_n_vec_set$',F: 'A_n_vec_set$'] :
( ( F @ ( E @ 'less_eq$' @ 'fun_app$g' ) )
=> ( F @ ( C @ 'fun_app$f' ) @ ( E @ ( C @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom615) ).
thf(996,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set_a_n_vec_set_fun$',D: 'A_n_vec_set$'] :
( ( ! [E: 'A_n_vec_set$',F: 'A_n_vec_set$'] :
( ( F @ ( E @ 'less_eq$' @ 'fun_app$g' ) )
=> ( F @ ( C @ 'fun_app$f' ) @ ( E @ ( C @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(222,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom548) ).
thf(1771,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(462,axiom,
! [A: 'A_set$',B: 'A_set$',C: 'A_set$'] :
( ( C @ ( B @ ( A @ 'times$d' @ 'fun_app$l' ) @ 'times$d' @ 'fun_app$l' ) )
= ( C @ ( B @ 'times$d' @ 'fun_app$l' ) @ ( A @ 'times$d' @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom297) ).
thf(2943,plain,
! [A: 'A_set$',B: 'A_set$',C: 'A_set$'] :
( ( C @ ( B @ ( A @ 'times$d' @ 'fun_app$l' ) @ 'times$d' @ 'fun_app$l' ) )
= ( C @ ( B @ 'times$d' @ 'fun_app$l' ) @ ( A @ 'times$d' @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(228,axiom,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxi$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uwv$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom87) ).
thf(1801,plain,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxi$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uwv$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(703,axiom,
! [A: 'N_a_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$a' @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( B @ ( A @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom358) ).
thf(4154,plain,
! [A: 'N_a_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$a' @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( B @ ( A @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(403,axiom,
! [A: 'N$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'column$c' ) )
= ( B @ ( A @ 'uvp$' ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom391) ).
thf(2610,plain,
! [A: 'N$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'column$c' ) )
= ( B @ ( A @ 'uvp$' ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(600,axiom,
! [A: 'A_a_m_vec_fun$',B: 'A_n_vec_m_vec$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwc$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$z' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom81) ).
thf(3668,plain,
! [A: 'A_a_m_vec_fun$',B: 'A_n_vec_m_vec$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwc$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$z' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(673,axiom,
! [A: 'A$'] :
( ( A @ ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom241) ).
thf(4028,plain,
! [A: 'A$'] :
( ( A @ ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(239,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_row_row$c' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uwb$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom403) ).
thf(1862,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_row_row$c' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uwb$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(47,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom624) ).
thf(943,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(376,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( ( ( A @ ( 'zero$k' @ 'column$' ) )
!= 'zero$b' )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( 'zero$k' @ ( 'zero$j' @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom421) ).
thf(2461,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( ( ( A @ ( 'zero$k' @ 'column$' ) )
!= 'zero$b' )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( 'zero$k' @ ( 'zero$j' @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(421,axiom,
! [A: tlbool,B: 'A_m_vec$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'zero$a' @ 'times$b' @ 'fun_app$k' ) )
= 'zero$a' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'zero$a' @ 'times$b' @ 'fun_app$k' ) )
= B ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'one$a' @ 'times$b' @ 'fun_app$k' ) )
= 'zero$a' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'one$a' @ 'times$b' @ 'fun_app$k' ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom332) ).
thf(2710,plain,
! [A: tlbool,B: 'A_m_vec$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'zero$a' @ 'times$b' @ 'fun_app$k' ) )
= 'zero$a' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'zero$a' @ 'times$b' @ 'fun_app$k' ) )
= B ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'one$a' @ 'times$b' @ 'fun_app$k' ) )
= 'zero$a' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'one$a' @ 'times$b' @ 'fun_app$k' ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(22,axiom,
! [A: 'A_n_vec_set$'] :
( ( A @ 'the_elem$a' )
= ( A @ 'uye$' @ 'the$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom648) ).
thf(811,plain,
! [A: 'A_n_vec_set$'] :
( ( A @ 'the_elem$a' )
= ( A @ 'uye$' @ 'the$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(316,axiom,
! [A: 'A$'] :
( ( 'zero$a' @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom663) ).
thf(2182,plain,
! [A: 'A$'] :
( ( 'zero$a' @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(19,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec$'] :
( ( ( B @ ( A @ 'fun_app$e' ) )
& ? [C: 'A_n_vec$'] :
( ! [D: 'A_n_vec$'] :
( ( D @ ( A @ 'fun_app$e' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$e' ) ) ) )
=> ( ( A @ 'the$a' )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom216) ).
thf(799,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec$'] :
( ( ( B @ ( A @ 'fun_app$e' ) )
& ? [C: 'A_n_vec$'] :
( ! [D: 'A_n_vec$'] :
( ( D @ ( A @ 'fun_app$e' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$e' ) ) ) )
=> ( ( A @ 'the$a' )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(98,axiom,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_column$' ) ) )
= ( C @ ( B @ ( A @ 'uxg$' ) ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom444) ).
thf(1162,plain,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_column$' ) ) )
= ( C @ ( B @ ( A @ 'uxg$' ) ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(663,axiom,
! [A: 'A_n_vec_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxb$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$c' ) )
=> ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom439) ).
thf(3971,plain,
! [A: 'A_n_vec_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxb$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$c' ) )
=> ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(586,axiom,
! [A: 'N_bool_fun$',B: 'N_bool_fun$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$c' ) )
=> ( C @ ( B @ 'fun_app$c' ) ) )
& ? [C: 'N$'] :
( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$c' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$c' ) ) ) )
=> ( A @ 'the$' @ ( B @ 'fun_app$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom327) ).
thf(3583,plain,
! [A: 'N_bool_fun$',B: 'N_bool_fun$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$c' ) )
=> ( C @ ( B @ 'fun_app$c' ) ) )
& ? [C: 'N$'] :
( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$c' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$c' ) ) ) )
=> ( A @ 'the$' @ ( B @ 'fun_app$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(187,axiom,
! [A: 'A_m_vec_bool_fun$',B: 'A_m_vec_bool_fun$'] :
( ! [C: 'A_m_vec$'] :
( ( C @ ( A @ 'fun_app$o' ) )
<=> ( C @ ( B @ 'fun_app$o' ) ) )
=> ( ( A @ 'collect$a' )
= ( B @ 'collect$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom227) ).
thf(1556,plain,
! [A: 'A_m_vec_bool_fun$',B: 'A_m_vec_bool_fun$'] :
( ! [C: 'A_m_vec$'] :
( ( ( C @ ( B @ 'fun_app$o' ) )
=> ( C @ ( A @ 'fun_app$o' ) ) )
& ( ( C @ ( A @ 'fun_app$o' ) )
=> ( C @ ( B @ 'fun_app$o' ) ) ) )
=> ( ( A @ 'collect$a' )
= ( B @ 'collect$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(164,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'A_m_vec_n_vec$'] :
( ( C @ ( B @ ( A @ 'times$' @ 'fun_app$h' ) @ 'times$' @ 'fun_app$h' ) )
= ( C @ ( B @ 'times$' @ 'fun_app$h' ) @ ( A @ 'times$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom288) ).
thf(1460,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'A_m_vec_n_vec$'] :
( ( C @ ( B @ ( A @ 'times$' @ 'fun_app$h' ) @ 'times$' @ 'fun_app$h' ) )
= ( C @ ( B @ 'times$' @ 'fun_app$h' ) @ ( A @ 'times$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(398,axiom,
! [A: 'A_n_vec_set$'] :
( ( 'bot$' @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom506) ).
thf(2578,plain,
! [A: 'A_n_vec_set$'] :
( ( ( A = 'bot$' )
=> ( 'bot$' @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( 'bot$' @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(210,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom617) ).
thf(1688,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(40,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ~ ( A @ ( B @ 'less$b' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom743) ).
thf(912,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ~ ( A @ ( B @ 'less$b' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(104,axiom,
! [A: 'M$',B: 'A_m_vec_m_vec_n_vec$'] :
( ( B @ ( A @ 'column$e' ) )
= ( B @ ( A @ 'uvm$' ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom388) ).
thf(1198,plain,
! [A: 'M$',B: 'A_m_vec_m_vec_n_vec$'] :
( ( B @ ( A @ 'column$e' ) )
= ( B @ ( A @ 'uvm$' ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(422,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$h' ) @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom125) ).
thf(2725,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$h' ) @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(556,axiom,
! [A: tlbool,B: 'A$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'zero$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'zero$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= B ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom333) ).
thf(3423,plain,
! [A: tlbool,B: 'A$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'zero$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'zero$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= B ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( B @ ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ) )
& ( ( A = tltrue )
=> ( ( B @ ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(199,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( A @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B @ ( C @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom619) ).
thf(1643,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( A @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B @ ( C @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(36,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( 'one$b' = A )
<=> ( A = 'one$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom253) ).
thf(883,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( ( A = 'one$b' )
=> ( 'one$b' = A ) )
& ( ( 'one$b' = A )
=> ( A = 'one$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(358,axiom,
'bot$' @ ( 'v$' @ 'insert$' @ 'fun_app$f' ) @ ( 'uvk$' @ 'collect$c' @ 'minus$b' @ 'fun_app$f' ) @ ( 'xa$' @ 'member$' @ 'fun_app$g' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom446) ).
thf(2369,plain,
'bot$' @ ( 'v$' @ 'insert$' @ 'fun_app$f' ) @ ( 'uvk$' @ 'collect$c' @ 'minus$b' @ 'fun_app$f' ) @ ( 'xa$' @ 'member$' @ 'fun_app$g' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(101,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( A @ ( 'finite$' @ 'fun_app$g' ) )
=> ( A @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom573) ).
thf(1176,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( A @ ( 'finite$' @ 'fun_app$g' ) )
=> ( A @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(501,axiom,
! [A: 'A_n_vec_n_vec_m_vec$'] :
( ( ( ( A @ ( 'zero$j' @ 'column$g' ) )
!= 'zero$e' )
& ( A @ 'reduced_row_echelon_form$b' ) )
=> ( ( 'zero$j' @ ( 'zero$k' @ ( A @ 'vec_nth$j' ) @ 'vec_nth$c' @ 'fun_app$r' ) )
= 'one$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom418) ).
thf(3142,plain,
! [A: 'A_n_vec_n_vec_m_vec$'] :
( ( ( ( A @ ( 'zero$j' @ 'column$g' ) )
!= 'zero$e' )
& ( A @ 'reduced_row_echelon_form$b' ) )
=> ( ( 'zero$j' @ ( 'zero$k' @ ( A @ 'vec_nth$j' ) @ 'vec_nth$c' @ 'fun_app$r' ) )
= 'one$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(298,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuc$' @ 'fun_app$i' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom108) ).
thf(2101,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuc$' @ 'fun_app$i' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(313,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uvk$' @ 'fun_app$e' ) )
<=> ? [B: 'N$'] :
( ( ( 'a$' @ ( B @ 'row$' ) )
!= 'zero$a' )
& ( A
= ( 'a$' @ ( B @ 'uvj$' @ 'least$' @ 'column$' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).
thf(2156,plain,
! [A: 'A_n_vec$'] :
( ( ? [B: 'N$'] :
( ( ( 'a$' @ ( B @ 'row$' ) )
!= 'zero$a' )
& ( A
= ( 'a$' @ ( B @ 'uvj$' @ 'least$' @ 'column$' ) ) ) )
=> ( A @ ( 'uvk$' @ 'fun_app$e' ) ) )
& ( ( A @ ( 'uvk$' @ 'fun_app$e' ) )
=> ? [B: 'N$'] :
( ( ( 'a$' @ ( B @ 'row$' ) )
!= 'zero$a' )
& ( A
= ( 'a$' @ ( B @ 'uvj$' @ 'least$' @ 'column$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(578,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( A != 'zero$' )
=> ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom179) ).
thf(3539,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( A != 'zero$' )
=> ( ( ( B = C )
=> ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) )
& ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(56,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'minus$d' ) )
= ( B @ ( A @ 'uxl$' ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom477) ).
thf(983,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'minus$d' ) )
= ( B @ ( A @ 'uxl$' ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(74,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'collect$c' )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom519) ).
thf(1066,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'collect$c' )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(180,axiom,
! [A: 'A_n_vec_set$'] :
( ( A @ ( 'is_singleton$' @ 'fun_app$g' ) )
<=> ? [B: 'A_n_vec$'] :
( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom731) ).
thf(1528,plain,
! [A: 'A_n_vec_set$'] :
( ( ? [B: 'A_n_vec$'] :
( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'is_singleton$' @ 'fun_app$g' ) ) )
& ( ( A @ ( 'is_singleton$' @ 'fun_app$g' ) )
=> ? [B: 'A_n_vec$'] :
( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(57,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom544) ).
thf(986,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(340,axiom,
! [A: 'M$',B: 'A_m_vec_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvm$' ) @ 'fun_app$b' ) )
= ( A @ ( C @ ( B @ 'vec_nth$g' ) @ 'vec_nth$e' @ 'fun_app$t' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom51) ).
thf(2288,plain,
! [A: 'M$',B: 'A_m_vec_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvm$' ) @ 'fun_app$b' ) )
= ( A @ ( C @ ( B @ 'vec_nth$g' ) @ 'vec_nth$e' @ 'fun_app$t' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(330,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$' @ 'fun_app$h' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom128) ).
thf(2244,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$' @ 'fun_app$h' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(61,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_bool_fun$'] :
( ( ! [C: 'A_n_vec_set$'] :
( ( ! [D: 'A_n_vec$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) ) )
& ( A @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( C != 'bot$' )
& ( C @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( B @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( A @ ( B @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom604) ).
thf(1000,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_bool_fun$'] :
( ( ! [C: 'A_n_vec_set$'] :
( ( ! [D: 'A_n_vec$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) ) )
& ( A @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( C != 'bot$' )
& ( C @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( B @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( A @ ( B @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(144,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ( B @ ( A @ 'uxm$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
<=> ( ( B @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
& ( A @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom503) ).
thf(1364,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ( ( ( B @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
& ( A @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'uxm$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) )
& ( ( B @ ( A @ 'uxm$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
=> ( ( B @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
& ( A @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(116,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_bool_fun$'] :
( ( ! [C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ( D @ ( B @ 'fun_app$g' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( D != 'bot$' )
& ( D @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( D @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) ) )
& ! [C: 'A_n_vec$'] : ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( A @ ( B @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom588) ).
