%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP325_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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:37:42 AM UTC 2026
% Result : Theorem 19.35s 5.81s
% Output : Refutation 20.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 483
% Syntax : Number of formulae : 968 ( 521 unt; 0 typ; 0 def)
% Number of atoms : 2274 (1240 equ; 0 cnn)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 11199 ( 370 ~; 56 |; 486 &;9523 @)
% ( 82 <=>; 682 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 49 ( 48 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 234 ( 231 usr; 49 con; 0-4 aty)
% Number of variables : 2399 ( 0 ^;2345 !; 54 ?;2399 :)
% Comments :
%------------------------------------------------------------------------------
thf('B_a_b_vec_fun$_type',type,
'B_a_b_vec_fun$': $tType ).
thf('A_b_vec_n_vec_a_fun$_type',type,
'A_b_vec_n_vec_a_fun$': $tType ).
thf('N_a_b_vec_n_vec_bool_fun_fun$_type',type,
'N_a_b_vec_n_vec_bool_fun_fun$': $tType ).
thf('A_b_vec_n_vec$_type',type,
'A_b_vec_n_vec$': $tType ).
thf('N_a_b_vec_n_vec_n_vec_fun$_type',type,
'N_a_b_vec_n_vec_n_vec_fun$': $tType ).
thf('A_b_vec_a_b_vec_fun$_type',type,
'A_b_vec_a_b_vec_fun$': $tType ).
thf('A_a_n_vec_fun$_type',type,
'A_a_n_vec_fun$': $tType ).
thf('N_a_b_vec_bool_fun_fun$_type',type,
'N_a_b_vec_bool_fun_fun$': $tType ).
thf('A_n_vec_a_fun$_type',type,
'A_n_vec_a_fun$': $tType ).
thf('A_n_vec_b_vec$_type',type,
'A_n_vec_b_vec$': $tType ).
thf('A_b_vec_n_vec_n_vec$_type',type,
'A_b_vec_n_vec_n_vec$': $tType ).
thf('N_a_n_vec_fun$_type',type,
'N_a_n_vec_fun$': $tType ).
thf('A_n_vec_a_b_vec_fun$_type',type,
'A_n_vec_a_b_vec_fun$': $tType ).
thf('A_a_b_vec_fun$_type',type,
'A_a_b_vec_fun$': $tType ).
thf('A_b_vec_b_vec$_type',type,
'A_b_vec_b_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$': $tType ).
thf('B$_type',type,
'B$': $tType ).
thf('A_a_b_vec_n_vec_fun$_type',type,
'A_a_b_vec_n_vec_fun$': $tType ).
thf('A_b_vec$_type',type,
'A_b_vec$': $tType ).
thf('N$_type',type,
'N$': $tType ).
thf('N_a_b_vec_b_vec_fun$_type',type,
'N_a_b_vec_b_vec_fun$': $tType ).
thf('A_b_vec_n_vec_bool_fun$_type',type,
'A_b_vec_n_vec_bool_fun$': $tType ).
thf('B_a_fun$_type',type,
'B_a_fun$': $tType ).
thf(tlbool_type,type,
tlbool: $tType ).
thf('N_a_bool_fun_fun$_type',type,
'N_a_bool_fun_fun$': $tType ).
thf('A_bool_fun$_type',type,
'A_bool_fun$': $tType ).
thf('N_a_fun$_type',type,
'N_a_fun$': $tType ).
thf('N_a_b_vec_fun$_type',type,
'N_a_b_vec_fun$': $tType ).
thf('A_b_vec_n_vec_a_b_vec_n_vec_fun$_type',type,
'A_b_vec_n_vec_a_b_vec_n_vec_fun$': $tType ).
thf('A$_type',type,
'A$': $tType ).
thf('N_n_fun$_type',type,
'N_n_fun$': $tType ).
thf('A_n_vec$_type',type,
'A_n_vec$': $tType ).
thf('A_b_vec_b_vec_n_vec$_type',type,
'A_b_vec_b_vec_n_vec$': $tType ).
thf('A_n_vec_a_n_vec_fun$_type',type,
'A_n_vec_a_n_vec_fun$': $tType ).
thf('B_a_n_vec_fun$_type',type,
'B_a_n_vec_fun$': $tType ).
thf('A_a_fun$_type',type,
'A_a_fun$': $tType ).
thf('A_b_vec_n_vec_n_vec_n_vec$_type',type,
'A_b_vec_n_vec_n_vec_n_vec$': $tType ).
thf('A_n_vec_n_vec_n_vec$_type',type,
'A_n_vec_n_vec_n_vec$': $tType ).
thf('A_b_vec_a_fun$_type',type,
'A_b_vec_a_fun$': $tType ).
thf('A_b_vec_bool_fun$_type',type,
'A_b_vec_bool_fun$': $tType ).
thf('A_b_vec_n_vec_n_vec_a_b_vec_n_vec_n_vec_fun$_type',type,
'A_b_vec_n_vec_n_vec_a_b_vec_n_vec_n_vec_fun$': $tType ).
thf('A_n_vec_bool_fun$_type',type,
'A_n_vec_bool_fun$': $tType ).
thf('N_n_bool_fun_fun$_type',type,
'N_n_bool_fun_fun$': $tType ).
thf('B_a_bool_fun_fun$_type',type,
'B_a_bool_fun_fun$': $tType ).
thf('N_bool_fun$_type',type,
'N_bool_fun$': $tType ).
thf('N_a_b_vec_n_vec_fun$_type',type,
'N_a_b_vec_n_vec_fun$': $tType ).
thf('N_a_n_vec_n_vec_fun$_type',type,
'N_a_n_vec_n_vec_fun$': $tType ).
thf('uul$_decl',type,
'uul$': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N$' > 'N$' > 'N_a_b_vec_fun$' ).
thf('times$b_decl',type,
'times$b': 'A_b_vec$' > 'A_b_vec_a_b_vec_fun$' ).
thf('uwy$_decl',type,
'uwy$': 'A_b_vec_n_vec$' > 'N_a_b_vec_n_vec_fun$' ).
thf('interchange_columns$a_decl',type,
'interchange_columns$a': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N$' > 'A_b_vec_n_vec_n_vec$' ).
thf('uwg$_decl',type,
'uwg$': 'A_b_vec_n_vec$' > 'N$' > 'B$' > 'N_a_b_vec_fun$' ).
thf('fun_app$p_decl',type,
'fun_app$p': 'A_n_vec_a_n_vec_fun$' > 'A_n_vec$' > 'A_n_vec$' ).
thf('uxm$_decl',type,
'uxm$': 'A_b_vec_n_vec_n_vec$' > 'A_b_vec_n_vec_n_vec$' > 'N_a_b_vec_n_vec_fun$' ).
thf('uxg$_decl',type,
'uxg$': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'A_b_vec$' > 'N_a_b_vec_n_vec_fun$' ).
thf('uwl$_decl',type,
'uwl$': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N_a_b_vec_n_vec_fun$' ).
thf('uvm$_decl',type,
'uvm$': 'A_b_vec_a_fun$' > 'A_b_vec_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).
thf('uuk$_decl',type,
'uuk$': 'A_b_vec_b_vec$' > 'B$' > 'B$' > 'B_a_b_vec_fun$' ).
thf('interchange_columns_row$_decl',type,
'interchange_columns_row$': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N$' > 'N_a_b_vec_n_vec_fun$' ).
thf('less$_decl',type,
'less$': 'N_n_bool_fun_fun$' ).
thf('uminus$e_decl',type,
'uminus$e': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
thf('uub$_decl',type,
'uub$': 'A_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).
thf('uminus$f_decl',type,
'uminus$f': 'A_b_vec_b_vec$' > 'A_b_vec_b_vec$' ).
thf('uvq$_decl',type,
'uvq$': 'A_a_b_vec_n_vec_fun$' > 'A_n_vec_n_vec$' > 'N_a_b_vec_n_vec_n_vec_fun$' ).
thf('interchange_rows_row$b_decl',type,
'interchange_rows_row$b': 'A_b_vec_n_vec$' > 'N$' > 'N$' > 'N_a_b_vec_fun$' ).
thf('uva$_decl',type,
'uva$': 'A_a_b_vec_fun$' > 'A_n_vec_n_vec$' > 'N_a_b_vec_n_vec_fun$' ).
thf('uup$_decl',type,
'uup$': 'A_n_vec_n_vec$' > 'N$' > 'N$' > 'N$' > 'N_a_fun$' ).
thf('fun_app$k_decl',type,
'fun_app$k': 'A_b_vec_a_b_vec_fun$' > 'A_b_vec$' > 'A_b_vec$' ).
thf('columnvector$g_decl',type,
'columnvector$g': 'A_n_vec$' > 'A_b_vec_n_vec$' ).
thf('row_add_row$_decl',type,
'row_add_row$': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N$' > 'A_b_vec$' > 'N_a_b_vec_n_vec_fun$' ).
thf('one$c_decl',type,
'one$c': 'A_b_vec$' ).
thf('uxf$_decl',type,
'uxf$': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'A_b_vec$' > 'N$' > 'N_a_b_vec_fun$' ).
thf('uuy$_decl',type,
'uuy$': 'A_a_fun$' > 'A_b_vec_n_vec$' > 'N_a_b_vec_fun$' ).
thf('uwm$_decl',type,
'uwm$': 'A_b_vec_n_vec_n_vec$' > 'N_a_b_vec_n_vec_n_vec_fun$' ).
thf('least$_decl',type,
'least$': 'N_bool_fun$' > 'N$' ).
thf('fun_app$ad_decl',type,
'fun_app$ad': 'B_a_bool_fun_fun$' > 'B$' > 'A_bool_fun$' ).
thf('map_matrix$h_decl',type,
'map_matrix$h': 'A_b_vec_n_vec_a_fun$' > 'A_b_vec_n_vec_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
thf('uwf$_decl',type,
'uwf$': 'A_b_vec_n_vec$' > 'N$' > 'B$' > 'N_bool_fun$' ).
thf('a$a_decl',type,
'a$a': 'A_b_vec_n_vec$' ).
thf('mult_row$b_decl',type,
'mult_row$b': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'A_b_vec$' > 'A_b_vec_n_vec_n_vec$' ).
thf('uvg$_decl',type,
'uvg$': 'A_a_fun$' > 'A_b_vec_b_vec$' > 'B_a_b_vec_fun$' ).
thf('rowvector$b_decl',type,
'rowvector$b': 'A_b_vec_n_vec$' > 'A_b_vec_n_vec_n_vec$' ).
thf('uum$_decl',type,
'uum$': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N$' > 'N_a_b_vec_n_vec_fun$' ).
thf('uwc$_decl',type,
'uwc$': 'N_a_b_vec_fun$' ).
thf('uxl$_decl',type,
'uxl$': 'A_n_vec$' > 'A_n_vec$' > 'N_a_fun$' ).
thf('uux$_decl',type,
'uux$': 'A_a_fun$' > 'A_b_vec_n_vec$' > 'N$' > 'B_a_fun$' ).
thf('times$e_decl',type,
'times$e': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
thf('row_add_row$b_decl',type,
'row_add_row$b': 'A_b_vec_n_vec$' > 'N$' > 'N$' > 'A$' > 'N_a_b_vec_fun$' ).
thf('uud$_decl',type,
'uud$': 'A_n_vec$' > 'N_a_fun$' ).
thf('interchange_rows$_decl',type,
'interchange_rows$': 'A_b_vec_n_vec$' > 'N$' > 'N_a_b_vec_n_vec_fun$' ).
thf('uvn$_decl',type,
'uvn$': 'A_n_vec_a_fun$' > 'A_n_vec_n_vec_n_vec$' > 'N$' > 'N_a_fun$' ).
thf('one$d_decl',type,
'one$d': 'A_b_vec_n_vec_n_vec$' ).
thf('uuc$_decl',type,
'uuc$': 'A_b_vec_b_vec$' > 'B_a_b_vec_fun$' ).