thf(1250,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_bool_fun$'] :
( ( ! [C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ( D @ ( B @ 'fun_app$g' ) )
& ~ ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( D != 'bot$' )
& ( D @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( D @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) ) )
& ! [C: 'A_n_vec$'] : ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( A @ ( B @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(483,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'bot$e' @ 'fun_app$e' ) )
<=> ( 'bot$' @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom650) ).
thf(3031,plain,
! [A: 'A_n_vec$'] :
( ( ( 'bot$' @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( A @ ( 'bot$e' @ 'fun_app$e' ) ) )
& ( ( A @ ( 'bot$e' @ 'fun_app$e' ) )
=> ( 'bot$' @ ( A @ 'member$' @ 'fun_app$g' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(296,axiom,
( ( 'a$' @ ( 'y$' @ 'row$' ) )
!= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom328) ).
thf(2096,plain,
( ( 'a$' @ ( 'y$' @ 'row$' ) )
!= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(219,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( C @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom595) ).
thf(1758,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( C @ ( A @ 'minus$b' @ 'fun_app$f' ) @ 'minus$b' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(106,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( A @ ( C @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom574) ).
thf(1203,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( A @ ( C @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(413,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( B @ ( A @ 'uum$' @ 'fun_app$e' ) )
<=> ( A @ ( B @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom14) ).
thf(2665,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] :
( ( ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
=> ( B @ ( A @ 'uum$' @ 'fun_app$e' ) ) )
& ( ( B @ ( A @ 'uum$' @ 'fun_app$e' ) )
=> ( A @ ( B @ 'member$' @ 'fun_app$g' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(432,axiom,
! [A: 'A$',B: 'A_m_vec$',C: 'A$'] :
( ( ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= ( B @ ( C @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) ) )
<=> ( ( B = 'zero$a' )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom661) ).
thf(2784,plain,
! [A: 'A$',B: 'A_m_vec$',C: 'A$'] :
( ( ( ( B = 'zero$a' )
| ( A = C ) )
=> ( ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= ( B @ ( C @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) ) ) )
& ( ( ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= ( B @ ( C @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) ) )
=> ( ( B = 'zero$a' )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(446,axiom,
! [A: 'A_n_vec_bool_fun$'] :
( ~ ( A @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
=> ? [B: 'A_n_vec$'] : ( B @ ( A @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom553) ).
thf(2878,plain,
! [A: 'A_n_vec_bool_fun$'] :
( ~ ( A @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
=> ? [B: 'A_n_vec$'] : ( B @ ( A @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(416,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N_a_n_vec_fun$'] :
( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( C @ ( B @ 'fun_app$r' ) ) )
<=> ( ( B @ 'vec_lambda$e' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom373) ).
thf(2684,plain,
! [A: 'A_n_vec_n_vec$',B: 'N_a_n_vec_fun$'] :
( ( ( ( B @ 'vec_lambda$e' )
= A )
=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( C @ ( B @ 'fun_app$r' ) ) ) )
& ( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( C @ ( B @ 'fun_app$r' ) ) )
=> ( ( B @ 'vec_lambda$e' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(168,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A = B )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom614) ).
thf(1472,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A = B )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(525,axiom,
! [A: 'N$'] :
( ( A @ 'uug$' @ 'the$' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom194) ).
thf(3278,plain,
! [A: 'N$'] :
( ( A @ 'uug$' @ 'the$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(528,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom299) ).
thf(3292,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(156,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) )
=> ( B @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom685) ).
thf(1413,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) )
=> ( B @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(76,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom528) ).
thf(1076,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(559,axiom,
! [A: 'A_n_vec_m_vec$',B: 'A_m_vec$',C: 'M$',D: 'M$'] :
( ( ( C != D )
& ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxb$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$c' ) )
=> ( ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom431) ).
thf(3444,plain,
! [A: 'A_n_vec_m_vec$',B: 'A_m_vec$',C: 'M$',D: 'M$'] :
( ( ( C != D )
& ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxb$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$c' ) )
=> ( ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(69,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ( ( B @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
| ( A @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'uxn$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom504) ).
thf(1034,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ( ( B @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
| ( A @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'uxn$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(126,axiom,
( 'zero$c'
= ( 'uws$' @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom412) ).
thf(1304,plain,
( 'zero$c'
= ( 'uws$' @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(243,axiom,
( 'zero$a'
= ( 'uwu$' @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom414) ).
thf(1873,plain,
( 'zero$a'
= ( 'uwu$' @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(506,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuz$' @ 'fun_app$j' ) )
= ( A @ ( 'times$a' @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom345) ).
thf(3161,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuz$' @ 'fun_app$j' ) )
= ( A @ ( 'times$a' @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(159,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A = B )
<=> ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom527) ).
thf(1420,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(43,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set_bool_fun$'] :
( ( ! [D: 'A_n_vec$',E: 'A_n_vec_set$'] :
( ( ( E @ ( C @ 'fun_app$g' ) )
& ~ ( E @ ( D @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
& ( E @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( E @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( C @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( A @ ( C @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom598) ).
thf(927,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set_bool_fun$'] :
( ( ! [D: 'A_n_vec$',E: 'A_n_vec_set$'] :
( ( ( E @ ( C @ 'fun_app$g' ) )
& ~ ( E @ ( D @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
& ( E @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( E @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'fun_app$g' ) ) )
& ( 'bot$' @ ( C @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> ( A @ ( C @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(282,axiom,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uvd$' ) @ 'fun_app$t' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ ( C @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom32) ).
thf(2037,plain,
! [A: 'A_m_vec_m_vec$',B: 'A_m_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uvd$' ) @ 'fun_app$t' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ ( C @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(681,axiom,
! [A: 'A$'] :
( ( 'zero$' = A )
<=> ( A = 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom286) ).
thf(4052,plain,
! [A: 'A$'] :
( ( ( A = 'zero$' )
=> ( 'zero$' = A ) )
& ( ( 'zero$' = A )
=> ( A = 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(305,axiom,
! [A: 'A_set$',B: 'A_set$',C: 'A_set$'] :
( ( C @ ( B @ ( A @ 'times$d' @ 'fun_app$l' ) @ 'times$d' @ 'fun_app$l' ) )
= ( C @ ( B @ 'times$d' @ 'fun_app$l' ) @ ( A @ 'times$d' @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom291) ).
thf(2124,plain,
! [A: 'A_set$',B: 'A_set$',C: 'A_set$'] :
( ( C @ ( B @ ( A @ 'times$d' @ 'fun_app$l' ) @ 'times$d' @ 'fun_app$l' ) )
= ( C @ ( B @ 'times$d' @ 'fun_app$l' ) @ ( A @ 'times$d' @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(708,axiom,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'M$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$b' ) ) @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$b' ) ) @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom341) ).
thf(4177,plain,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'M$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$b' ) ) @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_column_row$b' ) ) @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(457,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec_set$',C: 'A_m_vec_set$'] :
( ( ! [D: 'A_m_vec$',E: 'A_m_vec$'] :
( ( ( C @ ( E @ 'member$a' ) )
& ( B @ ( D @ 'member$a' ) )
& ( A
= ( E @ ( D @ 'times$b' @ 'fun_app$k' ) ) ) )
=> $false )
& ( C @ ( B @ 'times$j' ) @ ( A @ 'member$a' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom313) ).
thf(2927,plain,
! [A: 'A_m_vec$',B: 'A_m_vec_set$',C: 'A_m_vec_set$'] :
~ ( ! [D: 'A_m_vec$',E: 'A_m_vec$'] :
~ ( ( C @ ( E @ 'member$a' ) )
& ( B @ ( D @ 'member$a' ) )
& ( A
= ( E @ ( D @ 'times$b' @ 'fun_app$k' ) ) ) )
& ( C @ ( B @ 'times$j' ) @ ( A @ 'member$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(654,axiom,
! [A: 'N$',B: 'M$'] :
( ( B @ ( A @ 'uvj$' @ 'fun_app$' ) )
<=> ( ( B @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom22) ).
thf(3921,plain,
! [A: 'N$',B: 'M$'] :
( ( ( ( B @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
=> ( B @ ( A @ 'uvj$' @ 'fun_app$' ) ) )
& ( ( B @ ( A @ 'uvj$' @ 'fun_app$' ) )
=> ( ( B @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(137,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= ( B @ ( A @ 'uxw$' ) @ 'collect$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom556) ).
thf(1340,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= ( B @ ( A @ 'uxw$' ) @ 'collect$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(352,axiom,
! [A: 'A$',B: 'A_n_vec$',C: 'A$'] :
( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( B @ ( C @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) )
<=> ( ( B = 'zero$b' )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom662) ).
thf(2333,plain,
! [A: 'A$',B: 'A_n_vec$',C: 'A$'] :
( ( ( ( B = 'zero$b' )
| ( A = C ) )
=> ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( B @ ( C @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) ) )
& ( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( B @ ( C @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) )
=> ( ( B = 'zero$b' )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(441,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_fun$',C: 'A_n_vec$'] :
( ( B @ ( A @ 'uyi$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
=> ( ( ~ ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'sum$' ) )
= ( A @ ( B @ 'sum$' ) ) ) )
& ( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'sum$' ) )
= ( C @ ( B @ 'fun_app$v' ) @ ( A @ ( B @ 'sum$' ) @ 'minus$a' @ 'fun_app$m' ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom726) ).
thf(2846,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_fun$',C: 'A_n_vec$'] :
( ( B @ ( A @ 'uyi$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
=> ( ( ~ ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'sum$' ) )
= ( A @ ( B @ 'sum$' ) ) ) )
& ( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( B @ 'sum$' ) )
= ( C @ ( B @ 'fun_app$v' ) @ ( A @ ( B @ 'sum$' ) @ 'minus$a' @ 'fun_app$m' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(334,axiom,
! [A: 'A$'] :
( ( 'zero$b' @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom664) ).
thf(2256,plain,
! [A: 'A$'] :
( ( 'zero$b' @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(53,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
<=> ( B @ 'uum$' @ ( A @ 'uum$' @ 'less_eq$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom520) ).
thf(968,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ 'uum$' @ ( A @ 'uum$' @ 'less_eq$a' ) )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( B @ 'uum$' @ ( A @ 'uum$' @ 'less_eq$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(103,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec$',D: 'A_n_vec$'] :
( ( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'insert$' @ 'fun_app$f' ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom566) ).
thf(1181,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec$',D: 'A_n_vec$'] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'insert$' @ 'fun_app$f' ) ) ) )
& ( ( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'insert$' @ 'fun_app$f' ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(666,axiom,
! [A: 'M$'] :
( ( A @ ( 'uwu$' @ 'fun_app$a' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom112) ).
thf(3988,plain,
! [A: 'M$'] :
( ( A @ ( 'uwu$' @ 'fun_app$a' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(184,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_m_vec$'] :
( ( B @ ( A @ 'map_matrix$a' ) )
= ( B @ ( A @ 'uwj$' ) @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom407) ).
thf(1547,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_m_vec$'] :
( ( B @ ( A @ 'map_matrix$a' ) )
= ( B @ ( A @ 'uwj$' ) @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(612,axiom,
! [A: 'A_set$',B: 'A_set$'] :
( ( ( B @ ( A @ 'less_eq$c' ) )
& ( A @ ( 'times$e' @ 'dependent$a' ) ) )
=> ( B @ ( 'times$e' @ 'dependent$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom709) ).
thf(3737,plain,
! [A: 'A_set$',B: 'A_set$'] :
( ( ( B @ ( A @ 'less_eq$c' ) )
& ( A @ ( 'times$e' @ 'dependent$a' ) ) )
=> ( B @ ( 'times$e' @ 'dependent$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(34,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( 'one$b' @ ( A @ 'times$' @ 'fun_app$h' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom230) ).
thf(872,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( 'one$b' @ ( A @ 'times$' @ 'fun_app$h' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(468,axiom,
'uvk$' @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom442) ).
thf(2977,plain,
'uvk$' @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(216,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) )
<=> ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom501) ).
thf(1743,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) )
& ( ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(492,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( ~ ( A @ ( C @ 'is_zero_row$' ) )
& ~ ( A @ ( B @ 'is_zero_row$' ) )
& ( C @ ( B @ 'less$' @ 'fun_app$c' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( C @ ( A @ 'uxe$' ) @ 'least$' @ ( B @ ( A @ 'uxe$' ) @ 'least$' @ 'less$a' @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom733) ).
thf(3082,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( ~ ( A @ ( C @ 'is_zero_row$' ) )
& ~ ( A @ ( B @ 'is_zero_row$' ) )
& ( C @ ( B @ 'less$' @ 'fun_app$c' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( C @ ( A @ 'uxe$' ) @ 'least$' @ ( B @ ( A @ 'uxe$' ) @ 'least$' @ 'less$a' @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(597,axiom,
( ( 'i$' @ ( 'xa$' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom119) ).
thf(3659,plain,
( ( 'i$' @ ( 'xa$' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(563,axiom,
! [A: 'A$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) )
<=> ( ( B = C )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom653) ).
thf(3462,plain,
! [A: 'A$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( ( ( B = C )
| ( A = 'zero$' ) )
=> ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) ) )
& ( ( ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) )
=> ( ( B = C )
| ( A = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(498,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_n_vec_bool_fun_fun$',C: 'A_n_vec$',D: 'A_n_vec$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxt$' ) @ 'fun_app$q' ) @ 'fun_app$e' ) )
<=> ( ( C @ ( D @ ( B @ 'fun_app$q' ) @ 'fun_app$e' ) )
& ( A @ ( D @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom76) ).
thf(3129,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_n_vec_bool_fun_fun$',C: 'A_n_vec$',D: 'A_n_vec$'] :
( ( ( ( C @ ( D @ ( B @ 'fun_app$q' ) @ 'fun_app$e' ) )
& ( A @ ( D @ 'member$' @ 'fun_app$g' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uxt$' ) @ 'fun_app$q' ) @ 'fun_app$e' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uxt$' ) @ 'fun_app$q' ) @ 'fun_app$e' ) )
=> ( ( C @ ( D @ ( B @ 'fun_app$q' ) @ 'fun_app$e' ) )
& ( A @ ( D @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(224,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( B = C )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom625) ).
thf(1780,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( B = C )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(626,axiom,
~ ( 'bot$b' @ ( 'times$e' @ 'dependent$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom669) ).
thf(3786,plain,
~ ( 'bot$b' @ ( 'times$e' @ 'dependent$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(448,axiom,
! [A: 'A$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom665) ).
thf(2882,plain,
! [A: 'A$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( B @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(59,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'vec_nth$a' @ 'vec_lambda$b' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom366) ).
thf(993,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'vec_nth$a' @ 'vec_lambda$b' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(344,axiom,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxg$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvx$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom89) ).
thf(2298,plain,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxg$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvx$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(550,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$g' ) @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$k' ) @ 'vec_nth$c' @ 'fun_app$r' ) @ ( A @ 'fun_app$v' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom206) ).
thf(3391,plain,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$g' ) @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$k' ) @ 'vec_nth$c' @ 'fun_app$r' ) @ ( A @ 'fun_app$v' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(521,axiom,
( ( 'i$' @ ( 'v$' @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom120) ).
thf(3260,plain,
( ( 'i$' @ ( 'v$' @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(618,axiom,
! [A: 'A$'] :
( ( 'zero$' @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom142) ).
thf(3754,plain,
! [A: 'A$'] :
( ( 'zero$' @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(425,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( A = B )
<=> ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom164) ).
thf(2747,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: 'M$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(396,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uxm$' ) @ 'fun_app$e' ) )
<=> ( ( C @ ( B @ 'fun_app$e' ) )
| ( C @ ( A @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom54) ).
thf(2569,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( ( ( C @ ( B @ 'fun_app$e' ) )
| ( C @ ( A @ 'fun_app$e' ) ) )
=> ( C @ ( B @ ( A @ 'uxm$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uxm$' ) @ 'fun_app$e' ) )
=> ( ( C @ ( B @ 'fun_app$e' ) )
| ( C @ ( A @ 'fun_app$e' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(160,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) ) )
<=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom487) ).
thf(1432,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( A = C ) )
=> ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) ) ) )
& ( ( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) ) )
=> ( ( 'bot$' @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(18,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'uuh$' @ 'fun_app$q' ) @ 'fun_app$e' ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20) ).
thf(791,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( B = A )
=> ( B @ ( A @ ( 'uuh$' @ 'fun_app$q' ) @ 'fun_app$e' ) ) )
& ( ( B @ ( A @ ( 'uuh$' @ 'fun_app$q' ) @ 'fun_app$e' ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(70,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) )
<=> ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( C @ ( A @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom508) ).
thf(1038,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( C @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( C @ ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( C @ ( A @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(3,axiom,
! [A: 'A_n_vec_set$'] :
( ( A @ ( 'one$e' @ 'times$c' @ 'fun_app$f' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom263) ).
thf(717,plain,
! [A: 'A_n_vec_set$'] :
( ( A @ ( 'one$e' @ 'times$c' @ 'fun_app$f' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(514,axiom,
! [A: 'A_n_vec_a_m_vec_fun$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uyl$' ) @ 'fun_app$e' ) )
<=> ( ( ( C @ ( A @ 'fun_app$u' ) )
!= 'zero$a' )
& ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom45) ).
thf(3202,plain,
! [A: 'A_n_vec_a_m_vec_fun$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ( ( ( C @ ( A @ 'fun_app$u' ) )
!= 'zero$a' )
& ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'uyl$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uyl$' ) @ 'fun_app$e' ) )
=> ( ( ( C @ ( A @ 'fun_app$u' ) )
!= 'zero$a' )
& ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(117,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'insert$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom497) ).
thf(1262,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'insert$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(634,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom311) ).
thf(3823,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(79,axiom,
! [A: 'A_n_vec_m_vec$'] :
( ( A @ 'vec_nth$d' @ 'vec_lambda$d' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom362) ).
thf(1085,plain,
! [A: 'A_n_vec_m_vec$'] :
( ( A @ 'vec_nth$d' @ 'vec_lambda$d' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(554,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ 'minus$a' @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom471) ).
thf(3412,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ 'minus$a' @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(546,axiom,
! [A: 'A$',B: 'A$'] :
( ( A = B )
<=> ( ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) )
= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom467) ).
thf(3359,plain,
! [A: 'A$',B: 'A$'] :
( ( ( ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) )
= 'zero$' )
=> ( A = B ) )
& ( ( A = B )
=> ( ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) )
= 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(693,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'times$b' @ 'fun_app$k' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom127) ).
thf(4117,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'times$b' @ 'fun_app$k' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(354,axiom,
! [A: 'A_n_vec_set$'] :
( ( 'bot$' @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom632) ).
thf(2354,plain,
! [A: 'A_n_vec_set$'] :
( ( 'bot$' @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( A = 'bot$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(268,axiom,
! [A: tlbool,B: 'A_m_vec_m_vec$',C: 'A_m_vec_m_vec$',D: 'M$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( C @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( D @ ( C @ 'vec_nth$e' @ 'fun_app$t' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( D @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) ) ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( D @ ( C @ 'vec_nth$e' @ 'fun_app$t' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( D @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom154) ).
thf(1987,plain,
! [A: tlbool,B: 'A_m_vec_m_vec$',C: 'A_m_vec_m_vec$',D: 'M$'] :
( ( ( A != tltrue )
=> ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( D @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) ) ) ) )
& ( ( A = tltrue )
=> ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) )
= ( D @ ( C @ 'vec_nth$e' @ 'fun_app$t' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(325,axiom,
! [A: 'A_n_vec_set$'] :
( ? [B: 'A_n_vec$'] : ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
<=> ( A != 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom522) ).
thf(2224,plain,
! [A: 'A_n_vec_set$'] :
( ( ( A != 'bot$' )
=> ? [B: 'A_n_vec$'] : ( A @ ( B @ 'member$' @ 'fun_app$g' ) ) )
& ( ? [B: 'A_n_vec$'] : ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
=> ( A != 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(197,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom564) ).
thf(1637,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(628,axiom,
! [A: 'N$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'row$c' ) )
= ( A @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom385) ).
thf(3791,plain,
! [A: 'N$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'row$c' ) )
= ( A @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(622,axiom,
! [A: 'A_n_vec_m_vec$'] :
( ( ( ( 'zero$j' @ ( 'zero$k' @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$' )
& ( A @ 'reduced_row_echelon_form$c' ) )
=> ( ( A @ ( 'zero$j' @ 'column$b' ) )
= 'zero$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom422) ).
thf(3774,plain,
! [A: 'A_n_vec_m_vec$'] :
( ( ( ( 'zero$j' @ ( 'zero$k' @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$' )
& ( A @ 'reduced_row_echelon_form$c' ) )
=> ( ( A @ ( 'zero$j' @ 'column$b' ) )
= 'zero$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(231,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom547) ).
thf(1830,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
~ ( ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(182,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$g' ) )
=> ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom514) ).
thf(1538,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$g' ) )
=> ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(382,axiom,
! [A: 'N_a_n_vec_bool_fun_fun$'] :
( ! [B: 'N$'] :
? [C: 'A_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$ac' ) @ 'fun_app$e' ) )
<=> ? [B: 'A_n_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ ( C @ ( A @ 'fun_app$ac' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom168) ).
thf(2486,plain,
! [A: 'N_a_n_vec_bool_fun_fun$'] :
( ( ? [B: 'A_n_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ ( C @ ( A @ 'fun_app$ac' ) @ 'fun_app$e' ) )
=> ! [B: 'N$'] :
? [C: 'A_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$ac' ) @ 'fun_app$e' ) ) )
& ( ! [B: 'N$'] :
? [C: 'A_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$ac' ) @ 'fun_app$e' ) )
=> ? [B: 'A_n_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ ( C @ ( A @ 'fun_app$ac' ) @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(638,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwa$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwa$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).
thf(3847,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwa$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwa$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(21,axiom,
'zero$c' != 'one$b',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom271) ).
thf(808,plain,
'zero$c' != 'one$b',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(331,axiom,
! [A: 'M$',B: 'M_bool_fun$'] :
( ( B @ 'least$' @ ( A @ 'less$a' @ 'fun_app$' ) )
=> ~ ( A @ ( B @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom739) ).
thf(2247,plain,
! [A: 'M$',B: 'M_bool_fun$'] :
( ( B @ 'least$' @ ( A @ 'less$a' @ 'fun_app$' ) )
=> ~ ( A @ ( B @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(567,axiom,
( ( 'b$' @ ( 'v$' @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom150) ).
thf(3488,plain,
( ( 'b$' @ ( 'v$' @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(250,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> ( D @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( C @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom213) ).
thf(1898,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ( D @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> ( D @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( C @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(555,axiom,
! [A: 'A$'] :
( ( 'bot$b' @ ( A @ 'insert$b' ) @ ( 'times$e' @ 'dependent$a' ) )
<=> ( A = 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom680) ).
thf(3415,plain,
! [A: 'A$'] :
( ( ( A = 'zero$' )
=> ( 'bot$b' @ ( A @ 'insert$b' ) @ ( 'times$e' @ 'dependent$a' ) ) )
& ( ( 'bot$b' @ ( A @ 'insert$b' ) @ ( 'times$e' @ 'dependent$a' ) )
=> ( A = 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(545,axiom,
! [A: 'A$',B: 'A$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom656) ).
thf(3356,plain,
! [A: 'A$',B: 'A$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(109,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom567) ).
thf(1221,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( A = B )
=> ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) )
& ( ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(482,axiom,
! [A: 'A_set$',B: 'A_set_set$',C: 'A_set_set$'] :
( ( ! [D: 'A_set$',E: 'A_set$'] :
( ( ( C @ ( E @ 'member$e' ) )
& ( B @ ( D @ 'member$e' ) )
& ( A
= ( E @ ( D @ 'times$d' @ 'fun_app$l' ) ) ) )
=> $false )
& ( C @ ( B @ 'times$k' ) @ ( A @ 'member$e' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom314) ).
thf(3024,plain,
! [A: 'A_set$',B: 'A_set_set$',C: 'A_set_set$'] :
~ ( ! [D: 'A_set$',E: 'A_set$'] :
~ ( ( C @ ( E @ 'member$e' ) )
& ( B @ ( D @ 'member$e' ) )
& ( A
= ( E @ ( D @ 'times$d' @ 'fun_app$l' ) ) ) )
& ( C @ ( B @ 'times$k' ) @ ( A @ 'member$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(423,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uxz$' ) @ 'fun_app$e' ) )
<=> ( ( C @ ( B @ 'fun_app$e' ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom40) ).
thf(2728,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( ( ( C @ ( B @ 'fun_app$e' ) )
& ( A = C ) )
=> ( C @ ( B @ ( A @ 'uxz$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uxz$' ) @ 'fun_app$e' ) )
=> ( ( C @ ( B @ 'fun_app$e' ) )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(246,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ 'uug$' @ 'fun_app$c' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19) ).
thf(1881,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A = B )
=> ( B @ ( A @ 'uug$' @ 'fun_app$c' ) ) )
& ( ( B @ ( A @ 'uug$' @ 'fun_app$c' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(476,axiom,
! [A: 'A_n_vec_m_vec$',B: 'N$',C: 'A$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_column_row$' ) ) @ 'fun_app$s' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvv$' ) ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom397) ).
thf(3007,plain,
! [A: 'A_n_vec_m_vec$',B: 'N$',C: 'A$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_column_row$' ) ) @ 'fun_app$s' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvv$' ) ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(255,axiom,
! [A: 'A_n_vec_m_vec$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'uxb$' @ 'fun_app$o' ) )
<=> ? [C: 'M$'] :
( ( ( A @ ( C @ 'row$b' ) )
!= 'zero$b' )
& ( B
= ( A @ ( C @ ( A @ 'uxa$' ) @ 'least$a' @ 'column$b' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom25) ).
thf(1934,plain,
! [A: 'A_n_vec_m_vec$',B: 'A_m_vec$'] :
( ( ? [C: 'M$'] :
( ( ( A @ ( C @ 'row$b' ) )
!= 'zero$b' )
& ( B
= ( A @ ( C @ ( A @ 'uxa$' ) @ 'least$a' @ 'column$b' ) ) ) )
=> ( B @ ( A @ 'uxb$' @ 'fun_app$o' ) ) )
& ( ( B @ ( A @ 'uxb$' @ 'fun_app$o' ) )
=> ? [C: 'M$'] :
( ( ( A @ ( C @ 'row$b' ) )
!= 'zero$b' )
& ( B
= ( A @ ( C @ ( A @ 'uxa$' ) @ 'least$a' @ 'column$b' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(606,axiom,
! [A: 'A_n_vec_m_vec$',B: 'M$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxa$' ) @ 'fun_app$c' ) )
<=> ( ( C @ ( B @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom69) ).
thf(3697,plain,
! [A: 'A_n_vec_m_vec$',B: 'M$',C: 'N$'] :
( ( ( ( C @ ( B @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
=> ( C @ ( B @ ( A @ 'uxa$' ) @ 'fun_app$c' ) ) )
& ( ( C @ ( B @ ( A @ 'uxa$' ) @ 'fun_app$c' ) )
=> ( ( C @ ( B @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(472,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( D @ ( C @ 'fun_app$v' ) )
= 'zero$' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( A @ ( C @ 'sum$' ) )
= ( B @ ( C @ 'sum$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom724) ).
thf(2992,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( D @ ( C @ 'fun_app$v' ) )
= 'zero$' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( A @ ( C @ 'sum$' ) )
= ( B @ ( C @ 'sum$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(181,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$',D: 'A_n_vec_set$'] :
( ( ( D @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( D @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( C @ ( A @ 'times$c' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom459) ).
thf(1536,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$',D: 'A_n_vec_set$'] :
( ( ( D @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( D @ ( B @ 'times$c' @ 'fun_app$f' ) @ ( C @ ( A @ 'times$c' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(267,axiom,
! [A: 'M_bool_fun$',B: 'M$'] :
( ( ! [C: 'M$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( ( A @ 'least$' )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom641) ).
thf(1981,plain,
! [A: 'M_bool_fun$',B: 'M$'] :
( ( ! [C: 'M$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'less_eq$b' @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( ( A @ 'least$' )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(140,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'times$' @ 'fun_app$h' ) )
= ( A @ ( B @ 'times$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom300) ).
thf(1353,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'times$' @ 'fun_app$h' ) )
= ( A @ ( B @ 'times$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(355,axiom,
! [A: 'A_n_vec$'] :
( ( 'one$c' @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom267) ).
thf(2357,plain,
! [A: 'A_n_vec$'] :
( ( 'one$c' @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(260,axiom,
! [A: 'M_bool_fun$',B: 'M$',C: 'M_bool_fun$'] :
( ( ! [D: 'M$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom630) ).