thf('uue$_decl',type,
'uue$': 'A_b_vec_n_vec_n_vec$' > 'N_a_b_vec_n_vec_fun$' ).
thf('m$_decl',type,
'm$': 'N$' ).
thf('uvp$_decl',type,
'uvp$': 'A_a_b_vec_n_vec_fun$' > 'A_n_vec_n_vec$' > 'N$' > 'N_a_b_vec_n_vec_fun$' ).
thf('uua$_decl',type,
'uua$': 'A_b_vec_n_vec$' > 'A_b_vec_n_vec$' > 'N_a_b_vec_fun$' ).
thf('uvi$_decl',type,
'uvi$': 'A_a_n_vec_fun$' > 'A_n_vec_n_vec$' > 'N_a_n_vec_n_vec_fun$' ).
thf('zero$b_decl',type,
'zero$b': 'A_b_vec_n_vec$' ).
thf('interchange_columns_row$b_decl',type,
'interchange_columns_row$b': 'A_b_vec_n_vec$' > 'B$' > 'B$' > 'N_a_b_vec_fun$' ).
thf('uxo$_decl',type,
'uxo$': 'A_b_vec_n_vec$' > 'A_b_vec_n_vec$' > 'N_a_b_vec_fun$' ).
thf('zero$c_decl',type,
'zero$c': 'A_n_vec$' ).
thf('uwn$_decl',type,
'uwn$': 'A_b_vec$' > 'B$' > 'N_a_fun$' ).
thf('uvu$_decl',type,
'uvu$': 'B_a_fun$' ).
thf('zero$e_decl',type,
'zero$e': 'A_n_vec_n_vec$' ).
thf('map_matrix$a_decl',type,
'map_matrix$a': 'A_a_fun$' > 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
thf('uwi$_decl',type,
'uwi$': 'A_b_vec$' > 'B_a_b_vec_fun$' ).
thf('map_matrix$e_decl',type,
'map_matrix$e': 'A_a_n_vec_fun$' > 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_n_vec$' ).
thf('vec_nth$c_decl',type,
'vec_nth$c': 'A_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).
thf('fun_app$f_decl',type,
'fun_app$f': 'N_a_n_vec_fun$' > 'N$' > 'A_n_vec$' ).
thf('uvh$_decl',type,
'uvh$': 'A_a_n_vec_fun$' > 'A_n_vec_n_vec$' > 'N$' > 'N_a_n_vec_fun$' ).
thf('vec_nth$a_decl',type,
'vec_nth$a': 'A_b_vec_n_vec$' > 'N_a_b_vec_fun$' ).
thf('uvz$_decl',type,
'uvz$': 'B_a_b_vec_fun$' ).
thf('vec_lambda$e_decl',type,
'vec_lambda$e': 'N_a_b_vec_n_vec_fun$' > 'A_b_vec_n_vec_n_vec$' ).
thf('uxu$_decl',type,
'uxu$': 'A_n_vec_a_n_vec_fun$' ).
thf('fun_app$a_decl',type,
'fun_app$a': 'B_a_fun$' > 'B$' > 'A$' ).
thf('vec_nth$b_decl',type,
'vec_nth$b': 'A_b_vec_n_vec_n_vec$' > 'N_a_b_vec_n_vec_fun$' ).
thf('uxj$_decl',type,
'uxj$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).
thf('vec_lambda$a_decl',type,
'vec_lambda$a': 'N_a_b_vec_fun$' > 'A_b_vec_n_vec$' ).
thf('fun_app$ae_decl',type,
'fun_app$ae': 'A_b_vec_bool_fun$' > 'A_b_vec$' > $o ).
thf('vec_lambda$_decl',type,
'vec_lambda$': 'B_a_fun$' > 'A_b_vec$' ).
thf('i$_decl',type,
'i$': 'N$' ).
thf('n$_decl',type,
'n$': 'N$' ).
thf('uvo$_decl',type,
'uvo$': 'A_n_vec_a_fun$' > 'A_n_vec_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).
thf('zero$d_decl',type,
'zero$d': 'A_b_vec$' ).
thf('fun_app$q_decl',type,
'fun_app$q': 'A_n_vec_a_fun$' > 'A_n_vec$' > 'A$' ).
thf('fun_app$j_decl',type,
'fun_app$j': 'N_a_b_vec_n_vec_n_vec_fun$' > 'N$' > 'A_b_vec_n_vec_n_vec$' ).
thf('uxx$_decl',type,
'uxx$': 'A_b_vec_a_b_vec_fun$' ).
thf('uuv$_decl',type,
'uuv$': 'A_b_vec_n_vec$' > 'N$' > 'N$' > 'N$' > 'B_a_fun$' ).
thf('uminus$c_decl',type,
'uminus$c': 'A_a_fun$' ).
thf('fun_app$h_decl',type,
'fun_app$h': 'N_a_n_vec_n_vec_fun$' > 'N$' > 'A_n_vec_n_vec$' ).
thf('uxt$_decl',type,
'uxt$': 'A_a_fun$' ).
thf('fun_app$o_decl',type,
'fun_app$o': 'A_b_vec_n_vec_a_b_vec_n_vec_fun$' > 'A_b_vec_n_vec$' > 'A_b_vec_n_vec$' ).
thf('one$_decl',type,
'one$': 'A$' ).
thf('uve$_decl',type,
'uve$': 'A_a_fun$' > 'A_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).
thf('uvy$_decl',type,
'uvy$': 'N_a_n_vec_fun$' ).
thf('times$d_decl',type,
'times$d': 'A_b_vec_n_vec_n_vec$' > 'A_b_vec_n_vec_n_vec_a_b_vec_n_vec_n_vec_fun$' ).
thf('uvj$_decl',type,
'uvj$': 'A_a_b_vec_fun$' > 'A_b_vec_n_vec$' > 'N$' > 'B_a_b_vec_fun$' ).
thf('uvb$_decl',type,
'uvb$': 'A_b_vec_a_b_vec_fun$' > 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N_a_b_vec_fun$' ).
thf('uwa$_decl',type,
'uwa$': 'B_a_fun$' ).
thf('uuq$_decl',type,
'uuq$': 'A_n_vec_n_vec$' > 'N$' > 'N$' > 'N_a_n_vec_fun$' ).
thf('a$_decl',type,
'a$': 'A_b_vec_n_vec$' ).
thf('uvv$_decl',type,
'uvv$': 'N_a_b_vec_n_vec_fun$' ).
thf('fun_app$r_decl',type,
'fun_app$r': 'A_b_vec_a_fun$' > 'A_b_vec$' > 'A$' ).
thf('interchange_rows$a_decl',type,
'interchange_rows$a': 'A_n_vec_n_vec$' > 'N$' > 'N_a_n_vec_n_vec_fun$' ).
thf('map_matrix$i_decl',type,
'map_matrix$i': 'A_a_b_vec_n_vec_fun$' > 'A_n_vec_n_vec$' > 'A_b_vec_n_vec_n_vec_n_vec$' ).
thf(tltrue_decl,type,
tltrue: tlbool ).
thf('map_matrix$_decl',type,
'map_matrix$': 'A_a_fun$' > 'A_b_vec_n_vec$' > 'A_b_vec_n_vec$' ).
thf('fun_app$d_decl',type,
'fun_app$d': 'N_a_b_vec_n_vec_fun$' > 'N$' > 'A_b_vec_n_vec$' ).
thf('row_add$a_decl',type,
'row_add$a': 'A_n_vec_n_vec$' > 'N$' > 'N$' > 'A$' > 'A_n_vec_n_vec$' ).
thf('vec_lambda$b_decl',type,
'vec_lambda$b': 'N_a_fun$' > 'A_n_vec$' ).
thf('vec_nth$d_decl',type,
'vec_nth$d': 'A_b_vec_b_vec$' > 'B_a_b_vec_fun$' ).
thf('less_eq$_decl',type,
'less_eq$': 'N_n_bool_fun_fun$' ).
thf('uun$_decl',type,
'uun$': 'A_b_vec_n_vec$' > 'B$' > 'B$' > 'N$' > 'B_a_fun$' ).
thf('fun_app$ab_decl',type,
'fun_app$ab': 'A_bool_fun$' > 'A$' > $o ).
thf('fun_app$ag_decl',type,
'fun_app$ag': 'N_n_fun$' > 'N$' > 'N$' ).
thf('thesis$_decl',type,
'thesis$': $o ).
thf('uuf$_decl',type,
'uuf$': 'A_b_vec$' > 'B_a_fun$' ).
thf('uuw$_decl',type,
'uuw$': 'A_b_vec_n_vec$' > 'N$' > 'N$' > 'N_a_b_vec_fun$' ).
thf('fun_app$af_decl',type,
'fun_app$af': 'N_a_b_vec_bool_fun_fun$' > 'N$' > 'A_b_vec_bool_fun$' ).
thf('uwb$_decl',type,
'uwb$': 'N_a_b_vec_n_vec_fun$' ).
thf('j$_decl',type,
'j$': 'B$' ).
thf('interchange_rows_row$_decl',type,
'interchange_rows_row$': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N$' > 'N_a_b_vec_n_vec_fun$' ).
thf('uvr$_decl',type,
'uvr$': 'N_a_fun$' ).
thf('uwk$_decl',type,
'uwk$': 'A_b_vec$' > 'N_a_b_vec_fun$' ).
thf('uug$_decl',type,
'uug$': 'A_b_vec_n_vec$' > 'N_a_b_vec_fun$' ).
thf('uxs$_decl',type,
'uxs$': 'A_b_vec_a_b_vec_fun$' ).
thf('uvw$_decl',type,
'uvw$': 'N_a_b_vec_fun$' ).
thf('fun_app$v_decl',type,
'fun_app$v': 'A_n_vec_a_b_vec_fun$' > 'A_n_vec$' > 'A_b_vec$' ).
thf('one$b_decl',type,
'one$b': 'A_n_vec$' ).
thf('uwv$_decl',type,
'uwv$': 'A_b_vec$' > 'B$' > 'B_a_fun$' ).
thf('vec_nth$g_decl',type,
'vec_nth$g': 'A_b_vec_n_vec_n_vec_n_vec$' > 'N$' > 'A_b_vec_n_vec_n_vec$' ).
thf('times$c_decl',type,
'times$c': 'A$' > 'A_a_fun$' ).
thf('fun_app$_decl',type,
'fun_app$': 'N_bool_fun$' > 'N$' > $o ).
thf('uxi$_decl',type,
'uxi$': 'A_b_vec_n_vec$' > 'N$' > 'A$' > 'N_a_b_vec_fun$' ).
thf('map_matrix$b_decl',type,
'map_matrix$b': 'A_a_b_vec_fun$' > 'A_n_vec_n_vec$' > 'A_b_vec_n_vec_n_vec$' ).
thf('uu$_decl',type,
'uu$': 'N_bool_fun$' ).
thf('times$_decl',type,
'times$': 'A_b_vec_n_vec$' > 'A_b_vec_n_vec_a_b_vec_n_vec_fun$' ).
thf('fun_app$t_decl',type,
'fun_app$t': 'A_a_b_vec_fun$' > 'A$' > 'A_b_vec$' ).
thf('uwx$_decl',type,
'uwx$': 'A_b_vec_n_vec$' > 'N$' > 'N_a_b_vec_fun$' ).
thf('interchange_rows$b_decl',type,
'interchange_rows$b': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N_a_b_vec_n_vec_n_vec_fun$' ).
thf('fun_app$s_decl',type,
'fun_app$s': 'A_a_n_vec_fun$' > 'A$' > 'A_n_vec$' ).
thf('divide$_decl',type,
'divide$': 'A$' > 'A_a_fun$' ).
thf('uxy$_decl',type,
'uxy$': 'A_a_fun$' ).
thf('fun_app$m_decl',type,
'fun_app$m': 'A_a_fun$' > 'A$' > 'A$' ).
thf('uvd$_decl',type,
'uvd$': 'A_a_fun$' > 'A_n_vec_n_vec$' > 'N$' > 'N_a_fun$' ).