thf(1955,plain,
! [A: 'M_bool_fun$',B: 'M$',C: 'M_bool_fun$'] :
( ( ! [D: 'M$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(172,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'vec_nth$a' @ 'vec_lambda$b' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom382) ).
thf(1485,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'vec_nth$a' @ 'vec_lambda$b' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(691,axiom,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uxc$' ) @ 'fun_app$' ) )
<=> ( ( C @ ( B @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom71) ).
thf(4106,plain,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'M$'] :
( ( ( ( C @ ( B @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
=> ( C @ ( B @ ( A @ 'uxc$' ) @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'uxc$' ) @ 'fun_app$' ) )
=> ( ( C @ ( B @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(177,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set_a_n_vec_set_fun$',D: 'A_n_vec_set$'] :
( ( ! [E: 'A_n_vec_set$',F: 'A_n_vec_set$'] :
( ( F @ ( E @ 'less_eq$' @ 'fun_app$g' ) )
=> ( F @ ( C @ 'fun_app$f' ) @ ( E @ ( C @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( B @ ( C @ 'fun_app$f' ) )
= D )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom612) ).
thf(1504,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set_a_n_vec_set_fun$',D: 'A_n_vec_set$'] :
( ( ! [E: 'A_n_vec_set$',F: 'A_n_vec_set$'] :
( ( F @ ( E @ 'less_eq$' @ 'fun_app$g' ) )
=> ( F @ ( C @ 'fun_app$f' ) @ ( E @ ( C @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( B @ ( C @ 'fun_app$f' ) )
= D )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(5,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C @ ( B @ 'fun_app$e' ) ) )
& ? [C: 'A_n_vec$'] :
( ! [D: 'A_n_vec$'] :
( ( D @ ( A @ 'fun_app$e' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$e' ) ) ) )
=> ( A @ 'the$a' @ ( B @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom326) ).
thf(727,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_bool_fun$'] :
( ( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C @ ( B @ 'fun_app$e' ) ) )
& ? [C: 'A_n_vec$'] :
( ! [D: 'A_n_vec$'] :
( ( D @ ( A @ 'fun_app$e' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$e' ) ) ) )
=> ( A @ 'the$a' @ ( B @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(91,axiom,
( 'uuq$'
= ( 'one$d' @ 'times$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom278) ).
thf(1140,plain,
( 'uuq$'
= ( 'one$d' @ 'times$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(388,axiom,
! [A: tlbool,B: 'A_m_vec_n_vec$',C: 'A_m_vec_n_vec$',D: 'N$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( C @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( C @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( C @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom159) ).
thf(2511,plain,
! [A: tlbool,B: 'A_m_vec_n_vec$',C: 'A_m_vec_n_vec$',D: 'N$'] :
( ( ( A != tltrue )
=> ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) )
& ( ( A = tltrue )
=> ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( C @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(444,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_fun$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uyb$' ) @ 'fun_app$e' ) )
<=> ( ( ( C @ ( B @ 'fun_app$v' ) )
!= 'one$' )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom44) ).
thf(2860,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_a_fun$',C: 'A_n_vec$'] :
( ( ( ( ( C @ ( B @ 'fun_app$v' ) )
!= 'one$' )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'uyb$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uyb$' ) @ 'fun_app$e' ) )
=> ( ( ( C @ ( B @ 'fun_app$v' ) )
!= 'one$' )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(464,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_fun$',D: 'A_n_vec_a_fun$'] :
( ( ! [E: 'A_n_vec$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( D @ 'fun_app$v' ) )
= ( E @ ( C @ 'fun_app$v' ) ) ) )
& ! [E: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$v' ) )
= 'zero$' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( A @ ( D @ 'sum$' ) )
= ( B @ ( C @ 'sum$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom720) ).
thf(2949,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_fun$',D: 'A_n_vec_a_fun$'] :
( ( ! [E: 'A_n_vec$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( D @ 'fun_app$v' ) )
= ( E @ ( C @ 'fun_app$v' ) ) ) )
& ! [E: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$v' ) )
= 'zero$' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( A @ ( D @ 'sum$' ) )
= ( B @ ( C @ 'sum$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(62,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$'] :
( ( B @ 'collect$c' @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'uxu$' ) @ 'collect$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom554) ).
thf(1008,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$'] :
( ( B @ 'collect$c' @ ( A @ 'insert$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'uxu$' ) @ 'collect$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(375,axiom,
! [A: 'M$'] :
( ( A @ ( 'zero$d' @ 'vec_nth$e' @ 'fun_app$t' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom129) ).
thf(2458,plain,
! [A: 'M$'] :
( ( A @ ( 'zero$d' @ 'vec_nth$e' @ 'fun_app$t' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(699,axiom,
! [A: 'A_set$',B: 'A_set$'] :
( ( ( B @ ( A @ 'less_eq$c' ) )
& ( A @ ( 'times$e' @ 'dependent$a' ) ) )
=> ( B @ ( 'times$e' @ 'dependent$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom683) ).
thf(4138,plain,
! [A: 'A_set$',B: 'A_set$'] :
( ( ( B @ ( A @ 'less_eq$c' ) )
& ( A @ ( 'times$e' @ 'dependent$a' ) ) )
=> ( B @ ( 'times$e' @ 'dependent$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(619,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( B @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
<=> ( ( B = 'zero$' )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom148) ).
thf(3757,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( ( B = 'zero$' )
| ( A = C ) )
=> ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( B @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) )
& ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( B @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
=> ( ( B = 'zero$' )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(582,axiom,
! [A: 'A$',B: 'A$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom688) ).
thf(3565,plain,
! [A: 'A$',B: 'A$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( C @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(285,axiom,
! [A: 'N$',B: 'N$',C: 'N$',D: 'A_m_vec_n_vec$'] :
( ( ( C != B )
& ( A != B ) )
=> ( ( B @ ( C @ ( A @ ( D @ 'interchange_rows$' ) ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( D @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom740) ).
thf(2045,plain,
! [A: 'N$',B: 'N$',C: 'N$',D: 'A_m_vec_n_vec$'] :
( ( ( C != B )
& ( A != B ) )
=> ( ( B @ ( C @ ( A @ ( D @ 'interchange_rows$' ) ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( D @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(449,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_a_n_vec_fun$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uxy$' ) @ 'fun_app$e' ) )
<=> ? [D: 'A_n_vec$'] :
( ( D @ ( A @ 'fun_app$e' ) )
& ( C
= ( D @ ( B @ 'fun_app$i' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom72) ).
thf(2885,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_a_n_vec_fun$',C: 'A_n_vec$'] :
( ( ? [D: 'A_n_vec$'] :
( ( D @ ( A @ 'fun_app$e' ) )
& ( C
= ( D @ ( B @ 'fun_app$i' ) ) ) )
=> ( C @ ( B @ ( A @ 'uxy$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uxy$' ) @ 'fun_app$e' ) )
=> ? [D: 'A_n_vec$'] :
( ( D @ ( A @ 'fun_app$e' ) )
& ( C
= ( D @ ( B @ 'fun_app$i' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(186,axiom,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'A_m_vec_n_vec$'] :
( ( C @ ( B @ 'times$' @ 'fun_app$h' ) @ ( A @ 'times$' @ 'fun_app$h' ) )
= ( C @ ( A @ 'times$' @ 'fun_app$h' ) @ ( B @ 'times$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom306) ).
thf(1553,plain,
! [A: 'A_m_vec_n_vec$',B: 'A_m_vec_n_vec$',C: 'A_m_vec_n_vec$'] :
( ( C @ ( B @ 'times$' @ 'fun_app$h' ) @ ( A @ 'times$' @ 'fun_app$h' ) )
= ( C @ ( A @ 'times$' @ 'fun_app$h' ) @ ( B @ 'times$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(96,axiom,
! [A: 'N$',B: 'A_m_vec_n_vec_n_vec$'] :
( ( B @ ( A @ 'column$d' ) )
= ( B @ ( A @ 'uvl$' ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom387) ).
thf(1157,plain,
! [A: 'N$',B: 'A_m_vec_n_vec_n_vec$'] :
( ( B @ ( A @ 'column$d' ) )
= ( B @ ( A @ 'uvl$' ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(560,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwk$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom82) ).
thf(3447,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwk$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(511,axiom,
! [A: 'M_bool_fun$',B: 'M$'] :
( ( B @ ( A @ 'fun_app$' ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom631) ).
thf(3188,plain,
! [A: 'M_bool_fun$',B: 'M$'] :
( ( B @ ( A @ 'fun_app$' ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(488,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_fun$',D: 'A_n_vec_a_fun$'] :
( ( ! [E: 'A_n_vec$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$v' ) )
= ( E @ ( D @ 'fun_app$v' ) ) ) )
& ! [E: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$v' ) )
= 'zero$' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( B @ ( C @ 'sum$' ) )
= ( A @ ( D @ 'sum$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom718) ).
thf(3056,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_fun$',D: 'A_n_vec_a_fun$'] :
( ( ! [E: 'A_n_vec$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$v' ) )
= ( E @ ( D @ 'fun_app$v' ) ) ) )
& ! [E: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( E @ 'member$' @ 'fun_app$g' ) )
=> ( ( E @ ( C @ 'fun_app$v' ) )
= 'zero$' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( B @ ( C @ 'sum$' ) )
= ( A @ ( D @ 'sum$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(655,axiom,
( 'uus$'
= ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom280) ).
thf(3929,plain,
( 'uus$'
= ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(630,axiom,
! [A: 'A$',B: 'A_m_vec$'] :
( ( ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' )
<=> ( ( B = 'zero$a' )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom670) ).
thf(3797,plain,
! [A: 'A$',B: 'A_m_vec$'] :
( ( ( ( B = 'zero$a' )
| ( A = 'zero$' ) )
=> ( ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' ) )
& ( ( ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) )
= 'zero$a' )
=> ( ( B = 'zero$a' )
| ( A = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(370,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uxv$' ) @ 'fun_app$e' ) )
<=> ( ( B @ ( C @ 'member$' @ 'fun_app$g' ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom38) ).
thf(2435,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ( ( B @ ( C @ 'member$' @ 'fun_app$g' ) )
| ( C = A ) )
=> ( C @ ( B @ ( A @ 'uxv$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uxv$' ) @ 'fun_app$e' ) )
=> ( ( B @ ( C @ 'member$' @ 'fun_app$g' ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(527,axiom,
! [A: 'N$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'is_zero_row$' ) )
<=> ! [C: 'M$'] :
( ( C @ ( A @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom704) ).
thf(3284,plain,
! [A: 'N$',B: 'A_m_vec_n_vec$'] :
( ( ! [C: 'M$'] :
( ( C @ ( A @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' )
=> ( B @ ( A @ 'is_zero_row$' ) ) )
& ( ( B @ ( A @ 'is_zero_row$' ) )
=> ! [C: 'M$'] :
( ( C @ ( A @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(28,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less$b' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom751) ).
thf(845,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) )
=> ( C @ ( A @ 'less$b' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(552,axiom,
! [A: tlbool,B: 'A_n_vec$',C: 'A_n_vec$',D: 'N$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( C @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) ) ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom157) ).
thf(3400,plain,
! [A: tlbool,B: 'A_n_vec$',C: 'A_n_vec$',D: 'N$'] :
( ( ( A != tltrue )
=> ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) ) ) ) )
& ( ( A = tltrue )
=> ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ 'vec_nth$b' @ 'fun_app$d' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(456,axiom,
! [A: 'N$',B: 'A_m_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvl$' ) @ 'fun_app$b' ) )
= ( A @ ( C @ ( B @ 'vec_nth$f' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom48) ).
thf(2924,plain,
! [A: 'N$',B: 'A_m_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvl$' ) @ 'fun_app$b' ) )
= ( A @ ( C @ ( B @ 'vec_nth$f' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(234,axiom,
! [A: 'N_a_m_vec_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$b' @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( A @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom360) ).
thf(1839,plain,
! [A: 'N_a_m_vec_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$b' @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( A @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(500,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'one$c' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom238) ).
thf(3139,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'one$c' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(348,axiom,
! [A: 'A_m_vec$'] :
( ( 'one$a' @ ( A @ 'times$b' @ 'fun_app$k' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom231) ).
thf(2310,plain,
! [A: 'A_m_vec$'] :
( ( 'one$a' @ ( A @ 'times$b' @ 'fun_app$k' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(236,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'times$b' @ 'fun_app$k' ) )
= ( B @ ( A @ 'uvh$' ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom353) ).
thf(1844,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'times$b' @ 'fun_app$k' ) )
= ( B @ ( A @ 'uvh$' ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(351,axiom,
! [A: 'A_n_vec_set$'] :
( ( 'bot$' @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom633) ).
thf(2325,plain,
! [A: 'A_n_vec_set$'] :
( ( ( A = 'bot$' )
=> ( 'bot$' @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( 'bot$' @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(10,axiom,
! [A: 'A_n_vec_set$'] :
( ( 'one$e' @ ( A @ 'times$c' @ 'fun_app$f' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom269) ).
thf(759,plain,
! [A: 'A_n_vec_set$'] :
( ( 'one$e' @ ( A @ 'times$c' @ 'fun_app$f' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(682,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( A @ 'vec_nth$b' )
= ( B @ 'vec_nth$b' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom175) ).
thf(4061,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( A = B )
=> ( ( A @ 'vec_nth$b' )
= ( B @ 'vec_nth$b' ) ) )
& ( ( ( A @ 'vec_nth$b' )
= ( B @ 'vec_nth$b' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(13,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'fun_app$e' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).
thf(771,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( A = B )
=> ( B @ ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'fun_app$e' ) ) )
& ( ( B @ ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'fun_app$e' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(120,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( A = C ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom499) ).
thf(1276,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ~ ( B @ ( A @ 'member$' @ 'fun_app$g' ) )
=> ( A = C ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(8,axiom,
! [A: 'A_n_vec_bool_fun$'] :
( ? [B: 'A_n_vec$'] :
( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$e' ) ) )
=> ( A @ 'the$a' @ ( A @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom320) ).
thf(748,plain,
! [A: 'A_n_vec_bool_fun$'] :
( ? [B: 'A_n_vec$'] :
( ! [C: 'A_n_vec$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$e' ) ) )
=> ( A @ 'the$a' @ ( A @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(207,axiom,
'zero$a' != 'one$a',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom274) ).
thf(1674,plain,
'zero$a' != 'one$a',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(394,axiom,
! [A: 'M_a_m_vec_bool_fun_fun$'] :
( ! [B: 'M$'] :
? [C: 'A_m_vec$'] : ( C @ ( B @ ( A @ 'fun_app$aa' ) @ 'fun_app$o' ) )
<=> ? [B: 'A_m_vec_m_vec$'] :
! [C: 'M$'] : ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ ( C @ ( A @ 'fun_app$aa' ) @ 'fun_app$o' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom166) ).
thf(2554,plain,
! [A: 'M_a_m_vec_bool_fun_fun$'] :
( ( ? [B: 'A_m_vec_m_vec$'] :
! [C: 'M$'] : ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ ( C @ ( A @ 'fun_app$aa' ) @ 'fun_app$o' ) )
=> ! [B: 'M$'] :
? [C: 'A_m_vec$'] : ( C @ ( B @ ( A @ 'fun_app$aa' ) @ 'fun_app$o' ) ) )
& ( ! [B: 'M$'] :
? [C: 'A_m_vec$'] : ( C @ ( B @ ( A @ 'fun_app$aa' ) @ 'fun_app$o' ) )
=> ? [B: 'A_m_vec_m_vec$'] :
! [C: 'M$'] : ( C @ ( B @ 'vec_nth$e' @ 'fun_app$t' ) @ ( C @ ( A @ 'fun_app$aa' ) @ 'fun_app$o' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(391,axiom,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'M$',D: 'N$',E: 'M$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwv$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwv$' ) ) ) @ 'fun_app$a' ) )
= ( B @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwv$' ) ) ) @ 'fun_app$a' ) )
= ( C @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).
thf(2532,plain,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'M$',D: 'N$',E: 'M$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwv$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwv$' ) ) ) @ 'fun_app$a' ) )
= ( B @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uwv$' ) ) ) @ 'fun_app$a' ) )
= ( C @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(48,axiom,
! [A: 'A_n_vec_set$'] :
( ( A @ ( 'bot$' @ 'minus$b' @ 'fun_app$f' ) )
= 'bot$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom511) ).
thf(946,plain,
! [A: 'A_n_vec_set$'] :
( ( A @ ( 'bot$' @ 'minus$b' @ 'fun_app$f' ) )
= 'bot$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(667,axiom,
! [A: 'A$'] :
( ( A @ ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom264) ).
thf(3991,plain,
! [A: 'A$'] :
( ( A @ ( 'one$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(467,axiom,
! [A: 'A$',B: 'A_bool_fun$'] :
( ( B @ 'collect$' @ ( A @ 'member$c' ) )
<=> ( A @ ( B @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom219) ).
thf(2971,plain,
! [A: 'A$',B: 'A_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$p' ) )
=> ( B @ 'collect$' @ ( A @ 'member$c' ) ) )
& ( ( B @ 'collect$' @ ( A @ 'member$c' ) )
=> ( A @ ( B @ 'fun_app$p' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(114,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] : ( A @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom570) ).
thf(1244,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec$'] : ( A @ ( B @ 'insert$' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(624,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uxk$' ) @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom37) ).
thf(3780,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uxk$' ) @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(611,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( A != 'zero$' )
=> ( ( ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( A @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom178) ).
thf(3729,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( A != 'zero$' )
=> ( ( ( B = C )
=> ( ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( A @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) )
& ( ( ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( A @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(695,axiom,
! [A: 'A$',B: 'A$'] :
( ( B @ ( A @ 'uvc$' @ 'fun_app$m' ) )
= ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).
thf(4121,plain,
! [A: 'A$',B: 'A$'] :
( ( B @ ( A @ 'uvc$' @ 'fun_app$m' ) )
= ( A @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(315,axiom,
! [A: 'A_n_vec_set$'] :
( ! [B: 'A_n_vec$'] :
~ ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
<=> ( A = 'bot$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom493) ).
thf(2174,plain,
! [A: 'A_n_vec_set$'] :
( ( ( A = 'bot$' )
=> ! [B: 'A_n_vec$'] :
~ ( A @ ( B @ 'member$' @ 'fun_app$g' ) ) )
& ( ! [B: 'A_n_vec$'] :
~ ( A @ ( B @ 'member$' @ 'fun_app$g' ) )
=> ( A = 'bot$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(169,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uww$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom426) ).
thf(1476,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uww$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(517,axiom,
! [A: tlbool,B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'fun_app$c' ) )
<=> ( ( ( ( A = tltrue )
<=> $false )
=> ( D = C ) )
& ( ( ( A = tltrue )
<=> $true )
=> ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom75) ).
thf(3220,plain,
! [A: tlbool,B: 'N$',C: 'N$',D: 'N$'] :
( ( ( ( ( A != tltrue )
=> ( D = C ) )
& ( ( A = tltrue )
=> ( D = B ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'fun_app$c' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'fun_app$c' ) )
=> ( ( ( A != tltrue )
=> ( D = C ) )
& ( ( A = tltrue )
=> ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(678,axiom,
! [A: 'N_a_bool_fun_fun$'] :
( ! [B: 'N$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ad' ) @ 'fun_app$p' ) )
<=> ? [B: 'A_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$ad' ) @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom169) ).
thf(4042,plain,
! [A: 'N_a_bool_fun_fun$'] :
( ( ? [B: 'A_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$ad' ) @ 'fun_app$p' ) )
=> ! [B: 'N$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ad' ) @ 'fun_app$p' ) ) )
& ( ! [B: 'N$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ad' ) @ 'fun_app$p' ) )
=> ? [B: 'A_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$ad' ) @ 'fun_app$p' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(616,axiom,
! [A: 'A$',B: 'A$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom655) ).
thf(3748,plain,
! [A: 'A$',B: 'A$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) @ ( A @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(280,axiom,
! [A: tlbool,B: 'A_n_vec_m_vec$',C: 'A_n_vec_m_vec$',D: 'M$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( C @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( D @ ( C @ 'vec_nth$d' @ 'fun_app$s' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( D @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) ) ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( D @ ( C @ 'vec_nth$d' @ 'fun_app$s' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( D @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom155) ).
thf(2026,plain,
! [A: tlbool,B: 'A_n_vec_m_vec$',C: 'A_n_vec_m_vec$',D: 'M$'] :
( ( ( A != tltrue )
=> ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( D @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) ) ) ) )
& ( ( A = tltrue )
=> ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) )
= ( D @ ( C @ 'vec_nth$d' @ 'fun_app$s' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(499,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwq$' ) ) @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$h' ) @ 'vec_nth$d' @ 'fun_app$s' ) @ ( A @ 'fun_app$v' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom78) ).
thf(3136,plain,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwq$' ) ) @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$h' ) @ 'vec_nth$d' @ 'fun_app$s' ) @ ( A @ 'fun_app$v' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(547,axiom,
! [A: 'A$',B: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A )
<=> ( ( B = 'one$' )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom250) ).
thf(3368,plain,
! [A: 'A$',B: 'A$'] :
( ( ( ( B = 'one$' )
| ( A = 'zero$' ) )
=> ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A ) )
& ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= A )
=> ( ( B = 'one$' )
| ( A = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(458,axiom,
! [A: 'A_set$',B: 'A_set$',C: 'A_set$'] :
( ( C @ ( B @ 'times$d' @ 'fun_app$l' ) @ ( A @ 'times$d' @ 'fun_app$l' ) )
= ( C @ ( A @ 'times$d' @ 'fun_app$l' ) @ ( B @ 'times$d' @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom309) ).
thf(2934,plain,
! [A: 'A_set$',B: 'A_set$',C: 'A_set$'] :
( ( C @ ( B @ 'times$d' @ 'fun_app$l' ) @ ( A @ 'times$d' @ 'fun_app$l' ) )
= ( C @ ( A @ 'times$d' @ 'fun_app$l' ) @ ( B @ 'times$d' @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(336,axiom,
! [A: 'M_a_fun$',B: 'M$'] :
( ( B @ ( A @ 'vec_lambda$' @ 'vec_nth$' @ 'fun_app$a' ) )
= ( B @ ( A @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom359) ).
thf(2262,plain,
! [A: 'M_a_fun$',B: 'M$'] :
( ( B @ ( A @ 'vec_lambda$' @ 'vec_nth$' @ 'fun_app$a' ) )
= ( B @ ( A @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(274,axiom,
! [A: 'A_n_vec_set$'] :
( ( A @ ( 'zero$b' @ 'member$' @ 'fun_app$g' ) )
=> ( A @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom696) ).
thf(2009,plain,
! [A: 'A_n_vec_set$'] :
( ( A @ ( 'zero$b' @ 'member$' @ 'fun_app$g' ) )
=> ( A @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(174,axiom,
! [A: 'A_n_vec_set$'] :
( ( ! [B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ( A
= ( B @ ( C @ 'insert$' @ 'fun_app$f' ) ) ) )
=> $false )
& ( ( A = 'bot$' )
=> $false )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom591) ).
thf(1491,plain,
! [A: 'A_n_vec_set$'] :
~ ( ! [B: 'A_n_vec_set$',C: 'A_n_vec$'] :
~ ( ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ( A
= ( B @ ( C @ 'insert$' @ 'fun_app$f' ) ) ) )
& ( A != 'bot$' )
& ( A @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(379,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom290) ).
thf(2475,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= ( C @ ( B @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) @ ( A @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(538,axiom,
! [A: 'A_a_fun$',B: 'A_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom199) ).
thf(3324,plain,
! [A: 'A_a_fun$',B: 'A_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(41,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuh$' @ 'fun_app$q' ) @ 'the$a' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom195) ).
thf(914,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uuh$' @ 'fun_app$q' ) @ 'the$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(570,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom293) ).
thf(3497,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(212,axiom,
( 'one$e'
= ( 'bot$' @ ( 'one$c' @ 'insert$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom461) ).
thf(1706,plain,
( 'one$e'
= ( 'bot$' @ ( 'one$c' @ 'insert$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(108,axiom,
! [A: tlbool,B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( ( A != tltrue )
=> ( C
= ( C @ ( B @ ( A @ 'uut$' ) @ 'fun_app$q' ) @ 'the$a' ) ) )
& ( ( A = tltrue )
=> ( B
= ( C @ ( B @ ( A @ 'uut$' ) @ 'fun_app$q' ) @ 'the$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom324) ).
thf(1212,plain,
! [A: tlbool,B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( ( A != tltrue )
=> ( C
= ( C @ ( B @ ( A @ 'uut$' ) @ 'fun_app$q' ) @ 'the$a' ) ) )
& ( ( A = tltrue )
=> ( B
= ( C @ ( B @ ( A @ 'uut$' ) @ 'fun_app$q' ) @ 'the$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(203,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( A = B ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom626) ).
thf(1661,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( C @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( A = B ) )
=> ( C @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(684,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom474) ).
thf(4074,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(161,axiom,
! [A: 'A_n_vec_set_bool_fun$',B: 'A_n_vec_set$'] :
( ( ! [C: 'A_n_vec_set$'] :
( ( C @ ( A @ 'fun_app$g' ) )
=> ? [D: 'A_n_vec$'] :
( ( ~ ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) )
| ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'fun_app$g' ) ) )
& ( C @ ( D @ 'member$' @ 'fun_app$g' ) ) ) )
& ( B @ ( A @ 'fun_app$g' ) ) )
=> ~ ( B @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom602) ).
thf(1442,plain,
! [A: 'A_n_vec_set_bool_fun$',B: 'A_n_vec_set$'] :
( ( ! [C: 'A_n_vec_set$'] :
( ( C @ ( A @ 'fun_app$g' ) )
=> ? [D: 'A_n_vec$'] :
( ( ~ ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'minus$b' @ 'fun_app$f' ) @ ( 'finite$' @ 'fun_app$g' ) )
| ( 'bot$' @ ( D @ 'insert$' @ 'fun_app$f' ) @ ( C @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'fun_app$g' ) ) )
& ( C @ ( D @ 'member$' @ 'fun_app$g' ) ) ) )
& ( B @ ( A @ 'fun_app$g' ) ) )
=> ~ ( B @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(430,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom536) ).
thf(2779,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B @ ( C @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(71,axiom,
! [A: 'A_n_vec_set$'] :
( ( A @ ( 'finite$' @ 'fun_app$g' ) )
<=> ( ? [B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ( A
= ( B @ ( C @ 'insert$' @ 'fun_app$f' ) ) ) )
| ( A = 'bot$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom590) ).
thf(1045,plain,
! [A: 'A_n_vec_set$'] :
( ( ( ? [B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ( A
= ( B @ ( C @ 'insert$' @ 'fun_app$f' ) ) ) )
| ( A = 'bot$' ) )
=> ( A @ ( 'finite$' @ 'fun_app$g' ) ) )
& ( ( A @ ( 'finite$' @ 'fun_app$g' ) )
=> ( ? [B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( B @ ( 'finite$' @ 'fun_app$g' ) )
& ( A
= ( B @ ( C @ 'insert$' @ 'fun_app$f' ) ) ) )
| ( A = 'bot$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(367,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'zero$b' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom136) ).
thf(2421,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'zero$b' @ ( 'times$a' @ 'fun_app$j' ) @ 'fun_app$i' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(128,axiom,
! [A: 'A_n_vec_n_vec$'] :
( ( A @ 'vec_nth$c' @ 'vec_lambda$e' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom363) ).
thf(1309,plain,
! [A: 'A_n_vec_n_vec$'] :
( ( A @ 'vec_nth$c' @ 'vec_lambda$e' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(595,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
<=> ( ( B = C )
| ( A = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom149) ).
thf(3645,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( ( ( B = C )
| ( A = 'zero$' ) )
=> ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) )
& ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
=> ( ( B = C )
| ( A = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(677,axiom,
! [A: 'A$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom666) ).
thf(4039,plain,
! [A: 'A$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ ( 'vector_scalar_mult$a' @ 'fun_app$ah' ) @ 'fun_app$k' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(607,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec$',C: 'N$',D: 'N$'] :
( ( ( ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uwz$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$e' ) )
=> ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom434) ).
thf(3705,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec$',C: 'N$',D: 'N$'] :
( ( ( ( D @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uwz$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$e' ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(362,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'one$' @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom657) ).