thf('uwz$_decl',type,
'uwz$': 'A_n_vec$' > 'N$' > 'B_a_fun$' ).
thf('uwd$_decl',type,
'uwd$': 'A_n_vec_n_vec$' > 'N$' > 'N_n_bool_fun_fun$' ).
thf('interchange_rows_row$a_decl',type,
'interchange_rows_row$a': 'A_n_vec_n_vec$' > 'N$' > 'N$' > 'N_a_n_vec_fun$' ).
thf('times$a_decl',type,
'times$a': 'A_n_vec$' > 'A_n_vec_a_n_vec_fun$' ).
thf('uur$_decl',type,
'uur$': 'A_b_vec_b_vec$' > 'B$' > 'B$' > 'B$' > 'B_a_fun$' ).
thf('uuz$_decl',type,
'uuz$': 'A_a_b_vec_fun$' > 'A_n_vec_n_vec$' > 'N$' > 'N_a_b_vec_fun$' ).
thf('fun_app$x_decl',type,
'fun_app$x': 'A_b_vec_n_vec_bool_fun$' > 'A_b_vec_n_vec$' > $o ).
thf('uwr$_decl',type,
'uwr$': 'A_b_vec_n_vec$' > 'N$' > 'B_a_b_vec_fun$' ).
thf('interchange_columns$c_decl',type,
'interchange_columns$c': 'A_b_vec_b_vec$' > 'B$' > 'B$' > 'A_b_vec_b_vec$' ).
thf('uvt$_decl',type,
'uvt$': 'B_a_b_vec_fun$' ).
thf('uuu$_decl',type,
'uuu$': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N$' > 'N_a_b_vec_n_vec_fun$' ).
thf('row_add_row$a_decl',type,
'row_add_row$a': 'A_n_vec_n_vec$' > 'N$' > 'N$' > 'A$' > 'N_a_n_vec_fun$' ).
thf('fun_app$u_decl',type,
'fun_app$u': 'A_b_vec_n_vec_n_vec_a_b_vec_n_vec_n_vec_fun$' > 'A_b_vec_n_vec_n_vec$' > 'A_b_vec_n_vec_n_vec$' ).
thf('uxd$_decl',type,
'uxd$': 'A_b_vec_b_vec$' > 'B$' > 'A$' > 'B$' > 'B_a_fun$' ).
thf('uvc$_decl',type,
'uvc$': 'A_b_vec_a_b_vec_fun$' > 'A_b_vec_n_vec_n_vec$' > 'N_a_b_vec_n_vec_fun$' ).
thf('fun_app$n_decl',type,
'fun_app$n': 'A_a_b_vec_n_vec_fun$' > 'A$' > 'A_b_vec_n_vec$' ).
thf('rowvector$c_decl',type,
'rowvector$c': 'A_b_vec$' > 'A_b_vec_n_vec$' ).
thf('fun_app$e_decl',type,
'fun_app$e': 'B_a_b_vec_fun$' > 'B$' > 'A_b_vec$' ).
thf('mult_row$c_decl',type,
'mult_row$c': 'A_b_vec_b_vec$' > 'B$' > 'A$' > 'A_b_vec_b_vec$' ).
thf('gauss_Jordan_in_ij$_decl',type,
'gauss_Jordan_in_ij$': 'A_b_vec_n_vec$' > 'N$' > 'B$' > 'A_b_vec_n_vec$' ).
thf('times$f_decl',type,
'times$f': 'A_b_vec_b_vec$' > 'A_b_vec_b_vec$' > 'A_b_vec_b_vec$' ).
thf('row_add$_decl',type,
'row_add$': 'A_b_vec_n_vec$' > 'N$' > 'N$' > 'A_a_b_vec_n_vec_fun$' ).
thf('uxe$_decl',type,
'uxe$': 'A_b_vec_b_vec$' > 'B$' > 'A$' > 'B_a_b_vec_fun$' ).
thf('fun_app$l_decl',type,
'fun_app$l': 'N_a_fun$' > 'N$' > 'A$' ).
thf('uminus$d_decl',type,
'uminus$d': 'A_b_vec_n_vec_n_vec$' > 'A_b_vec_n_vec_n_vec$' ).
thf('one$a_decl',type,
'one$a': 'A_b_vec_n_vec$' ).
thf('uxc$_decl',type,
'uxc$': 'A_n_vec_n_vec$' > 'N$' > 'A$' > 'N_a_n_vec_fun$' ).
thf('mult_row_row$a_decl',type,
'mult_row_row$a': 'A_n_vec_n_vec$' > 'N$' > 'A$' > 'N_a_n_vec_fun$' ).
thf('interchange_columns_row$a_decl',type,
'interchange_columns_row$a': 'A_n_vec_n_vec$' > 'N$' > 'N$' > 'N_a_n_vec_fun$' ).
thf('row_add$b_decl',type,
'row_add$b': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N$' > 'A_b_vec$' > 'A_b_vec_n_vec_n_vec$' ).
thf('uvf$_decl',type,
'uvf$': 'A_a_fun$' > 'A_b_vec_b_vec$' > 'B$' > 'B_a_fun$' ).
thf('fun_app$z_decl',type,
'fun_app$z': 'A_n_vec_bool_fun$' > 'A_n_vec$' > $o ).
thf('one$f_decl',type,
'one$f': 'A_b_vec_b_vec$' ).
thf('mult_row_row$b_decl',type,
'mult_row_row$b': 'A_b_vec_n_vec$' > 'N$' > 'A$' > 'N_a_b_vec_fun$' ).
thf('zero$_decl',type,
'zero$': 'A$' ).
thf('interchange_A$_decl',type,
'interchange_A$': 'A_b_vec_n_vec$' ).
thf('uwt$_decl',type,
'uwt$': 'A_n_vec$' > 'N$' > 'N_a_fun$' ).
thf('columnvector$e_decl',type,
'columnvector$e': 'A_b_vec$' > 'A_b_vec_b_vec$' ).
thf('uvx$_decl',type,
'uvx$': 'N_a_fun$' ).
thf('uvl$_decl',type,
'uvl$': 'A_b_vec_a_fun$' > 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N_a_fun$' ).
thf(tlfalse_decl,type,
tlfalse: tlbool ).
thf('fun_app$b_decl',type,
'fun_app$b': 'N_a_b_vec_fun$' > 'N$' > 'A_b_vec$' ).
thf('mult_row$a_decl',type,
'mult_row$a': 'A_n_vec_n_vec$' > 'N$' > 'A$' > 'A_n_vec_n_vec$' ).
thf('uxb$_decl',type,
'uxb$': 'A_n_vec_n_vec$' > 'N$' > 'A$' > 'N$' > 'N_a_fun$' ).
thf('uwe$_decl',type,
'uwe$': 'A_n_vec_n_vec$' > 'N$' > 'N$' > 'N_a_n_vec_fun$' ).
thf('vec_nth$_decl',type,
'vec_nth$': 'A_b_vec$' > 'B_a_fun$' ).
thf('uminus$_decl',type,
'uminus$': 'A_b_vec_n_vec$' > 'A_b_vec_n_vec$' ).
thf('map_matrix$j_decl',type,
'map_matrix$j': 'A_a_fun$' > 'A_b_vec_b_vec$' > 'A_b_vec_b_vec$' ).
thf('zero$a_decl',type,
'zero$a': 'A_b_vec_n_vec_n_vec$' ).
thf('fun_app$c_decl',type,
'fun_app$c': 'N_n_bool_fun_fun$' > 'N$' > 'N_bool_fun$' ).
thf('uwu$_decl',type,
'uwu$': 'A_n_vec$' > 'N_a_n_vec_fun$' ).
thf('mult_row$_decl',type,
'mult_row$': 'A_b_vec_n_vec$' > 'N$' > 'A_a_b_vec_n_vec_fun$' ).
thf('uxn$_decl',type,
'uxn$': 'A_b_vec$' > 'A_b_vec$' > 'B_a_fun$' ).
thf('uwp$_decl',type,
'uwp$': 'A_n_vec_n_vec$' > 'N$' > 'N_a_n_vec_fun$' ).
thf('uminus$b_decl',type,
'uminus$b': 'A_b_vec_a_b_vec_fun$' ).
thf('uuj$_decl',type,
'uuj$': 'A_b_vec_b_vec$' > 'B$' > 'B$' > 'B$' > 'B_a_fun$' ).
thf('uxk$_decl',type,
'uxk$': 'A_b_vec_b_vec$' > 'A_b_vec_b_vec$' > 'B_a_b_vec_fun$' ).
thf('gauss_Jordan_in_ij$a_decl',type,
'gauss_Jordan_in_ij$a': 'A_n_vec_n_vec$' > 'N$' > 'N$' > 'A_n_vec_n_vec$' ).
thf('uww$_decl',type,
'uww$': 'A_b_vec$' > 'B_a_b_vec_fun$' ).
thf('interchange_columns$b_decl',type,
'interchange_columns$b': 'A_b_vec_n_vec$' > 'B$' > 'B$' > 'A_b_vec_n_vec$' ).
thf('uuo$_decl',type,
'uuo$': 'A_b_vec_n_vec$' > 'B$' > 'B$' > 'N_a_b_vec_fun$' ).
thf('vec_nth$e_decl',type,
'vec_nth$e': 'A_n_vec$' > 'N_a_fun$' ).
thf('map_matrix$f_decl',type,
'map_matrix$f': 'A_b_vec_a_b_vec_fun$' > 'A_b_vec_n_vec_n_vec$' > 'A_b_vec_n_vec_n_vec$' ).
thf('uut$_decl',type,
'uut$': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'N$' > 'N$' > 'N_a_b_vec_fun$' ).
thf('uminus$a_decl',type,
'uminus$a': 'A_n_vec$' > 'A_n_vec$' ).
thf('fun_app$y_decl',type,
'fun_app$y': 'N_a_b_vec_n_vec_bool_fun_fun$' > 'N$' > 'A_b_vec_n_vec_bool_fun$' ).
thf('uuh$_decl',type,
'uuh$': 'A_n_vec_n_vec$' > 'N$' > 'N$' > 'N$' > 'N_a_fun$' ).
thf('uwh$_decl',type,
'uwh$': 'A_n_vec$' > 'N_a_n_vec_fun$' ).
thf('vec_lambda$h_decl',type,
'vec_lambda$h': 'N_a_b_vec_n_vec_n_vec_fun$' > 'A_b_vec_n_vec_n_vec_n_vec$' ).
thf('uxr$_decl',type,
'uxr$': 'A_b_vec_n_vec_a_b_vec_n_vec_fun$' ).
thf('vec_nth$f_decl',type,
'vec_nth$f': 'A_n_vec_n_vec_n_vec$' > 'N$' > 'A_n_vec_n_vec$' ).
thf('uxa$_decl',type,
'uxa$': 'A_n_vec$' > 'N_a_b_vec_fun$' ).
thf('mult_row_row$_decl',type,
'mult_row_row$': 'A_b_vec_n_vec_n_vec$' > 'N$' > 'A_b_vec$' > 'N_a_b_vec_n_vec_fun$' ).
thf('uui$_decl',type,
'uui$': 'A_n_vec_n_vec$' > 'N$' > 'N$' > 'N_a_n_vec_fun$' ).
thf('fun_app$aa_decl',type,
'fun_app$aa': 'N_a_n_vec_bool_fun_fun$' > 'N$' > 'A_n_vec_bool_fun$' ).
thf('rowvector$a_decl',type,
'rowvector$a': 'A_b_vec$' > 'A_b_vec_b_vec$' ).
thf('map_matrix$c_decl',type,
'map_matrix$c': 'A_b_vec_a_fun$' > 'A_b_vec_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
thf('uus$_decl',type,
'uus$': 'A_b_vec_b_vec$' > 'B$' > 'B$' > 'B_a_b_vec_fun$' ).
thf('zero$f_decl',type,
'zero$f': 'A_b_vec_b_vec$' ).