thf(2385,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'one$' @ ( 'vector_scalar_mult$' @ 'fun_app$ag' ) @ 'fun_app$i' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(194,axiom,
! [A: 'A_n_vec_a_m_vec_fun$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'uyl$' ) @ 'collect$c' @ ( A @ 'sum$a' ) )
= ( B @ ( A @ 'sum$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom717) ).
thf(1625,plain,
! [A: 'A_n_vec_a_m_vec_fun$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'uyl$' ) @ 'collect$c' @ ( A @ 'sum$a' ) )
= ( B @ ( A @ 'sum$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(93,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= ( B @ 'uum$' @ ( A @ 'uum$' @ 'minus$e' ) @ 'collect$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom521) ).
thf(1148,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= ( B @ 'uum$' @ ( A @ 'uum$' @ 'minus$e' ) @ 'collect$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(252,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N_a_m_vec_fun$'] :
( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'fun_app$b' ) ) )
<=> ( ( B @ 'vec_lambda$b' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom376) ).
thf(1908,plain,
! [A: 'A_m_vec_n_vec$',B: 'N_a_m_vec_fun$'] :
( ( ( ( B @ 'vec_lambda$b' )
= A )
=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'fun_app$b' ) ) ) )
& ( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'fun_app$b' ) ) )
=> ( ( B @ 'vec_lambda$b' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(272,axiom,
! [A: 'M$'] :
( ( A @ ( 'one$f' @ 'vec_nth$e' @ 'fun_app$t' ) )
= 'one$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom243) ).
thf(2003,plain,
! [A: 'M$'] :
( ( A @ ( 'one$f' @ 'vec_nth$e' @ 'fun_app$t' ) )
= 'one$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(548,axiom,
! [A: 'N$'] :
( ( A @ ( 'uwt$' @ 'fun_app$d' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).
thf(3379,plain,
! [A: 'N$'] :
( ( A @ ( 'uwt$' @ 'fun_app$d' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(178,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( A = B )
<=> ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom621) ).
thf(1512,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
& ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(223,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_m_vec_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( D @ ( C @ 'fun_app$u' ) )
= 'zero$a' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( A @ ( C @ 'sum$a' ) )
= ( B @ ( C @ 'sum$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom725) ).
thf(1774,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_m_vec_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( D @ ( C @ 'fun_app$u' ) )
= 'zero$a' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( A @ ( C @ 'sum$a' ) )
= ( B @ ( C @ 'sum$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(671,axiom,
! [A: 'N$'] :
( ( A @ ( 'one$c' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom246) ).
thf(4014,plain,
! [A: 'N$'] :
( ( A @ ( 'one$c' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(692,axiom,
! [A: 'N$',B: 'A_n_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uvn$' ) @ 'fun_app$a' ) )
= ( A @ ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom50) ).
thf(4114,plain,
! [A: 'N$',B: 'A_n_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uvn$' ) @ 'fun_app$a' ) )
= ( A @ ( C @ ( B @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(470,axiom,
'zero$b' != 'one$c',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom272) ).
thf(2983,plain,
'zero$b' != 'one$c',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(641,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$b' ) @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom201) ).
thf(3865,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$b' ) @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(326,axiom,
! [A: 'A_set$',B: 'A_set_set$',C: 'A_set$',D: 'A_set_set$'] :
( ( ( D @ ( C @ 'member$e' ) )
& ( B @ ( A @ 'member$e' ) ) )
=> ( D @ ( B @ 'times$k' ) @ ( C @ ( A @ 'times$d' @ 'fun_app$l' ) @ 'member$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom211) ).
thf(2233,plain,
! [A: 'A_set$',B: 'A_set_set$',C: 'A_set$',D: 'A_set_set$'] :
( ( ( D @ ( C @ 'member$e' ) )
& ( B @ ( A @ 'member$e' ) ) )
=> ( D @ ( B @ 'times$k' ) @ ( C @ ( A @ 'times$d' @ 'fun_app$l' ) @ 'member$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(110,axiom,
( 'uuo$'
= ( 'one$a' @ 'times$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom276) ).
thf(1229,plain,
( 'uuo$'
= ( 'one$a' @ 'times$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(589,axiom,
! [A: 'A_n_vec_m_vec$',B: 'A_m_vec$',C: 'M$',D: 'M$'] :
( ( ( ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxb$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$c' ) )
=> ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom435) ).
thf(3601,plain,
! [A: 'A_n_vec_m_vec$',B: 'A_m_vec$',C: 'M$',D: 'M$'] :
( ( ( ( D @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( A @ 'uxb$' @ 'collect$a' @ ( B @ 'member$a' ) )
& ( A @ 'reduced_row_echelon_form$c' ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(636,axiom,
! [A: 'A$'] :
( ( 'zero$' @ ( A @ 'minus$a' @ 'fun_app$m' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom450) ).
thf(3837,plain,
! [A: 'A$'] :
( ( 'zero$' @ ( A @ 'minus$a' @ 'fun_app$m' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(147,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'times$h' ) )
= ( B @ ( A @ 'uvf$' ) @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom351) ).
thf(1380,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'times$h' ) )
= ( B @ ( A @ 'uvf$' ) @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(6,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
<=> ( ( A = B )
| ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom748) ).
thf(735,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( ( A = B )
| ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ( A = B )
| ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(507,axiom,
! [A: 'A_m_vec$'] :
( ( A @ ( A @ 'minus$' @ 'fun_app$k' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom455) ).
thf(3164,plain,
! [A: 'A_m_vec$'] :
( ( A @ ( A @ 'minus$' @ 'fun_app$k' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(502,axiom,
! [A: 'A_n_vec$'] :
( ( 'bot$' @ ( A @ 'member$' @ 'fun_app$g' ) )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom494) ).
thf(3145,plain,
! [A: 'A_n_vec$'] :
~ ( 'bot$' @ ( A @ 'member$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(479,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxh$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uwb$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom88) ).
thf(3015,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxh$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uwb$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(660,axiom,
! [A: 'A_n_vec_m_vec$'] :
( ( ( ( A @ ( 'zero$j' @ 'column$b' ) )
!= 'zero$a' )
& ( A @ 'reduced_row_echelon_form$c' ) )
=> ( ( 'zero$j' @ ( 'zero$k' @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom419) ).
thf(3956,plain,
! [A: 'A_n_vec_m_vec$'] :
( ( ( ( A @ ( 'zero$j' @ 'column$b' ) )
!= 'zero$a' )
& ( A @ 'reduced_row_echelon_form$c' ) )
=> ( ( 'zero$j' @ ( 'zero$k' @ ( A @ 'vec_nth$d' @ 'fun_app$s' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(321,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'uxs$' ) @ 'fun_app$e' ) )
<=> ( ( C @ ( B @ 'fun_app$e' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom39) ).
thf(2201,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_bool_fun$',C: 'A_n_vec$'] :
( ( ( ( C @ ( B @ 'fun_app$e' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) )
=> ( C @ ( B @ ( A @ 'uxs$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uxs$' ) @ 'fun_app$e' ) )
=> ( ( C @ ( B @ 'fun_app$e' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(542,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uwz$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$e' ) )
=> ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom438) ).
thf(3347,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
!= 'zero$' )
& ( A @ 'uwz$' @ 'collect$c' @ ( B @ 'member$' @ 'fun_app$g' ) )
& ( A @ 'reduced_row_echelon_form$e' ) )
=> ( ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(704,axiom,
! [A: 'A$'] :
( ( A @ ( 'zero$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom138) ).
thf(4157,plain,
! [A: 'A$'] :
( ( A @ ( 'zero$' @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(122,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_a_n_vec_set_fun$',C: 'A_n_vec_set$',D: 'A_n_vec_set$'] :
( ( ! [E: 'A_n_vec_set$',F: 'A_n_vec_set$'] :
( ( F @ ( E @ 'less_eq$' @ 'fun_app$g' ) )
=> ( F @ ( B @ 'fun_app$f' ) @ ( E @ ( B @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( D @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( A
= ( C @ ( B @ 'fun_app$f' ) ) ) )
=> ( D @ ( B @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom613) ).
thf(1288,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set_a_n_vec_set_fun$',C: 'A_n_vec_set$',D: 'A_n_vec_set$'] :
( ( ! [E: 'A_n_vec_set$',F: 'A_n_vec_set$'] :
( ( F @ ( E @ 'less_eq$' @ 'fun_app$g' ) )
=> ( F @ ( B @ 'fun_app$f' ) @ ( E @ ( B @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( D @ ( C @ 'less_eq$' @ 'fun_app$g' ) )
& ( A
= ( C @ ( B @ 'fun_app$f' ) ) ) )
=> ( D @ ( B @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(675,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom472) ).
thf(4034,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'minus$a' @ 'fun_app$m' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= ( C @ ( B @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ ( C @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(283,axiom,
! [A: 'A_n_vec$'] :
( ( 'bot$' @ ( A @ 'member$' @ 'fun_app$g' ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom525) ).
thf(2040,plain,
! [A: 'A_n_vec$'] :
~ ( 'bot$' @ ( A @ 'member$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(573,axiom,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'M$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvu$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvu$' ) ) ) @ 'fun_app$a' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).
thf(3506,plain,
! [A: 'A_m_vec_m_vec$',B: 'M$',C: 'A$',D: 'M$',E: 'M$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvu$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvu$' ) ) ) @ 'fun_app$a' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(52,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$'] :
( ( ~ ( A @ ( B @ 'fun_app$e' ) )
=> ( ( B @ ( A @ 'uxz$' ) @ 'collect$c' )
= 'bot$' ) )
& ( ( A @ ( B @ 'fun_app$e' ) )
=> ( ( B @ ( A @ 'uxz$' ) @ 'collect$c' )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom581) ).
thf(960,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_bool_fun$'] :
( ( ~ ( A @ ( B @ 'fun_app$e' ) )
=> ( ( B @ ( A @ 'uxz$' ) @ 'collect$c' )
= 'bot$' ) )
& ( ( A @ ( B @ 'fun_app$e' ) )
=> ( ( B @ ( A @ 'uxz$' ) @ 'collect$c' )
= ( 'bot$' @ ( A @ 'insert$' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(433,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec_bool_fun$'] :
( ( B @ 'collect$a' @ ( A @ 'member$a' ) )
<=> ( A @ ( B @ 'fun_app$o' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom220) ).
thf(2795,plain,
! [A: 'A_m_vec$',B: 'A_m_vec_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$o' ) )
=> ( B @ 'collect$a' @ ( A @ 'member$a' ) ) )
& ( ( B @ 'collect$a' @ ( A @ 'member$a' ) )
=> ( A @ ( B @ 'fun_app$o' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(4,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ~ ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom746) ).
thf(720,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ 'less$b' @ 'fun_app$g' ) ) )
& ( ~ ( B @ ( A @ 'less$b' @ 'fun_app$g' ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(99,axiom,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uwv$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom425) ).
thf(1165,plain,
! [A: 'A_m_vec_n_vec$',B: 'M$',C: 'M$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uwv$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(664,axiom,
! [A: 'A$',B: 'A$'] :
( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= B )
<=> ( ( A = 'one$' )
| ( B = 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom252) ).
thf(3974,plain,
! [A: 'A$',B: 'A$'] :
( ( ( ( A = 'one$' )
| ( B = 'zero$' ) )
=> ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= B ) )
& ( ( ( B @ ( A @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) )
= B )
=> ( ( A = 'one$' )
| ( B = 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(119,axiom,
! [A: 'A_n_vec_set$'] :
( ( A @ ( 'is_singleton$' @ 'fun_app$g' ) )
<=> ( A
= ( 'bot$' @ ( A @ 'the_elem$a' @ 'insert$' @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom728) ).
thf(1268,plain,
! [A: 'A_n_vec_set$'] :
( ( ( A
= ( 'bot$' @ ( A @ 'the_elem$a' @ 'insert$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'is_singleton$' @ 'fun_app$g' ) ) )
& ( ( A @ ( 'is_singleton$' @ 'fun_app$g' ) )
=> ( A
= ( 'bot$' @ ( A @ 'the_elem$a' @ 'insert$' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(378,axiom,
! [A: 'N_set$',B: 'N$'] :
( ( B @ ( A @ 'uyd$' @ 'fun_app$c' ) )
<=> ( A
= ( 'bot$a' @ ( B @ 'insert$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).
thf(2467,plain,
! [A: 'N_set$',B: 'N$'] :
( ( ( A
= ( 'bot$a' @ ( B @ 'insert$a' ) ) )
=> ( B @ ( A @ 'uyd$' @ 'fun_app$c' ) ) )
& ( ( B @ ( A @ 'uyd$' @ 'fun_app$c' ) )
=> ( A
= ( 'bot$a' @ ( B @ 'insert$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(185,axiom,
! [A: 'A_a_fun$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$' ) )
= ( B @ ( A @ 'uwn$' ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom409) ).
thf(1550,plain,
! [A: 'A_a_fun$',B: 'A_m_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$' ) )
= ( B @ ( A @ 'uwn$' ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(632,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom456) ).
thf(3817,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ ( 'minus$c' @ 'fun_app$j' ) @ 'fun_app$i' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'minus$a' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(386,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'reduced_row_echelon_form$' )
=> ! [B: 'N$'] :
( ( A @ ( B @ 'is_zero_row$' ) )
=> ~ ? [C: 'N$'] :
( ~ ( A @ ( C @ 'is_zero_row$' ) )
& ( C @ ( B @ 'less$' @ 'fun_app$c' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom742) ).
thf(2507,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'reduced_row_echelon_form$' )
=> ! [B: 'N$'] :
( ( A @ ( B @ 'is_zero_row$' ) )
=> ~ ? [C: 'N$'] :
( ~ ( A @ ( C @ 'is_zero_row$' ) )
& ( C @ ( B @ 'less$' @ 'fun_app$c' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(254,axiom,
! [A: tlbool,B: 'A_n_vec_n_vec$',C: 'A_n_vec_n_vec$',D: 'N$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( C @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( D @ ( C @ 'vec_nth$c' @ 'fun_app$r' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( D @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) ) ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( D @ ( C @ 'vec_nth$c' @ 'fun_app$r' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( D @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom156) ).
thf(1925,plain,
! [A: tlbool,B: 'A_n_vec_n_vec$',C: 'A_n_vec_n_vec$',D: 'N$'] :
( ( ( A != tltrue )
=> ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( D @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) ) ) ) )
& ( ( A = tltrue )
=> ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) )
= ( D @ ( C @ 'vec_nth$c' @ 'fun_app$r' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(646,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'M$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$c' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$c' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom338) ).