thf('map_matrix$g_decl',type,
'map_matrix$g': 'A_n_vec_a_b_vec_fun$' > 'A_n_vec_n_vec_n_vec$' > 'A_b_vec_n_vec_n_vec$' ).
thf('map_matrix$d_decl',type,
'map_matrix$d': 'A_n_vec_a_fun$' > 'A_n_vec_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
thf('uwj$_decl',type,
'uwj$': 'A_b_vec_n_vec$' > 'N_a_b_vec_n_vec_fun$' ).
thf('vec_lambda$c_decl',type,
'vec_lambda$c': 'B_a_b_vec_fun$' > 'A_b_vec_b_vec$' ).
thf('uwq$_decl',type,
'uwq$': 'A_n_vec_n_vec$' > 'N_a_n_vec_n_vec_fun$' ).
thf('uxh$_decl',type,
'uxh$': 'A_b_vec_n_vec$' > 'N$' > 'A$' > 'N$' > 'B_a_fun$' ).
thf('columnvector$f_decl',type,
'columnvector$f': 'A_b_vec_n_vec$' > 'A_b_vec_n_vec_n_vec$' ).
thf('fun_app$ac_decl',type,
'fun_app$ac': 'N_a_bool_fun_fun$' > 'N$' > 'A_bool_fun$' ).
thf('one$e_decl',type,
'one$e': 'A_n_vec_n_vec$' ).
thf('uxw$_decl',type,
'uxw$': 'A_b_vec_n_vec_a_b_vec_n_vec_fun$' ).
thf('vec_lambda$d_decl',type,
'vec_lambda$d': 'N_a_n_vec_fun$' > 'A_n_vec_n_vec$' ).
thf('fun_app$w_decl',type,
'fun_app$w': 'A_b_vec_n_vec_a_fun$' > 'A_b_vec_n_vec$' > 'A$' ).
thf('interchange_rows$c_decl',type,
'interchange_rows$c': 'A_b_vec_b_vec$' > 'B$' > 'B$' > 'A_b_vec_b_vec$' ).
thf(201,axiom,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( B @ ( A @ 'fun_app$' ) )
=> ( B @ ( A @ 'least$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom186) ).
thf(1322,plain,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( B @ ( A @ 'fun_app$' ) )
=> ( B @ ( A @ 'least$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(136,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ ( A @ 'uuw$' ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom396) ).
thf(1036,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ ( A @ 'uuw$' ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(205,axiom,
! [A: 'N$',B: 'N$'] :
( ( A = B )
<=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom231) ).
thf(1337,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(216,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uub$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'uminus$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).
thf(1411,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uub$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'uminus$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(80,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom380) ).
thf(760,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(228,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom365) ).
thf(1454,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(435,axiom,
! [A: 'A_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uxa$' @ 'fun_app$b' ) )
= ( B @ ( A @ 'uwz$' ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(2412,plain,
! [A: 'A_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uxa$' @ 'fun_app$b' ) )
= ( B @ ( A @ 'uwz$' ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(44,axiom,
! [A: 'A_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwu$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'uwt$' ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).
thf(628,plain,
! [A: 'A_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwu$' @ 'fun_app$f' ) )
= ( B @ ( A @ 'uwt$' ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(11,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'A_b_vec$'] :
( ( C @ ( B @ ( A @ 'mult_row$b' ) ) )
= ( C @ ( B @ ( A @ 'uxg$' ) ) @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom449) ).
thf(518,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'A_b_vec$'] :
( ( C @ ( B @ ( A @ 'mult_row$b' ) ) )
= ( C @ ( B @ ( A @ 'uxg$' ) ) @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(439,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'A_b_vec$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxf$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxf$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ 'times$b' @ 'fun_app$k' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom78) ).
thf(2427,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'A_b_vec$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxf$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxf$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ 'times$b' @ 'fun_app$k' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(405,axiom,
! [A: 'N$'] :
( ( A @ ( 'uu$' @ 'fun_app$' ) )
<=> ( ( A @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( 'j$' @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom0) ).
thf(2250,plain,
! [A: 'N$'] :
( ( ( ( A @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( 'j$' @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) )
=> ( A @ ( 'uu$' @ 'fun_app$' ) ) )
& ( ( A @ ( 'uu$' @ 'fun_app$' ) )
=> ( ( A @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( 'j$' @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(387,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuw$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom62) ).
thf(2163,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuw$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(50,axiom,
! [A: 'A_n_vec_n_vec$'] :
( ( A @ 'uminus$e' )
= ( A @ 'uub$' @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom319) ).
thf(645,plain,
! [A: 'A_n_vec_n_vec$'] :
( ( A @ 'uminus$e' )
= ( A @ 'uub$' @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(109,axiom,
( 'uxr$'
= ( 'zero$b' @ 'times$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom489) ).
thf(892,plain,
( 'uxr$'
= ( 'zero$b' @ 'times$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(258,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom376) ).
thf(1586,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( ( B = A )
=> ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(444,axiom,
! [A: 'A_a_fun$',B: 'A_b_vec_n_vec$',C: 'N$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$' ) @ '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$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).
thf(2452,plain,
! [A: 'A_a_fun$',B: 'A_b_vec_n_vec$',C: 'N$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$' ) @ '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$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(84,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_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',axiom136) ).
thf(777,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$'] :
( ( ! [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)],[84]) ).
thf(21,axiom,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$c' ) ) )
= ( C @ ( B @ ( A @ 'uxe$' ) ) @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom448) ).
thf(555,plain,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$c' ) ) )
= ( C @ ( B @ ( A @ 'uxe$' ) ) @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(81,axiom,
( 'uxs$'
= ( 'zero$d' @ 'times$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom490) ).
thf(762,plain,
( 'uxs$'
= ( 'zero$d' @ 'times$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(142,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom347) ).
thf(1068,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(310,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uxu$' @ 'fun_app$p' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom84) ).
thf(1808,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'uxu$' @ 'fun_app$p' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(174,axiom,
( 'n$'
= ( 'uu$' @ 'least$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom179) ).
thf(1205,plain,
( 'n$'
= ( 'uu$' @ 'least$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(374,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'B$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$b' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$b' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$b' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom175) ).
thf(2099,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'B$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$b' ) ) @ 'fun_app$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$b' ) ) @ 'fun_app$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$b' ) ) @ 'fun_app$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)],[374]) ).
thf(376,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom70) ).
thf(2114,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(307,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom354) ).
thf(1793,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(282,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom360) ).
thf(1692,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(168,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uminus$e' @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'uminus$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom245) ).
thf(1173,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uminus$e' @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'uminus$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(126,axiom,
! [A: 'A_n_vec$'] :
( ( A @ 'columnvector$g' )
= ( A @ 'uxa$' @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom439) ).
thf(994,plain,
! [A: 'A_n_vec$'] :
( ( A @ 'columnvector$g' )
= ( A @ 'uxa$' @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(458,axiom,
! [A: 'A_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uminus$a' @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( B @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom246) ).
thf(2527,plain,
! [A: 'A_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uminus$a' @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( B @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(475,axiom,
! [A: 'A_n_vec$',B: 'N$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uwz$' ) @ 'fun_app$a' ) )
= ( B @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom31) ).
thf(2590,plain,
! [A: 'A_n_vec$',B: 'N$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uwz$' ) @ 'fun_app$a' ) )
= ( B @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(214,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( B @ ( A @ 'times$a' @ 'fun_app$p' ) )
!= 'zero$c' )
=> ( ( B != 'zero$c' )
& ( A != 'zero$c' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom476) ).
thf(1401,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( B @ ( A @ 'times$a' @ 'fun_app$p' ) )
!= 'zero$c' )
=> ( ( B != 'zero$c' )
& ( A != 'zero$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(53,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwq$' @ 'fun_app$h' ) )
= ( B @ ( A @ 'uwp$' ) @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).
thf(655,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwq$' @ 'fun_app$h' ) )
= ( B @ ( A @ 'uwp$' ) @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(428,axiom,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$b' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uun$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom427) ).
thf(2380,plain,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$b' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uun$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(395,axiom,
! [A: 'A_b_vec$',B: 'A_b_vec$'] :
( ( ( A @ 'vec_nth$' )
= ( B @ 'vec_nth$' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom129) ).
thf(2195,plain,
! [A: 'A_b_vec$',B: 'A_b_vec$'] :
( ( ( A = B )
=> ( ( A @ 'vec_nth$' )
= ( B @ 'vec_nth$' ) ) )
& ( ( ( A @ 'vec_nth$' )
= ( B @ 'vec_nth$' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(263,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false )
& ( ( A = B )
=> $false )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom284) ).
thf(1608,plain,
! [A: 'N$',B: 'N$'] :
~ ( ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A != B )
& ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(160,axiom,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom232) ).
thf(1137,plain,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(199,axiom,
! [A: tlbool,B: 'A_n_vec_n_vec$',C: 'A_n_vec_n_vec$',D: 'N$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( C @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( D @ ( C @ 'vec_nth$c' @ 'fun_app$f' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( D @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) ) ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( D @ ( C @ 'vec_nth$c' @ 'fun_app$f' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( D @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom165) ).
thf(1310,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$f' ) )
= ( D @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) ) ) ) )
& ( ( A = tltrue )
=> ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( D @ ( C @ 'vec_nth$c' @ 'fun_app$f' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(70,axiom,
! [A: 'A_b_vec_a_fun$',B: 'A_b_vec_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$c' ) )
= ( B @ ( A @ 'uvm$' ) @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom405) ).
thf(715,plain,
! [A: 'A_b_vec_a_fun$',B: 'A_b_vec_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$c' ) )
= ( B @ ( A @ 'uvm$' ) @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(382,axiom,
! [A: 'N_a_b_vec_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$a' @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( A @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom254) ).
thf(2141,plain,
! [A: 'N_a_b_vec_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$a' @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( A @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(323,axiom,
! [A: 'N$'] :
( ( A @ ( 'one$d' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom106) ).
thf(1872,plain,
! [A: 'N$'] :
( ( A @ ( 'one$d' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'one$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(203,axiom,
! [A: 'N$'] :
( ( A @ ( 'uwb$' @ 'fun_app$d' ) )
= 'one$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom98) ).
thf(1327,plain,
! [A: 'N$'] :
( ( A @ ( 'uwb$' @ 'fun_app$d' ) )
= 'one$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(447,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' )
= ( C @ ( B @ ( A @ 'interchange_rows_row$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom202) ).
thf(2476,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' )
= ( C @ ( B @ ( A @ 'interchange_rows_row$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(338,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom214) ).
thf(1919,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(362,axiom,
! [A: 'A_b_vec$',B: 'A_b_vec$',C: 'A_b_vec$'] :
( ( 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',axiom501) ).
thf(2042,plain,
! [A: 'A_b_vec$',B: 'A_b_vec$',C: 'A_b_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$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(354,axiom,
'zero$b' != 'one$a',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom156) ).
thf(1999,plain,
'zero$b' != 'one$a',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(417,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$' ) @ 'fun_app$n' ) @ 'vec_nth$a' )
= ( C @ ( B @ ( A @ 'mult_row_row$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom124) ).
thf(2316,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$' ) @ 'fun_app$n' ) @ 'vec_nth$a' )
= ( C @ ( B @ ( A @ 'mult_row_row$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(78,axiom,
! [A: 'N$',B: 'N$',C: tlbool] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( C = tltrue ) )
<=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom314) ).
thf(747,plain,
! [A: 'N$',B: 'N$',C: tlbool] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( C = tltrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(113,axiom,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( C @ 'fun_app$ag' ) )
= D )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom237) ).
thf(913,plain,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( C @ 'fun_app$ag' ) )
= D )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(56,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( B @ ( C @ ( B @ ( A @ 'interchange_rows$b' ) @ 'fun_app$j' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom183) ).
thf(670,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( B @ ( C @ ( B @ ( A @ 'interchange_rows$b' ) @ 'fun_app$j' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(472,axiom,
! [A: 'B$'] :
( ( A @ ( 'one$c' @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom109) ).
thf(2575,plain,
! [A: 'B$'] :
( ( A @ ( 'one$c' @ 'vec_nth$' @ 'fun_app$a' ) )
= 'one$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(465,axiom,
! [A: 'A_a_b_vec_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$i' ) @ 'vec_nth$g' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom120) ).
thf(2548,plain,
! [A: 'A_a_b_vec_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$i' ) @ 'vec_nth$g' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(68,axiom,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$c' ) ) )
= ( C @ ( B @ ( A @ 'uus$' ) ) @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom394) ).
thf(709,plain,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$c' ) ) )
= ( C @ ( B @ ( A @ 'uus$' ) ) @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(123,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom367) ).
thf(973,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(340,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom216) ).
thf(1935,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(208,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom356) ).
thf(1359,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(308,axiom,
! [A: 'A_n_vec$'] :
( ( A @ 'uminus$a' )
= ( A @ 'uud$' @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom321) ).
thf(1803,plain,
! [A: 'A_n_vec$'] :
( ( A @ 'uminus$a' )
= ( A @ 'uud$' @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(188,axiom,
! [A: 'N_bool_fun$',B: 'N$'] :
( ! [C: 'N$'] :
( ! [D: 'N$'] :
( ( C @ ( D @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( D @ ( A @ 'fun_app$' ) ) )
=> ( C @ ( A @ 'fun_app$' ) ) )
=> ( B @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom278) ).
thf(1265,plain,
! [A: 'N_bool_fun$',B: 'N$'] :
( ! [C: 'N$'] :
( ! [D: 'N$'] :
( ( C @ ( D @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( D @ ( A @ 'fun_app$' ) ) )
=> ( C @ ( A @ 'fun_app$' ) ) )
=> ( B @ ( A @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(328,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom370) ).
thf(1887,plain,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(215,axiom,
! [A: 'N$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom172) ).
thf(1409,plain,
! [A: 'N$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(223,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'row_add$a' ) ) ) @ 'vec_nth$c' )
= ( D @ ( C @ ( B @ ( A @ 'row_add_row$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom441) ).
thf(1430,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'row_add$a' ) ) ) @ 'vec_nth$c' )
= ( D @ ( C @ ( B @ ( A @ 'row_add_row$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(351,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom296) ).
thf(1985,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(361,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom226) ).
thf(2039,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(298,axiom,
! [A: 'B$'] :
( ( A @ ( 'uvt$' @ 'fun_app$e' ) )
= 'zero$d' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom95) ).
thf(1760,plain,
! [A: 'B$'] :
( ( A @ ( 'uvt$' @ 'fun_app$e' ) )
= 'zero$d' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(452,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( B @ ( C @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom185) ).
thf(2501,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( B @ ( C @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(89,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false )
& ( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false )
& ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false )
& ( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false )
& ( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false )
& ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom211) ).
thf(802,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
~ ( ~ ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ~ ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ~ ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ~ ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ~ ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ~ ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(255,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'one$b' @ 'times$a' @ 'fun_app$p' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom461) ).
thf(1577,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'one$b' @ 'times$a' @ 'fun_app$p' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(377,axiom,
! [A: 'A_b_vec$',B: 'A_b_vec$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uxn$' ) @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ 'times$c' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom25) ).
thf(2126,plain,
! [A: 'A_b_vec$',B: 'A_b_vec$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uxn$' ) @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ 'times$c' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(158,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom270) ).
thf(1132,plain,
! [A: 'N$',B: 'N$'] :
~ ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(204,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom282) ).
thf(1330,plain,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( ( A = B )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(400,axiom,
! [A: tlbool,B: 'A_b_vec$',C: 'A_b_vec$',D: 'B$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( C @ 'vec_nth$' @ '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$a' ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom167) ).
thf(2217,plain,
! [A: tlbool,B: 'A_b_vec$',C: 'A_b_vec$',D: 'B$'] :
( ( ( 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)],[400]) ).
thf(65,axiom,
! [A: 'A_a_fun$',B: 'A_b_vec_b_vec$'] :
( ( B @ ( A @ 'map_matrix$j' ) )
= ( B @ ( A @ 'uvg$' ) @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom402) ).
thf(702,plain,
! [A: 'A_a_fun$',B: 'A_b_vec_b_vec$'] :
( ( B @ ( A @ 'map_matrix$j' ) )
= ( B @ ( A @ 'uvg$' ) @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(79,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( 'zero$b' = A )
<=> ( A = 'zero$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom151) ).
thf(751,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( ( A = 'zero$b' )
=> ( 'zero$b' = A ) )
& ( ( 'zero$b' = A )
=> ( A = 'zero$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(100,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false )
& ( ( B = A )
=> $false )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom285) ).
thf(853,plain,
! [A: 'N$',B: 'N$'] :
~ ( ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B != A )
& ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(330,axiom,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'interchange_columns$b' ) ) )
= ( C @ ( B @ ( A @ 'uuo$' ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom328) ).
thf(1892,plain,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'interchange_columns$b' ) ) )
= ( C @ ( B @ ( A @ 'uuo$' ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(389,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uug$' @ 'fun_app$b' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ ( 'uminus$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom11) ).
thf(2169,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uug$' @ 'fun_app$b' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ ( 'uminus$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(163,axiom,
! [A: 'N_bool_fun$'] :
( ? [B: 'N$'] : ( B @ ( A @ 'fun_app$' ) )
<=> ? [B: 'N$'] :
( ! [C: 'N$'] :
( ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( C @ ( A @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom291) ).
thf(1147,plain,
! [A: 'N_bool_fun$'] :
( ( ? [B: 'N$'] :
( ! [C: 'N$'] :
( ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( C @ ( A @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ? [B: 'N$'] : ( B @ ( A @ 'fun_app$' ) ) )
& ( ? [B: 'N$'] : ( B @ ( A @ 'fun_app$' ) )
=> ? [B: 'N$'] :
( ! [C: 'N$'] :
( ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( C @ ( A @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(200,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom443) ).
thf(1319,plain,
! [A: 'N$',B: 'N$'] :
( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(122,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B = A )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).
thf(969,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(252,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom369) ).
thf(1568,plain,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(385,axiom,
( 'a$a'
= ( 'j$' @ ( 'i$' @ ( 'interchange_A$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( 'i$' @ ( 'interchange_A$' @ 'mult_row$' ) @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom105) ).
thf(2158,plain,
( 'a$a'
= ( 'j$' @ ( 'i$' @ ( 'interchange_A$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( 'i$' @ ( 'interchange_A$' @ 'mult_row$' ) @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(346,axiom,
! [A: 'N_a_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$b' @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( B @ ( A @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom251) ).
thf(1963,plain,
! [A: 'N_a_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$b' @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( B @ ( A @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(324,axiom,
! [A: 'N_bool_fun$',B: 'N_bool_fun$'] :
( ( ! [C: 'N$'] :
( ( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
& ? [C: 'N$'] : ( C @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( B @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom187) ).
thf(1875,plain,
! [A: 'N_bool_fun$',B: 'N_bool_fun$'] :
( ( ! [C: 'N$'] :
( ( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
& ? [C: 'N$'] : ( C @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( B @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(460,axiom,
! [A: 'A_a_fun$',B: 'A_b_vec_n_vec$',C: 'N$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uux$' ) ) @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom56) ).
thf(2533,plain,
! [A: 'A_a_fun$',B: 'A_b_vec_n_vec$',C: 'N$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uux$' ) ) @ '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)],[460]) ).
thf(295,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom371) ).
thf(1741,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(106,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( 'one$a' @ ( A @ 'times$' @ 'fun_app$o' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom468) ).
thf(881,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( 'one$a' @ ( A @ 'times$' @ 'fun_app$o' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(237,axiom,
! [A: 'A_b_vec_n_vec_a_fun$',B: 'A_b_vec_n_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$g' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$w' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom119) ).
thf(1489,plain,
! [A: 'A_b_vec_n_vec_a_fun$',B: 'A_b_vec_n_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$g' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ ( A @ 'fun_app$w' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(115,axiom,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$'] :
( ( ( B @ ( A @ 'times$' @ 'fun_app$o' ) )
!= 'zero$b' )
=> ( ( B != 'zero$b' )
& ( A != 'zero$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom478) ).
thf(924,plain,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$'] :
( ( ( B @ ( A @ 'times$' @ 'fun_app$o' ) )
!= 'zero$b' )
=> ( ( B != 'zero$b' )
& ( A != 'zero$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(274,axiom,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( B @ ( A @ 'fun_app$' ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom193) ).
thf(1664,plain,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( B @ ( A @ 'fun_app$' ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(86,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom359) ).
thf(789,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(311,axiom,
( 'one$c'
= ( 'uwa$' @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom417) ).
thf(1811,plain,
( 'one$c'
= ( 'uwa$' @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(210,axiom,
! [A: 'A_n_vec$',B: 'N_a_fun$'] :
( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( C @ ( B @ 'fun_app$l' ) ) )
<=> ( ( B @ 'vec_lambda$b' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom337) ).
thf(1373,plain,
! [A: 'A_n_vec$',B: 'N_a_fun$'] :
( ( ( ( B @ 'vec_lambda$b' )
= A )
=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( C @ ( B @ 'fun_app$l' ) ) ) )
& ( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( C @ ( B @ 'fun_app$l' ) ) )
=> ( ( B @ 'vec_lambda$b' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(268,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A = C )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom294) ).
thf(1632,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A = C )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(406,axiom,
! [A: 'B_a_bool_fun_fun$'] :
( ! [B: 'B$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ad' ) @ 'fun_app$ab' ) )
<=> ? [B: 'A_b_vec$'] :
! [C: 'B$'] : ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'fun_app$ad' ) @ 'fun_app$ab' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom134) ).
thf(2259,plain,
! [A: 'B_a_bool_fun_fun$'] :
( ( ? [B: 'A_b_vec$'] :
! [C: 'B$'] : ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'fun_app$ad' ) @ 'fun_app$ab' ) )
=> ! [B: 'B$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ad' ) @ 'fun_app$ab' ) ) )
& ( ! [B: 'B$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ad' ) @ 'fun_app$ab' ) )
=> ? [B: 'A_b_vec$'] :
! [C: 'B$'] : ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'fun_app$ad' ) @ 'fun_app$ab' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(1,conjecture,
( 'a$a'
= ( 'j$' @ ( 'i$' @ ( 'interchange_A$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( 'i$' @ ( 'interchange_A$' @ 'mult_row$' ) @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture104) ).
thf(2,negated_conjecture,
( 'a$a'
!= ( 'j$' @ ( 'i$' @ ( 'interchange_A$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( 'i$' @ ( 'interchange_A$' @ 'mult_row$' ) @ 'fun_app$n' ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(485,plain,
( 'a$a'
!= ( 'j$' @ ( 'i$' @ ( 'interchange_A$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( 'i$' @ ( 'interchange_A$' @ 'mult_row$' ) @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(321,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom391) ).
thf(1864,plain,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(359,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom357) ).
thf(2034,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(345,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom210) ).
thf(1960,plain,
! [A: 'N$',B: 'N$'] :
~ ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(121,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvn$' ) ) @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$f' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ ( A @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom48) ).
thf(966,plain,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvn$' ) ) @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$f' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ ( A @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(91,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$'] :
( ( B @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom199) ).
thf(821,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$'] :
( ( B @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(371,axiom,
! [A: 'A_a_fun$',B: 'A_b_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uuy$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( A @ 'uux$' ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom43) ).
thf(2090,plain,
! [A: 'A_a_fun$',B: 'A_b_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uuy$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ ( A @ 'uux$' ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(32,axiom,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'interchange_columns$c' ) ) )
= ( C @ ( B @ ( A @ 'uuk$' ) ) @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom326) ).
thf(591,plain,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'interchange_columns$c' ) ) )
= ( C @ ( B @ ( A @ 'uuk$' ) ) @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(170,axiom,
( 'uxu$'
= ( 'one$b' @ 'times$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom492) ).