thf(3886,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'M$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$c' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'mult_row_row$c' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(30,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ ( 'one$b' @ 'times$' @ 'fun_app$h' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom259) ).
thf(850,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ ( 'one$b' @ 'times$' @ 'fun_app$h' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(124,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom620) ).
thf(1299,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( A @ ( B @ 'less_eq$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(360,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ 'uwz$' @ 'fun_app$e' ) )
<=> ? [C: 'N$'] :
( ( ( A @ ( C @ 'row$c' ) )
!= 'zero$b' )
& ( B
= ( A @ ( C @ ( A @ 'uwy$' ) @ 'least$a' @ 'column$c' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom26) ).
thf(2372,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec$'] :
( ( ? [C: 'N$'] :
( ( ( A @ ( C @ 'row$c' ) )
!= 'zero$b' )
& ( B
= ( A @ ( C @ ( A @ 'uwy$' ) @ 'least$a' @ 'column$c' ) ) ) )
=> ( B @ ( A @ 'uwz$' @ 'fun_app$e' ) ) )
& ( ( B @ ( A @ 'uwz$' @ 'fun_app$e' ) )
=> ? [C: 'N$'] :
( ( ( A @ ( C @ 'row$c' ) )
!= 'zero$b' )
& ( B
= ( A @ ( C @ ( A @ 'uwy$' ) @ 'least$a' @ 'column$c' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(329,axiom,
! [A: 'N$',B: 'A_n_vec_m_vec$'] :
( ( B @ ( A @ 'column$b' ) )
= ( B @ ( A @ 'uvn$' ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom389) ).
thf(2241,plain,
! [A: 'N$',B: 'A_n_vec_m_vec$'] :
( ( B @ ( A @ 'column$b' ) )
= ( B @ ( A @ 'uvn$' ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(306,axiom,
! [A: 'M_a_bool_fun_fun$'] :
( ! [B: 'M$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ae' ) @ 'fun_app$p' ) )
<=> ? [B: 'A_m_vec$'] :
! [C: 'M$'] : ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom170) ).
thf(2127,plain,
! [A: 'M_a_bool_fun_fun$'] :
( ( ? [B: 'A_m_vec$'] :
! [C: 'M$'] : ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'fun_app$p' ) )
=> ! [B: 'M$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ae' ) @ 'fun_app$p' ) ) )
& ( ! [B: 'M$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ae' ) @ 'fun_app$p' ) )
=> ? [B: 'A_m_vec$'] :
! [C: 'M$'] : ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'fun_app$p' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(266,axiom,
! [A: 'M_bool_fun$',B: 'M_bool_fun$'] :
( ( ! [C: 'M$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
& ? [C: 'M$'] : ( C @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( B @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom628) ).
thf(1977,plain,
! [A: 'M_bool_fun$',B: 'M_bool_fun$'] :
( ( ! [C: 'M$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
& ? [C: 'M$'] : ( C @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( B @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(90,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_bool_fun$'] :
( ! [D: 'A_n_vec$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( D @ ( C @ 'fun_app$e' ) ) )
<=> ( ! [D: 'A_n_vec$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( D @ ( C @ 'fun_app$e' ) ) )
& ( A @ ( C @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom710) ).
thf(1129,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_bool_fun$'] :
( ( ( ! [D: 'A_n_vec$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( D @ ( C @ 'fun_app$e' ) ) )
& ( A @ ( C @ 'fun_app$e' ) ) )
=> ! [D: 'A_n_vec$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( D @ ( C @ 'fun_app$e' ) ) ) )
& ( ! [D: 'A_n_vec$'] :
( ( B @ ( A @ 'insert$' @ 'fun_app$f' ) @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( D @ ( C @ 'fun_app$e' ) ) )
=> ( ! [D: 'A_n_vec$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( D @ ( C @ 'fun_app$e' ) ) )
& ( A @ ( C @ 'fun_app$e' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(337,axiom,
! [A: 'A$'] :
( ( 'one$' = A )
<=> ( A = 'one$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom258) ).
thf(2265,plain,
! [A: 'A$'] :
( ( ( A = 'one$' )
=> ( 'one$' = A ) )
& ( ( 'one$' = A )
=> ( A = 'one$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(66,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
( ( ( ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> $false )
& ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom549) ).
thf(1019,plain,
! [A: 'A_n_vec$',B: 'A_n_vec_set$',C: 'A_n_vec_set$'] :
~ ( ~ ( ~ ( C @ ( A @ 'member$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$g' ) ) )
& ( C @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'member$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(490,axiom,
! [A: 'A_m_vec_m_vec$'] :
( ( ( ( A @ ( 'zero$k' @ 'column$a' ) )
!= 'zero$a' )
& ( A @ 'reduced_row_echelon_form$d' ) )
=> ( ( 'zero$k' @ ( 'zero$k' @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom420) ).
thf(3076,plain,
! [A: 'A_m_vec_m_vec$'] :
( ( ( ( A @ ( 'zero$k' @ 'column$a' ) )
!= 'zero$a' )
& ( A @ 'reduced_row_echelon_form$d' ) )
=> ( ( 'zero$k' @ ( 'zero$k' @ ( A @ 'vec_nth$e' @ 'fun_app$t' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(683,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uvh$' ) @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom34) ).
thf(4071,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uvh$' ) @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(551,axiom,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( ( B @ ( A @ 'fun_app$c' ) )
& ? [C: 'N$'] :
( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$c' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$c' ) ) ) )
=> ( ( A @ 'the$' )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom217) ).
thf(3394,plain,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( ( B @ ( A @ 'fun_app$c' ) )
& ? [C: 'N$'] :
( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$c' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$c' ) ) ) )
=> ( ( A @ 'the$' )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(381,axiom,
( 'one$c'
= ( 'uvt$' @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom395) ).
thf(2484,plain,
( 'one$c'
= ( 'uvt$' @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(569,axiom,
! [A: 'N_set$'] :
( ( A @ 'the_elem$' )
= ( A @ 'uyd$' @ 'the$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom647) ).
thf(3494,plain,
! [A: 'N_set$'] :
( ( A @ 'the_elem$' )
= ( A @ 'uyd$' @ 'the$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(151,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ~ ( A @ ( 'finite$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ~ ( B @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom562) ).
thf(1399,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ~ ( A @ ( 'finite$' @ 'fun_app$g' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ~ ( B @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(653,axiom,
! [A: 'A_a_m_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$z' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).
thf(3918,plain,
! [A: 'A_a_m_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$z' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(687,axiom,
! [A: 'A$'] :
( ( A @ ( 'uus$' @ 'fun_app$m' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom106) ).
thf(4088,plain,
! [A: 'A$'] :
( ( A @ ( 'uus$' @ 'fun_app$m' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(478,axiom,
! [A: 'M_bool_fun$'] :
( ? [B: 'M$'] : ( B @ ( A @ 'fun_app$' ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom629) ).
thf(3013,plain,
! [A: 'M_bool_fun$'] :
( ? [B: 'M$'] : ( B @ ( A @ 'fun_app$' ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(262,axiom,
~ ( 'uvk$' @ 'collect$c' @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom651) ).
thf(1962,plain,
~ ( 'uvk$' @ 'collect$c' @ ( 'vector_scalar_mult$' @ 'dependent$' @ 'fun_app$g' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(328,axiom,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'minus$' @ 'fun_app$k' ) )
= ( B @ ( A @ 'uxk$' ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom476) ).
thf(2238,plain,
! [A: 'A_m_vec$',B: 'A_m_vec$'] :
( ( B @ ( A @ 'minus$' @ 'fun_app$k' ) )
= ( B @ ( A @ 'uxk$' ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(373,axiom,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'reduced_row_echelon_form$' )
=> ~ ( A @ 'uwx$' @ 'collect$a' @ ( 'vector_scalar_mult$a' @ 'dependent$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom687) ).
thf(2453,plain,
! [A: 'A_m_vec_n_vec$'] :
( ( A @ 'reduced_row_echelon_form$' )
=> ~ ( A @ 'uwx$' @ 'collect$a' @ ( 'vector_scalar_mult$a' @ 'dependent$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(75,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( D @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
<=> ( ~ ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( D @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom596) ).
thf(1069,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$',D: 'A_n_vec_set$'] :
( ( ( ~ ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( D @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( D @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
& ( ( D @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ~ ( A @ ( C @ 'member$' @ 'fun_app$g' ) )
& ( D @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(669,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvw$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvw$' ) ) ) @ 'fun_app$d' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom91) ).
thf(4002,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvw$' ) ) ) @ 'fun_app$d' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uvw$' ) ) ) @ 'fun_app$d' ) )
= ( C @ ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$r' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( 'times$e' @ 'fun_app$n' ) @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(585,axiom,
'zero$' != 'one$',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom273) ).
thf(3580,plain,
'zero$' != 'one$',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(132,axiom,
! [A: 'A_n_vec_set$'] :
( ( ! [B: 'A_n_vec$'] :
( ( A
= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
=> $false )
& ( A @ ( 'is_singleton$' @ 'fun_app$g' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom732) ).
thf(1320,plain,
! [A: 'A_n_vec_set$'] :
~ ( ! [B: 'A_n_vec$'] :
( A
!= ( 'bot$' @ ( B @ 'insert$' @ 'fun_app$f' ) ) )
& ( A @ ( 'is_singleton$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(202,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= 'bot$' )
<=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom607) ).
thf(1653,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= 'bot$' ) )
& ( ( ( B @ ( A @ 'minus$b' @ 'fun_app$f' ) )
= 'bot$' )
=> ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(256,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_column_row$a' ) ) @ 'fun_app$r' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvw$' ) ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom398) ).
thf(1944,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'mult_column_row$a' ) ) @ 'fun_app$r' ) )
= ( D @ ( C @ ( B @ ( A @ 'uvw$' ) ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(46,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ ( C @ 'insert$' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom572) ).
thf(940,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec$'] :
( ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) )
=> ( B @ ( C @ 'insert$' @ 'fun_app$f' ) @ ( A @ ( C @ 'insert$' @ 'fun_app$f' ) @ 'less_eq$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(165,axiom,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_a_n_vec_fun$'] :
( ( A @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
=> ( B @ ( A @ 'uxy$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom580) ).
thf(1463,plain,
! [A: 'A_n_vec_bool_fun$',B: 'A_n_vec_a_n_vec_fun$'] :
( ( A @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) )
=> ( B @ ( A @ 'uxy$' ) @ 'collect$c' @ ( 'finite$' @ 'fun_app$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(473,axiom,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$h' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$g' ) @ 'vec_nth$e' @ 'fun_app$t' ) @ ( A @ 'fun_app$y' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom207) ).
thf(2998,plain,
! [A: 'A_m_vec_a_fun$',B: 'A_m_vec_m_vec_n_vec$',C: 'N$',D: 'M$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$h' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$g' ) @ 'vec_nth$e' @ 'fun_app$t' ) @ ( A @ 'fun_app$y' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(535,axiom,
! [A: 'N$'] :
( ( A @ ( 'zero$b' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom132) ).
thf(3316,plain,
! [A: 'N$'] :
( ( A @ ( 'zero$b' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(710,axiom,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( ( B != C )
& ~ ( A @ ( B @ 'is_zero_row$' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( B @ ( A @ 'uxe$' ) @ 'least$' @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom706) ).
thf(4189,plain,
! [A: 'A_m_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( ( B != C )
& ~ ( A @ ( B @ 'is_zero_row$' ) )
& ( A @ 'reduced_row_echelon_form$' ) )
=> ( ( B @ ( A @ 'uxe$' ) @ 'least$' @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(80,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'times$c' @ 'fun_app$f' ) )
= ( A @ ( B @ 'times$c' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom304) ).
thf(1088,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$'] :
( ( B @ ( A @ 'times$c' @ 'fun_app$f' ) )
= ( A @ ( B @ 'times$c' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(300,axiom,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( D @ ( C @ 'fun_app$v' ) )
= 'zero$' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( B @ ( C @ 'sum$' ) )
= ( A @ ( C @ 'sum$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom722) ).
thf(2106,plain,
! [A: 'A_n_vec_set$',B: 'A_n_vec_set$',C: 'A_n_vec_a_fun$'] :
( ( ! [D: 'A_n_vec$'] :
( ( A @ ( B @ 'minus$b' @ 'fun_app$f' ) @ ( D @ 'member$' @ 'fun_app$g' ) )
=> ( ( D @ ( C @ 'fun_app$v' ) )
= 'zero$' ) )
& ( B @ ( A @ 'less_eq$' @ 'fun_app$g' ) ) )
=> ( ( B @ ( C @ 'sum$' ) )
= ( A @ ( C @ 'sum$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(293,axiom,
! [A: 'A_set$'] :
( ( A @ 'uva$' )
= ( A @ 'times$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom346) ).
thf(2087,plain,
! [A: 'A_set$'] :
( ( A @ 'uva$' )
= ( A @ 'times$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(64,axiom,
! [A: 'A_m_vec_m_vec$'] :
( ( A @ 'vec_nth$e' @ 'vec_lambda$c' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom377) ).
thf(1014,plain,
! [A: 'A_m_vec_m_vec$'] :
( ( A @ 'vec_nth$e' @ 'vec_lambda$c' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(242,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uwj$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ ( A @ 'uwi$' ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).
thf(1870,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_m_vec$',C: 'M$'] :
( ( C @ ( B @ ( A @ 'uwj$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ ( A @ 'uwi$' ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(4287,plain,
$false,
inference(e,[status(thm)],[892,2630,1501,1337,3883,3661,3666,3167,2921,2427,2544,1179,1950,2199,3021,1665,4094,1024,1469,1168,3053,1315,2595,2495,3040,1401,3959,3912,1142,2854,3382,1855,3680,3534,1750,3185,4037,762,2940,1406,2104,2671,2014,2099,2282,1671,3745,2607,1756,2918,3175,814,2627,3826,1761,1640,3313,2146,1458,1078,1788,3217,3794,1608,3004,2035,4097,3942,4011,1999,2316,715,3338,3895,2360,3335,3350,3994,782,2020,3777,1645,1359,3898,3880,1482,1127,3915,3308,4124,1386,3281,2400,2825,1967,2136,1265,3688,2869,3263,3275,4151,785,3617,3148,4130,3353,3043,949,2703,3820,1628,3248,1409,2274,917,3485,2185,1577,2897,934,902,853,2857,1479,3084,2520,3708,1362,1875,2388,1847,3788,3840,1892,4194,2049,2301,1815,3322,1302,3199,2090,3295,1109,2259,2650,1677,2073,4205,1415,1418,3453,1334,3473,2880,834,3438,4050,1151,937,2291,1383,3771,821,2017,905,981,2058,1377,3685,2424,2137,1351,3327,1201,2804,3559,2586,1975,2833,3739,1447,956,3808,2523,3211,2154,1651,1206,3303,1306,2118,2737,2641,3037,3151,2011,3450,3503,4216,3591,1708,2093,2296,2307,2083,4031,2621,1868,2382,3550,4172,2000,1900,1091,2249,952,862,2133,2937,3154,788,2986,4160,1343,2560,3742,4091,3948,2445,4140,4192,3090,1296,2068,1836,2211,3727,974,2769,3191,2464,847,2758,2313,2492,2547,2344,2112,4080,3931,1740,3968,2115,2946,2801,1111,4048,2509,1878,869,2638,2498,3615,1541,1017,1953,1804,3862,2577,1064,2692,1498,3001,989,3087,3018,1567,1964,753,3094,3671,1889,2978,2781,1160,3311,1082,2023,3441,3010,2455,2196,1842,1700,2613,3656,2304,2836,2598,1231,1668,2006,2813,3628,3409,2756,2370,2968,1324,1114,2450,1099,1947,4120,2766,2052,1599,1246,3109,779,4163,3476,1318,1241,2043,3856,2368,1616,2662,1996,1732,2909,4148,3903,2208,805,765,3306,1466,2402,1026,1895,1680,1959,824,3491,3079,3985,745,3523,4017,2894,1631,2121,2235,1764,2413,2253,3871,3319,3240,2188,3945,875,3900,1403,3604,3868,2959,3536,1154,3547,1833,3768,1916,3636,2938,1784,1389,4077,843,1125,3266,2674,2695,1488,1786,4186,2293,1371,1312,1865,1058,1332,2706,3568,3751,4127,3594,1239,3783,2055,2166,3579,1356,2148,3719,1117,1011,2906,2839,3500,1122,3066,1282,2478,3251,2214,2624,3683,1524,3515,1589,996,1771,2943,1801,4154,2610,3668,4028,1862,943,2461,2710,811,2182,799,1162,3971,3583,1556,1460,2578,1688,912,1198,2725,3423,1643,883,2369,1176,3142,2101,2156,3539,983,1066,1528,986,2288,2244,1000,1364,1250,3031,2096,1758,1203,2665,2784,2878,2684,1472,3278,3292,1413,1076,3444,1034,1304,1873,3161,1420,927,2037,4052,2124,4177,2927,3921,1340,2333,2846,2256,968,1181,3988,1547,3737,872,2977,1743,3082,3659,3462,3129,1780,3786,2882,993,2298,3391,3260,3754,2747,2569,1432,791,1038,717,3202,1262,3823,1085,3412,3359,4117,2354,1987,2224,1637,3791,3774,1830,1538,2486,3847,808,2247,3488,1898,3415,3356,1221,3024,2728,1881,3007,1934,3697,2992,1536,1981,1353,2357,1955,1485,4106,1504,727,1140,2511,2860,2949,1008,2458,4138,3757,3565,2045,2885,1553,1157,3447,3188,3056,3929,3797,2435,3284,845,3400,2924,1839,3139,2310,1844,2325,759,4061,771,1276,748,1674,2554,2532,946,3991,2971,1244,3780,3729,4121,2174,1476,3220,4042,3748,2026,3136,3368,2934,2262,2009,1491,2475,3324,914,3497,1706,1212,1661,4074,1442,2779,1045,2421,1309,3645,4039,3705,2385,1625,1148,1908,2003,3379,1512,1774,4014,4114,2983,3865,2233,1229,3601,3837,1380,735,3164,3145,3015,3956,2201,3347,4157,1288,4034,2040,3506,960,2795,720,1165,3974,1268,2467,1550,3817,2507,1925,3886,850,1299,2372,2241,2127,1977,1129,2265,1019,3076,4071,3394,2484,3494,1399,3918,4088,3013,1962,2238,2453,1069,4002,3580,1320,1653,1944,940,1463,2998,3316,4189,1088,2106,2087,1014,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP327_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.41 % Computer : n020.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Fri Sep 25 19:08:18 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.25/1.69 % [INFO] Parsing done (684ms).
% 3.68/1.70 % [INFO] Running in sequential loop mode.
% 4.46/2.10 % [INFO] eprover registered as external prover.
% 4.46/2.10 % [INFO] Scanning for conjecture ...
% 5.09/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 754 axioms. Running axiom selection ...
% 6.79/2.74 % [INFO] Axiom selection finished. Selected 712 axioms (removed 42 axioms).
% 8.15/3.20 % [INFO] Problem is typed first-order (TPTP TFF).
% 8.41/3.23 % [INFO] Type checking passed.
% 8.41/3.24 % [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 ...
% 17.95/5.80 % [INFO] [Domain constraints] Detected constraint on tlbool
% 17.95/5.80 % [INFO] [Domain constraints] dom(tlbool) ⊆ {tltrue,tlfalse}
% 25.33/7.72 % External prover 'e' found a proof!
% 25.33/7.72 % [INFO] Killing All external provers ...
% 25.33/7.72 % Time passed: 7167ms (effective reasoning time: 6011ms)
% 25.33/7.72 % 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)>
% 25.33/7.73 % Axioms used in derivation (712): axiom326, axiom32, axiom635, axiom280, axiom127, axiom626, axiom546, axiom116, axiom452, axiom491, axiom241, axiom76, axiom702, axiom260, axiom273, axiom61, axiom527, axiom730, axiom611, axiom745, axiom717, axiom230, axiom100, axiom6, axiom503, axiom553, axiom549, axiom396, axiom25, axiom369, axiom14, axiom333, axiom564, axiom712, axiom295, axiom485, axiom54, axiom751, axiom723, axiom480, axiom474, axiom724, axiom214, axiom670, axiom516, axiom322, axiom307, axiom496, axiom284, axiom749, axiom662, axiom423, axiom734, axiom65, axiom709, axiom575, axiom36, axiom203, axiom142, axiom311, axiom169, axiom622, axiom739, axiom531, axiom291, axiom507, axiom430, axiom600, axiom50, axiom158, axiom131, axiom10, axiom386, axiom344, axiom138, axiom441, axiom699, axiom508, axiom392, axiom597, axiom337, axiom580, axiom728, axiom119, axiom210, axiom407, axiom191, axiom692, axiom17, axiom673, axiom401, axiom397, axiom460, axiom354, axiom587, axiom477, axiom467, axiom257, axiom579, axiom22, axiom619, axiom412, axiom654, axiom147, axiom434, axiom341, axiom504, axiom173, axiom109, axiom348, axiom184, axiom376, axiom684, axiom172, axiom535, axiom735, axiom266, axiom445, axiom524, axiom695, axiom42, axiom513, axiom239, axiom300, axiom350, axiom561, axiom329, axiom372, axiom162, axiom358, axiom632, axiom616, axiom542, axiom123, axiom592, axiom701, axiom383, axiom605, axiom2, axiom134, axiom195, axiom746, axiom161, axiom706, axiom33, axiom150, axiom741, axiom246, axiom713, axiom456, axiom87, axiom572, axiom568, axiom130, axiom235, axiom98, axiom643, axiom473, axiom39, axiom608, axiom499, axiom330, axiom650, axiom418, axiom484, axiom112, axiom304, axiom488, axiom520, axiom365, axiom251, axiom687, axiom64, axiom676, axiom578, axiom530, axiom283, axiom126, axiom539, axiom427, axiom625, axiom591, axiom742, axiom682, axiom59, axiom247, axiom48, axiom217, axiom27, axiom352, axiom411, axiom294, axiom179, axiom363, axiom705, axiom314, axiom289, axiom437, axiom601, axiom236, axiom151, axiom115, axiom623, axiom94, axiom83, axiom5, axiom336, axiom308, axiom321, axiom35, axiom647, axiom78, axiom24, axiom661, axiom668, axiom278, axiom272, axiom455, axiom475, axiom121, axiom132, formula_755, axiom56, axiom137, axiom563, axiom206, axiom318, axiom60, axiom631, axiom0, axiom574, axiom490, axiom671, axiom466, axiom240, axiom290, axiom750, axiom13, axiom53, axiom433, axiom143, axiom359, axiom416, axiom489, axiom545, axiom108, axiom395, axiom387, axiom459, axiom400, axiom258, axiom75, axiom325, axiom653, axiom698, axiom448, axiom552, axiom385, axiom157, axiom658, axiom90, axiom168, axiom528, axiom332, axiom9, axiom478, axiom693, axiom303, axiom612, axiom366, axiom207, axiom494, axiom538, axiom133, axiom80, axiom371, axiom567, axiom738, axiom586, axiom422, axiom185, axiom472, axiom202, axiom252, axiom146, axiom97, axiom192, axiom355, axiom391, axiom604, axiom263, axiom415, axiom589, axiom254, axiom444, axiom719, axiom657, axiom82, axiom694, axiom45, axiom679, axiom669, axiom541, axiom360, axiom398, axiom382, axiom483, axiom229, axiom174, axiom556, axiom639, axiom319, axiom672, axiom646, axiom180, axiom213, axiom534, axiom683, axiom450, axiom196, axiom523, axiom232, axiom615, axiom629, axiom310, axiom243, axiom426, axiom72, axiom461, axiom716, axiom449, axiom438, axiom727, axiom267, axiom89, axiom664, axiom731, axiom224, axiom122, axiom38, axiom419, axiom377, axiom500, axiom91, axiom1, axiom105, axiom218, axiom86, axiom163, axiom408, axiom111, axiom120, axiom720, axiom665, axiom512, axiom660, axiom297, axiom52, axiom156, axiom511, axiom390, axiom37, axiom331, axiom602, axiom432, axiom223, axiom571, axiom641, axiom12, axiom501, axiom342, axiom381, axiom193, axiom34, axiom630, axiom544, axiom152, axiom425, axiom607, axiom454, axiom205, axiom364, axiom628, axiom79, axiom747, axiom167, axiom190, axiom707, axiom573, axiom710, axiom443, axiom96, axiom149, axiom189, axiom375, axiom23, axiom560, axiom93, axiom595, axiom562, axiom41, axiom394, axiom667, axiom227, axiom182, axiom476, axiom216, axiom704, axiom409, axiom286, axiom313, axiom618, axiom63, axiom19, axiom743, axiom458, axiom613, axiom102, axiom410, axiom320, axiom30, axiom370, axiom201, axiom178, axiom479, axiom659, axiom428, axiom259, axiom74, axiom276, axiom451, axiom570, axiom509, axiom697, axiom233, axiom721, axiom220, axiom598, axiom302, axiom367, axiom57, formula_754, axiom599, axiom85, axiom652, axiom566, axiom145, axiom471, axiom506, axiom186, axiom497, axiom164, axiom726, axiom378, axiom374, axiom614, axiom748, axiom440, axiom678, axiom581, axiom244, axiom271, axiom287, axiom4, axiom255, axiom153, axiom324, axiom71, axiom462, axiom708, axiom15, axiom129, axiom620, axiom594, axiom136, axiom414, axiom106, axiom533, axiom718, axiom181, axiom403, axiom522, axiom436, axiom482, axiom555, axiom486, axiom346, axiom645, axiom262, axiom68, axiom686, axiom335, axiom737, axiom170, axiom656, axiom268, axiom293, axiom175, axiom237, axiom26, axiom493, axiom356, axiom439, axiom634, axiom469, axiom110, axiom125, axiom675, axiom603, axiom49, axiom219, axiom197, axiom690, axiom298, axiom46, axiom585, axiom732, axiom248, axiom421, axiom590, axiom577, axiom715, axiom18, axiom729, axiom338, axiom242, axiom666, axiom379, axiom691, axiom663, axiom510, axiom199, axiom547, axiom389, axiom226, axiom166, axiom526, axiom559, axiom457, axiom521, axiom651, axiom88, axiom442, axiom327, axiom92, axiom399, axiom740, axiom345, axiom464, axiom204, axiom296, axiom711, axiom569, axiom752, axiom700, axiom215, axiom576, axiom596, axiom141, axiom357, axiom274, axiom117, axiom621, axiom44, axiom222, axiom515, axiom323, axiom446, axiom84, axiom554, axiom269, axiom453, axiom81, axiom502, axiom103, axiom231, axiom306, axiom155, axiom495, axiom253, axiom368, axiom680, axiom689, axiom550, axiom565, axiom703, axiom99, axiom148, axiom128, axiom316, axiom285, axiom540, axiom537, axiom349, axiom249, axiom744, axiom183, axiom301, axiom649, axiom211, axiom29, axiom361, axiom429, axiom380, axiom532, axiom177, axiom31, axiom264, axiom431, axiom208, axiom20, axiom588, axiom627, axiom733, axiom159, axiom487, axiom609, axiom519, axiom402, axiom384, axiom551, axiom339, axiom154, axiom40, axiom265, axiom165, axiom47, axiom270, axiom113, axiom176, axiom171, axiom3, axiom714, axiom417, axiom305, axiom187, axiom288, axiom317, axiom277, axiom198, axiom529, axiom144, axiom435, axiom55, axiom736, axiom281, axiom424, axiom633, axiom593, axiom245, axiom644, axiom69, axiom685, axiom135, axiom536, axiom373, axiom95, axiom70, axiom238, axiom617, axiom465, axiom543, axiom299, axiom351, axiom413, axiom256, axiom334, axiom655, axiom696, axiom160, axiom514, axiom43, axiom722, axiom124, axiom505, axiom261, axiom725, axiom606, axiom77, axiom406, axiom388, axiom677, axiom582, axiom637, axiom420, axiom498, axiom648, axiom21, axiom139, axiom200, axiom292, axiom525, axiom234, axiom362, axiom51, axiom548, axiom309, axiom610, axiom470, axiom674, axiom62, axiom468, axiom492, axiom328, axiom140, axiom250, axiom688, axiom58, axiom624, axiom340, axiom194, axiom353
% 25.33/7.73 % No. of inferences in proof: 1428
% 25.33/7.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7167 ms resp. 6011 ms w/o parsing
% 27.36/8.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.36/8.30 % [INFO] Killing All external provers ...
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