thf(1183,plain,
( 'uxu$'
= ( 'one$b' @ 'times$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(193,axiom,
! [A: 'A$'] :
( ( 'zero$' = A )
<=> ( A = 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom153) ).
thf(1283,plain,
! [A: 'A$'] :
( ( ( A = 'zero$' )
=> ( 'zero$' = A ) )
& ( ( 'zero$' = A )
=> ( A = 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(60,axiom,
! [A: 'A_b_vec_b_vec$',B: 'A_b_vec_b_vec$'] :
( ( B @ ( A @ 'times$f' ) )
= ( B @ ( A @ 'uxk$' ) @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom482) ).
thf(687,plain,
! [A: 'A_b_vec_b_vec$',B: 'A_b_vec_b_vec$'] :
( ( B @ ( A @ 'times$f' ) )
= ( B @ ( A @ 'uxk$' ) @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(410,axiom,
! [A: 'A_a_b_vec_fun$',B: 'A_b_vec_n_vec$',C: 'N$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvj$' ) ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$t' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom54) ).
thf(2281,plain,
! [A: 'A_a_b_vec_fun$',B: 'A_b_vec_n_vec$',C: 'N$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvj$' ) ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$t' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(46,axiom,
! [A: 'A_n_vec_n_vec$'] :
( ( A @ 'vec_nth$c' @ 'vec_lambda$d' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom329) ).
thf(634,plain,
! [A: 'A_n_vec_n_vec$'] :
( ( A @ 'vec_nth$c' @ 'vec_lambda$d' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(459,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxi$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uxh$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom58) ).
thf(2530,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxi$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uxh$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(355,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( A = B )
| ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom388) ).
thf(2002,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( A = B )
| ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A = B )
| ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(224,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uve$' ) @ 'fun_app$f' ) )
= ( C @ ( B @ ( A @ 'uvd$' ) ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom40) ).
thf(1433,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uve$' ) @ 'fun_app$f' ) )
= ( C @ ( B @ ( A @ 'uvd$' ) ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(260,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom304) ).
thf(1600,plain,
! [A: 'N$',B: 'N$'] :
~ ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(432,axiom,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$',D: 'N$',E: 'B$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$b' ) ) @ 'fun_app$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$b' ) ) @ 'fun_app$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$b' ) ) @ 'fun_app$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',axiom178) ).
thf(2392,plain,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$',D: 'N$',E: 'B$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$b' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$b' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( B @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$b' ) ) @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(396,axiom,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuo$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uun$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom66) ).
thf(2205,plain,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuo$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uun$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(350,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( A != B )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom208) ).
thf(1975,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( A != B )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A != B )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(153,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwl$' ) @ 'fun_app$d' ) )
= ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom26) ).
thf(1104,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwl$' ) @ 'fun_app$d' ) )
= ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(284,axiom,
! [A: 'A_b_vec_a_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvm$' ) @ 'fun_app$f' ) )
= ( C @ ( B @ ( A @ 'uvl$' ) ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom36) ).
thf(1697,plain,
! [A: 'A_b_vec_a_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvm$' ) @ 'fun_app$f' ) )
= ( C @ ( B @ ( A @ 'uvl$' ) ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(272,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$'] :
( ( ( A @ 'vec_nth$b' )
= ( B @ 'vec_nth$b' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom126) ).
thf(1651,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$'] :
( ( ( A = B )
=> ( ( A @ 'vec_nth$b' )
= ( B @ 'vec_nth$b' ) ) )
& ( ( ( A @ 'vec_nth$b' )
= ( B @ 'vec_nth$b' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(144,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'A_b_vec$'] :
( ( D @ ( C @ ( B @ ( A @ 'row_add$b' ) ) ) @ 'vec_nth$b' )
= ( D @ ( C @ ( B @ ( A @ 'row_add_row$' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom440) ).
thf(1074,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'A_b_vec$'] :
( ( D @ ( C @ ( B @ ( A @ 'row_add$b' ) ) ) @ 'vec_nth$b' )
= ( D @ ( C @ ( B @ ( A @ 'row_add_row$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(9,axiom,
! [A: 'A_a_b_vec_fun$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$b' ) )
= ( B @ ( A @ 'uva$' ) @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom399) ).
thf(512,plain,
! [A: 'A_a_b_vec_fun$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$b' ) )
= ( B @ ( A @ 'uva$' ) @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(364,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom286) ).
thf(2047,plain,
! [A: 'N$',B: 'N$'] :
~ ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(372,axiom,
! [A: 'N$'] :
( ( A @ ( 'zero$b' @ 'vec_nth$a' @ 'fun_app$b' ) )
= 'zero$d' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom145) ).
thf(2093,plain,
! [A: 'N$'] :
( ( A @ ( 'zero$b' @ 'vec_nth$a' @ 'fun_app$b' ) )
= 'zero$d' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(306,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( A = B )
| ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom298) ).
thf(1783,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( A = B )
| ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A = B )
| ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(293,axiom,
! [A: 'B$'] :
( ( A @ ( 'uvz$' @ 'fun_app$e' ) )
= 'one$c' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).
thf(1736,plain,
! [A: 'B$'] :
( ( A @ ( 'uvz$' @ 'fun_app$e' ) )
= 'one$c' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(269,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom392) ).
thf(1636,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(291,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom341) ).
thf(1730,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(16,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_columns$a' ) ) )
= ( C @ ( B @ ( A @ 'uum$' ) ) @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom327) ).
thf(534,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_columns$a' ) ) )
= ( C @ ( B @ ( A @ 'uum$' ) ) @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(403,axiom,
! [A: tlbool,B: 'A_b_vec_n_vec$',C: 'A_b_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',axiom168) ).
thf(2232,plain,
! [A: tlbool,B: 'A_b_vec_n_vec$',C: 'A_b_vec_n_vec$',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$b' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(434,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxl$' ) @ 'fun_app$l' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) @ ( C @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) @ 'times$c' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom24) ).
thf(2409,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxl$' ) @ 'fun_app$l' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) @ ( C @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) @ 'times$c' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(333,axiom,
( 'one$b'
= ( 'uvx$' @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom414) ).
thf(1900,plain,
( 'one$b'
= ( 'uvx$' @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(110,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom446) ).
thf(894,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(469,axiom,
! [A: 'N$',B: 'N$',C: 'N$',D: 'A_b_vec_n_vec$'] :
( ( ( C != B )
& ( A != B ) )
=> ( ( B @ ( C @ ( A @ ( D @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( D @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).
thf(2560,plain,
! [A: 'N$',B: 'N$',C: 'N$',D: 'A_b_vec_n_vec$'] :
( ( ( C != B )
& ( A != B ) )
=> ( ( B @ ( C @ ( A @ ( D @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( D @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(138,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom386) ).
thf(1042,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(256,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ ( 'zero$b' @ 'times$' @ 'fun_app$o' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom453) ).
thf(1580,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ ( 'zero$b' @ 'times$' @ 'fun_app$o' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(253,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom277) ).
thf(1570,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(34,axiom,
! [A: 'A_a_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvi$' ) @ 'fun_app$h' ) )
= ( C @ ( B @ ( A @ 'uvh$' ) ) @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom38) ).
thf(598,plain,
! [A: 'A_a_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvi$' ) @ 'fun_app$h' ) )
= ( C @ ( B @ ( A @ 'uvh$' ) ) @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(241,axiom,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom207) ).
thf(1502,plain,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(23,axiom,
'zero$a' != 'one$d',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom155) ).
thf(561,plain,
'zero$a' != 'one$d',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(236,axiom,
( 'zero$b'
= ( 'uvw$' @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom413) ).
thf(1487,plain,
( 'zero$b'
= ( 'uvw$' @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(62,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$b' ) @ 'fun_app$j' ) )
= ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom395) ).
thf(693,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$b' ) @ 'fun_app$j' ) )
= ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(182,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'A_b_vec$'] :
( ( C @ ( B @ ( A @ 'mult_row$b' ) ) @ 'vec_nth$b' )
= ( C @ ( B @ ( A @ 'mult_row_row$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom122) ).
thf(1238,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'A_b_vec$'] :
( ( C @ ( B @ ( A @ 'mult_row$b' ) ) @ 'vec_nth$b' )
= ( C @ ( B @ ( A @ 'mult_row_row$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(326,axiom,
( 'uxw$'
= ( 'one$a' @ 'times$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom494) ).
thf(1883,plain,
( 'uxw$'
= ( 'one$a' @ 'times$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(190,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( 'zero$b' @ ( A @ 'times$' @ 'fun_app$o' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom458) ).
thf(1274,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( 'zero$b' @ ( A @ 'times$' @ 'fun_app$o' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(442,axiom,
! [A: 'A$',B: 'A$'] :
( ( ( B @ ( A @ 'times$c' @ 'fun_app$m' ) )
!= 'zero$' )
=> ( ( B != 'zero$' )
& ( A != 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom480) ).
thf(2441,plain,
! [A: 'A$',B: 'A$'] :
( ( ( B @ ( A @ 'times$c' @ 'fun_app$m' ) )
!= 'zero$' )
=> ( ( B != 'zero$' )
& ( A != 'zero$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(245,axiom,
! [A: 'A_n_vec$'] :
( ( 'one$b' = A )
<=> ( A = 'one$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom159) ).
thf(1519,plain,
! [A: 'A_n_vec$'] :
( ( ( A = 'one$b' )
=> ( 'one$b' = A ) )
& ( ( 'one$b' = A )
=> ( A = 'one$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(477,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwx$' ) @ 'fun_app$b' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom28) ).
thf(2596,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwx$' ) @ 'fun_app$b' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(379,axiom,
! [A: 'A_a_b_vec_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvp$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom51) ).
thf(2132,plain,
! [A: 'A_a_b_vec_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvp$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(73,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwm$' @ 'fun_app$j' ) )
= ( B @ ( A @ 'uwl$' ) @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).
thf(729,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwm$' @ 'fun_app$j' ) )
= ( B @ ( A @ 'uwl$' ) @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(250,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'times$a' @ 'fun_app$p' ) @ 'times$a' @ 'fun_app$p' ) )
= ( C @ ( B @ 'times$a' @ 'fun_app$p' ) @ ( A @ 'times$a' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom497) ).
thf(1555,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'A_n_vec$'] :
( ( C @ ( B @ ( A @ 'times$a' @ 'fun_app$p' ) @ 'times$a' @ 'fun_app$p' ) )
= ( C @ ( B @ 'times$a' @ 'fun_app$p' ) @ ( A @ 'times$a' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(195,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false )
& ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false )
& ( A != B ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom266) ).
thf(1296,plain,
! [A: 'N$',B: 'N$'] :
~ ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(265,axiom,
! [A: 'A_a_fun$',B: 'A_b_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$' ) )
= ( B @ ( A @ 'uuy$' ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom398) ).
thf(1624,plain,
! [A: 'A_a_fun$',B: 'A_b_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$' ) )
= ( B @ ( A @ 'uuy$' ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(29,axiom,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( A @ 'vec_nth$b' @ 'vec_lambda$e' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom332) ).
thf(583,plain,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( A @ 'vec_nth$b' @ 'vec_lambda$e' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(165,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom422) ).
thf(1159,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(176,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom368) ).
thf(1210,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(213,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( D @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( C @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
!= 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom46) ).
thf(1392,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( ( ( D @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( C @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
!= 'zero$' ) )
=> ( D @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( D @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( C @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
!= 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(97,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom352) ).
thf(842,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(446,axiom,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$',D: 'B$',E: 'B$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuj$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuj$' ) ) ) @ 'fun_app$a' ) )
= ( B @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuj$' ) ) ) @ 'fun_app$a' ) )
= ( C @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom77) ).
thf(2464,plain,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$',D: 'B$',E: 'B$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuj$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuj$' ) ) ) @ 'fun_app$a' ) )
= ( B @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuj$' ) ) ) @ 'fun_app$a' ) )
= ( C @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(341,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom229) ).
thf(1938,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(172,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom382) ).
thf(1195,plain,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(398,axiom,
! [A: 'B$'] :
( ( A @ ( 'uwa$' @ 'fun_app$a' ) )
= 'one$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom103) ).
thf(2211,plain,
! [A: 'B$'] :
( ( A @ ( 'uwa$' @ 'fun_app$a' ) )
= 'one$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(76,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom280) ).
thf(742,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(105,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom358) ).
thf(874,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(427,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uwr$' ) @ 'fun_app$e' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom29) ).
thf(2377,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uwr$' ) @ 'fun_app$e' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(40,axiom,
! [A: 'A_n_vec$'] :
( ( A @ 'vec_nth$e' @ 'vec_lambda$b' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom331) ).
thf(615,plain,
! [A: 'A_n_vec$'] :
( ( A @ 'vec_nth$e' @ 'vec_lambda$b' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(155,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ 'times$a' @ 'fun_app$p' ) )
= ( B @ ( A @ 'uxl$' ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom483) ).
thf(1111,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( B @ ( A @ 'times$a' @ 'fun_app$p' ) )
= ( B @ ( A @ 'uxl$' ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(318,axiom,
! [A: 'N$'] :
~ ( A @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom274) ).
thf(1856,plain,
! [A: 'N$'] :
~ ( A @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(38,axiom,
( 'one$e'
= ( 'uvy$' @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom415) ).
thf(610,plain,
( 'one$e'
= ( 'uvy$' @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(5,axiom,
! [A: 'A_n_vec$'] :
( ( A @ 'vec_nth$e' @ 'vec_lambda$b' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom257) ).
thf(499,plain,
! [A: 'A_n_vec$'] :
( ( A @ 'vec_nth$e' @ 'vec_lambda$b' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(101,axiom,
! [A: 'A_b_vec$'] :
( ( A @ ( 'one$c' @ 'times$b' @ 'fun_app$k' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom464) ).
thf(857,plain,
! [A: 'A_b_vec$'] :
( ( A @ ( 'one$c' @ 'times$b' @ 'fun_app$k' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(451,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$a' @ 'fun_app$p' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) @ ( C @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) @ 'times$c' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom473) ).
thf(2498,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$a' @ 'fun_app$p' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) @ ( C @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) @ 'times$c' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(181,axiom,
! [A: 'N$',B: 'N$'] :
( ( A = B )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom209) ).
thf(1234,plain,
! [A: 'N$',B: 'N$'] :
( ( A = B )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(248,axiom,
! [A: 'N$',B: 'N$'] :
( ( A != B )
<=> ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom267) ).
thf(1541,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(150,axiom,
! [A: 'A_n_vec$'] :
( ( A @ ( 'zero$c' @ 'times$a' @ 'fun_app$p' ) )
= 'zero$c' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom451) ).
thf(1096,plain,
! [A: 'A_n_vec$'] :
( ( A @ ( 'zero$c' @ 'times$a' @ 'fun_app$p' ) )
= 'zero$c' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(277,axiom,
! [A: 'A_a_fun$',B: 'A_b_vec_b_vec$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uvg$' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( A @ 'uvf$' ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom39) ).
thf(1672,plain,
! [A: 'A_a_fun$',B: 'A_b_vec_b_vec$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uvg$' ) @ 'fun_app$e' ) )
= ( C @ ( B @ ( A @ 'uvf$' ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(107,axiom,
! [A: 'N_a_n_vec_bool_fun_fun$'] :
( ! [B: 'N$'] :
? [C: 'A_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$aa' ) @ 'fun_app$z' ) )
<=> ? [B: 'A_n_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ ( C @ ( A @ 'fun_app$aa' ) @ 'fun_app$z' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom132) ).
thf(884,plain,
! [A: 'N_a_n_vec_bool_fun_fun$'] :
( ( ? [B: 'A_n_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ ( C @ ( A @ 'fun_app$aa' ) @ 'fun_app$z' ) )
=> ! [B: 'N$'] :
? [C: 'A_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$aa' ) @ 'fun_app$z' ) ) )
& ( ! [B: 'N$'] :
? [C: 'A_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$aa' ) @ 'fun_app$z' ) )
=> ? [B: 'A_n_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ ( C @ ( A @ 'fun_app$aa' ) @ 'fun_app$z' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(209,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( E @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( E @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom174) ).
thf(1361,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( E @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( E @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(194,axiom,
! [A: 'N$',B: 'N$',C: tlbool] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( C = tltrue ) )
<=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom283) ).
thf(1292,plain,
! [A: 'N$',B: 'N$',C: tlbool] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( C = tltrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(49,axiom,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( A @ 'uminus$d' )
= ( A @ 'uue$' @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom322) ).
thf(642,plain,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( A @ 'uminus$d' )
= ( A @ 'uue$' @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(217,axiom,
( 'uxx$'
= ( 'one$c' @ 'times$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom495) ).
thf(1414,plain,
( 'uxx$'
= ( 'one$c' @ 'times$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(47,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'times$e' ) )
= ( B @ ( A @ 'uxj$' ) @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom481) ).
thf(637,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'times$e' ) )
= ( B @ ( A @ 'uxj$' ) @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(285,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( B = A )
| ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom299) ).
thf(1700,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( B = A )
| ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B = A )
| ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(390,axiom,
( ( 'm$' @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( 'j$' @ ( 'm$' @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom125) ).
thf(2172,plain,
( ( 'm$' @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( 'j$' @ ( 'm$' @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(422,axiom,
'n$' @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom147) ).
thf(2349,plain,
'n$' @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(329,axiom,
! [A: 'A_b_vec$'] :
( ( 'one$c' @ ( A @ 'times$b' @ 'fun_app$k' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom469) ).
thf(1889,plain,
! [A: 'A_b_vec$'] :
( ( 'one$c' @ ( A @ 'times$b' @ 'fun_app$k' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(219,axiom,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom235) ).
thf(1419,plain,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(294,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom219) ).
thf(1739,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(230,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$d' @ 'fun_app$u' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'times$' @ 'fun_app$o' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom471) ).
thf(1461,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$d' @ 'fun_app$u' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'times$' @ 'fun_app$o' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(17,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( C @ ( B @ ( A @ 'interchange_rows$b' ) @ 'fun_app$j' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom180) ).
thf(537,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( C @ ( B @ ( A @ 'interchange_rows$b' ) @ 'fun_app$j' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(221,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uue$' @ 'fun_app$d' ) )
= ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'uminus$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
thf(1424,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uue$' @ 'fun_app$d' ) )
= ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'uminus$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(445,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'B$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxh$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxh$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ 'times$c' @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).
thf(2455,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'B$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxh$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxh$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ 'times$c' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(466,axiom,
! [A: 'A_a_b_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuz$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$t' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom53) ).
thf(2551,plain,
! [A: 'A_a_b_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuz$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$t' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(132,axiom,
! [A: 'N_n_bool_fun_fun$',B: 'N$',C: 'N$'] :
( ( ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ! [D: 'N$'] : ( D @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
& ! [D: 'N$',E: 'N$'] :
( ( E @ ( D @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ) )
=> ( C @ ( B @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom295) ).
thf(1016,plain,
! [A: 'N_n_bool_fun_fun$',B: 'N$',C: 'N$'] :
( ( ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ! [D: 'N$'] : ( D @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
& ! [D: 'N$',E: 'N$'] :
( ( E @ ( D @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ) )
=> ( C @ ( B @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(175,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ 'uminus$' )
= ( A @ 'uug$' @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom324) ).
thf(1207,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ 'uminus$' )
= ( A @ 'uug$' @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(264,axiom,
! [A: 'N$',B: 'N$'] :
( ( A = B )
<=> ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom221) ).
thf(1612,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(137,axiom,
! [A: 'A_b_vec$'] :
( ( A @ 'rowvector$c' )
= ( A @ 'uwk$' @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom431) ).
thf(1039,plain,
! [A: 'A_b_vec$'] :
( ( A @ 'rowvector$c' )
= ( A @ 'uwk$' @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(151,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$a' ) ) @ 'vec_nth$c' )
= ( C @ ( B @ ( A @ 'mult_row_row$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom123) ).
thf(1099,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$a' ) ) @ 'vec_nth$c' )
= ( C @ ( B @ ( A @ 'mult_row_row$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(461,axiom,
! [A: 'A_b_vec_a_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvl$' ) ) @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$r' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom50) ).
thf(2536,plain,
! [A: 'A_b_vec_a_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvl$' ) ) @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$r' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(227,axiom,
! [A: 'B_a_b_vec_fun$',B: 'B$'] :
( ( B @ ( A @ 'vec_lambda$c' @ 'vec_nth$d' @ 'fun_app$e' ) )
= ( B @ ( A @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom250) ).
thf(1451,plain,
! [A: 'B_a_b_vec_fun$',B: 'B$'] :
( ( B @ ( A @ 'vec_lambda$c' @ 'vec_nth$d' @ 'fun_app$e' ) )
= ( B @ ( A @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(229,axiom,
! [A: 'N_bool_fun$',B: 'N$',C: 'N_bool_fun$'] :
( ( ! [D: 'N$'] :
( ( ! [E: 'N$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom188) ).
thf(1456,plain,
! [A: 'N_bool_fun$',B: 'N$',C: 'N_bool_fun$'] :
( ( ! [D: 'N$'] :
( ( ! [E: 'N$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(180,axiom,
! [A: 'N$'] :
( ( A @ ( 'one$d' @ 'uminus$d' @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( 'one$a' @ 'uminus$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom261) ).
thf(1231,plain,
! [A: 'N$'] :
( ( A @ ( 'one$d' @ 'uminus$d' @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( 'one$a' @ 'uminus$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(249,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ 'rowvector$b' )
= ( A @ 'uwj$' @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom430) ).
thf(1552,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ 'rowvector$b' )
= ( A @ 'uwj$' @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(26,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuq$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( A @ 'uup$' ) ) ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom65) ).
thf(569,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuq$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( A @ 'uup$' ) ) ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(289,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom381) ).
thf(1720,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(266,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxc$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( A @ 'uxb$' ) ) ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom61) ).
thf(1627,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxc$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( A @ 'uxb$' ) ) ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(156,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom355) ).
thf(1114,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(202,axiom,
! [A: 'A_a_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$e' ) @ 'vec_nth$f' ) @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom116) ).
thf(1324,plain,
! [A: 'A_a_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$e' ) @ 'vec_nth$f' ) @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(453,axiom,
'zero$' != 'one$',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom158) ).
thf(2504,plain,
'zero$' != 'one$',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(304,axiom,
! [A: 'N_bool_fun$',B: 'N$',C: 'N_bool_fun$'] :
( ( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom194) ).
thf(1776,plain,
! [A: 'N_bool_fun$',B: 'N$',C: 'N_bool_fun$'] :
( ( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(127,axiom,
tltrue != tlfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_504) ).
thf(997,plain,
tltrue != tlfalse,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(10,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$a' ) ) )
= ( C @ ( B @ ( A @ 'uxc$' ) ) @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom447) ).
thf(515,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$a' ) ) )
= ( C @ ( B @ ( A @ 'uxc$' ) ) @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(455,axiom,
( 'interchange_A$'
= ( 'n$' @ ( 'i$' @ ( 'a$' @ 'interchange_rows$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom169) ).
thf(2519,plain,
( 'interchange_A$'
= ( 'n$' @ ( 'i$' @ ( 'a$' @ 'interchange_rows$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(173,axiom,
! [A: 'A_b_vec$',B: 'B$'] :
( ( B @ ( A @ 'uww$' @ 'fun_app$e' ) )
= ( B @ ( A @ 'uwv$' ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
thf(1202,plain,
! [A: 'A_b_vec$',B: 'B$'] :
( ( B @ ( A @ 'uww$' @ 'fun_app$e' ) )
= ( B @ ( A @ 'uwv$' ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(118,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uup$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uup$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uup$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom71) ).
thf(938,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uup$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uup$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uup$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(183,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom279) ).
thf(1241,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(397,axiom,
! [A: 'N$'] :
( ( A @ ( 'uvw$' @ 'fun_app$b' ) )
= 'zero$d' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom93) ).
thf(2208,plain,
! [A: 'N$'] :
( ( A @ ( 'uvw$' @ 'fun_app$b' ) )
= 'zero$d' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(8,axiom,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom346) ).
thf(508,plain,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(114,axiom,
! [A: 'N_a_b_vec_n_vec_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$e' @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( B @ ( A @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom252) ).
thf(921,plain,
! [A: 'N_a_b_vec_n_vec_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$e' @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( B @ ( A @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(22,axiom,
! [A: 'N$'] :
( ( A @ ( 'zero$e' @ 'vec_nth$c' @ 'fun_app$f' ) )
= 'zero$c' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom142) ).
thf(558,plain,
! [A: 'N$'] :
( ( A @ ( 'zero$e' @ 'vec_nth$c' @ 'fun_app$f' ) )
= 'zero$c' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(331,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom238) ).
thf(1895,plain,
! [A: 'N$',B: 'N$'] :
~ ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(171,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( B != A )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom206) ).
thf(1185,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( B != A )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B != A )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(71,axiom,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( C @ 'fun_app$ag' ) )
= D )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom309) ).
thf(718,plain,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( C @ 'fun_app$ag' ) )
= D )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(83,axiom,
! [A: 'N$',B: 'N$',C: 'N$',D: 'A_n_vec_n_vec$'] :
( ( ( C != B )
& ( A != B ) )
=> ( ( B @ ( C @ ( A @ ( D @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( B @ ( D @ 'vec_nth$c' @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom204) ).
thf(773,plain,
! [A: 'N$',B: 'N$',C: 'N$',D: 'A_n_vec_n_vec$'] :
( ( ( C != B )
& ( A != B ) )
=> ( ( B @ ( C @ ( A @ ( D @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( B @ ( D @ 'vec_nth$c' @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(30,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom292) ).
thf(586,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(383,axiom,
? [A: 'N$'] :
( ( A @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( 'j$' @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom121) ).
thf(2144,plain,
? [A: 'N$'] :
( ( A @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( 'j$' @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(290,axiom,
! [A: 'N$'] :
( ( A @ ( 'uvr$' @ 'fun_app$l' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).
thf(1727,plain,
! [A: 'N$'] :
( ( A @ ( 'uvr$' @ 'fun_app$l' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(479,axiom,
! [A: 'A_b_vec$'] :
( ( A @ 'vec_nth$' @ 'vec_lambda$' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom333) ).
thf(2602,plain,
! [A: 'A_b_vec$'] :
( ( A @ 'vec_nth$' @ 'vec_lambda$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(457,axiom,
! [A: 'A_b_vec$',B: 'B$'] :
( ( B @ ( A @ ( 'uminus$b' @ 'fun_app$k' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( B @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom247) ).
thf(2524,plain,
! [A: 'A_b_vec$',B: 'B$'] :
( ( B @ ( A @ ( 'uminus$b' @ 'fun_app$k' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( B @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(35,axiom,
! [A: 'A_b_vec_b_vec$'] :
( ( A @ 'vec_nth$d' @ 'vec_lambda$c' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom256) ).
thf(601,plain,
! [A: 'A_b_vec_b_vec$'] :
( ( A @ 'vec_nth$d' @ 'vec_lambda$c' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(159,axiom,
( 'one$a'
= ( 'uwc$' @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom419) ).
thf(1135,plain,
( 'one$a'
= ( 'uwc$' @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(271,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom271) ).
thf(1648,plain,
! [A: 'N$',B: 'N$'] :
~ ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(186,axiom,
! [A: 'N$',B: 'N$'] :
( ( A != B )
<=> ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom305) ).
thf(1251,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(41,axiom,
! [A: 'A_b_vec_b_vec$'] :
( ( A @ 'vec_nth$d' @ 'vec_lambda$c' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom330) ).
thf(618,plain,
! [A: 'A_b_vec_b_vec$'] :
( ( A @ 'vec_nth$d' @ 'vec_lambda$c' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(408,axiom,
! [A: 'A$'] :
( ( 'zero$' @ ( A @ 'times$c' @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom460) ).
thf(2275,plain,
! [A: 'A$'] :
( ( 'zero$' @ ( A @ 'times$c' @ 'fun_app$m' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(384,axiom,
! [A: 'A$'] :
( ( 'one$' = A )
<=> ( A = 'one$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom163) ).
thf(2149,plain,
! [A: 'A$'] :
( ( ( A = 'one$' )
=> ( 'one$' = A ) )
& ( ( 'one$' = A )
=> ( A = 'one$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(179,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( B @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( C @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom177) ).
thf(1219,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( B @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$a' ) ) @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( C @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(92,axiom,
! [A: 'A_b_vec$'] :
( ( A @ ( 'zero$d' @ 'times$b' @ 'fun_app$k' ) )
= 'zero$d' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom454) ).
thf(824,plain,
! [A: 'A_b_vec$'] :
( ( A @ ( 'zero$d' @ 'times$b' @ 'fun_app$k' ) )
= 'zero$d' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(74,axiom,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( A @ ( 'one$d' @ 'times$d' @ 'fun_app$u' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom462) ).
thf(732,plain,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( A @ ( 'one$d' @ 'times$d' @ 'fun_app$u' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(212,axiom,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom275) ).
thf(1389,plain,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(450,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( ( D != B )
=> ( ( D @ ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( 'uminus$c' @ 'fun_app$m' ) @ ( B @ ( D @ ( C @ ( B @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( B @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'mult_row$a' ) ) @ 'row_add$a' ) ) ) @ 'vec_nth$c' @ 'fun_app$f' ) ) ) )
& ( ( D = B )
=> ( ( D @ ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( B @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'mult_row$a' ) ) @ 'vec_nth$c' @ 'fun_app$f' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom45) ).
thf(2489,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( ( D != B )
=> ( ( D @ ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( 'uminus$c' @ 'fun_app$m' ) @ ( B @ ( D @ ( C @ ( B @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( B @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'mult_row$a' ) ) @ 'row_add$a' ) ) ) @ 'vec_nth$c' @ 'fun_app$f' ) ) ) )
& ( ( D = B )
=> ( ( D @ ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( B @ ( C @ ( B @ ( A @ 'uwd$' ) @ 'fun_app$c' ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'mult_row$a' ) ) @ 'vec_nth$c' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(357,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( A = B )
<=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom137) ).
thf(2016,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(157,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N_a_n_vec_fun$'] :
( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'fun_app$f' ) ) )
<=> ( ( B @ 'vec_lambda$d' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom335) ).
thf(1124,plain,
! [A: 'A_n_vec_n_vec$',B: 'N_a_n_vec_fun$'] :
( ( ( ( B @ 'vec_lambda$d' )
= A )
=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'fun_app$f' ) ) ) )
& ( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'fun_app$f' ) ) )
=> ( ( B @ 'vec_lambda$d' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(276,axiom,
'zero$d' != 'one$c',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom157) ).
thf(1669,plain,
'zero$d' != 'one$c',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(27,axiom,
! [A: 'A_b_vec$'] :
( ( A @ 'columnvector$e' )
= ( A @ 'uww$' @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom437) ).
thf(572,plain,
! [A: 'A_b_vec$'] :
( ( A @ 'columnvector$e' )
= ( A @ 'uww$' @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(292,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxm$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'times$' @ 'fun_app$o' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20) ).
thf(1733,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxm$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'times$' @ 'fun_app$o' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(154,axiom,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom233) ).
thf(1107,plain,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(148,axiom,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom342) ).
thf(1092,plain,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(468,axiom,
! [A: 'A_b_vec$'] :
( ( A @ 'vec_nth$' @ 'vec_lambda$' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom259) ).
thf(2557,plain,
! [A: 'A_b_vec$'] :
( ( A @ 'vec_nth$' @ 'vec_lambda$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(231,axiom,
! [A: 'N_n_bool_fun_fun$',B: 'N$',C: 'N$'] :
( ( ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ! [D: 'N$'] : ( D @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
& ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ) )
=> ( C @ ( B @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom297) ).
thf(1464,plain,
! [A: 'N_n_bool_fun_fun$',B: 'N$',C: 'N$'] :
( ( ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ! [D: 'N$'] : ( D @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
& ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ) )
=> ( C @ ( B @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(270,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( ( A @ 'vec_nth$c' )
= ( B @ 'vec_nth$c' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom127) ).
thf(1638,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$'] :
( ( ( A = B )
=> ( ( A @ 'vec_nth$c' )
= ( B @ 'vec_nth$c' ) ) )
& ( ( ( A @ 'vec_nth$c' )
= ( B @ 'vec_nth$c' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(189,axiom,
! [A: 'N$'] :
( ( A @ ( 'zero$a' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom141) ).
thf(1271,plain,
! [A: 'N$'] :
( ( A @ ( 'zero$a' @ 'vec_nth$b' @ 'fun_app$d' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(416,axiom,
! [A: 'A_b_vec$',B: 'B_a_fun$'] :
( ! [C: 'B$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'fun_app$a' ) ) )
<=> ( ( B @ 'vec_lambda$' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom339) ).
thf(2308,plain,
! [A: 'A_b_vec$',B: 'B_a_fun$'] :
( ( ( ( B @ 'vec_lambda$' )
= A )
=> ! [C: 'B$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'fun_app$a' ) ) ) )
& ( ! [C: 'B$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'fun_app$a' ) ) )
=> ( ( B @ 'vec_lambda$' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(388,axiom,
! [A: 'A$'] :
( ( 'one$' @ ( A @ 'times$c' @ 'fun_app$m' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom470) ).
thf(2166,plain,
! [A: 'A$'] :
( ( 'one$' @ ( A @ 'times$c' @ 'fun_app$m' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(147,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom389) ).
thf(1090,plain,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(418,axiom,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$' @ 'fun_app$o' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom475) ).
thf(2319,plain,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$' @ 'fun_app$o' ) @ '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)],[418]) ).
thf(207,axiom,
! [A: 'A_b_vec$',B: 'A_b_vec$'] :
( ( B @ ( A @ 'times$b' @ 'fun_app$k' ) )
= ( B @ ( A @ 'uxn$' ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom485) ).
thf(1356,plain,
! [A: 'A_b_vec$',B: 'A_b_vec$'] :
( ( B @ ( A @ 'times$b' @ 'fun_app$k' ) )
= ( B @ ( A @ 'uxn$' ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(278,axiom,
! [A: 'N$'] :
( ( A @ ( 'uvy$' @ 'fun_app$f' ) )
= 'one$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom99) ).
thf(1675,plain,
! [A: 'N$'] :
( ( A @ ( 'uvy$' @ 'fun_app$f' ) )
= 'one$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(18,axiom,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom312) ).
thf(540,plain,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(456,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvd$' ) ) @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom55) ).
thf(2521,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvd$' ) ) @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(111,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom377) ).
thf(900,plain,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( ( B = A )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(402,axiom,
! [A: 'A_b_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwk$' @ 'fun_app$b' ) )
= ( A @ 'vec_nth$' @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).
thf(2229,plain,
! [A: 'A_b_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwk$' @ 'fun_app$b' ) )
= ( A @ 'vec_nth$' @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(436,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$b' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom424) ).
thf(2415,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$b' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(206,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom373) ).
thf(1349,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(25,axiom,
( 'one$f'
= ( 'uvz$' @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom416) ).
thf(567,plain,
( 'one$f'
= ( 'uvz$' @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(162,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom230) ).
thf(1144,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(302,axiom,
! [A: 'N$'] :
( ( A @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom445) ).
thf(1771,plain,
! [A: 'N$'] :
~ ( A @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(82,axiom,
! [A: 'N_bool_fun$'] :
( ? [B: 'N$'] : ( B @ ( A @ 'fun_app$' ) )
<=> ? [B: 'N$'] :
( ! [C: 'N$'] :
( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( C @ ( A @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom288) ).
thf(764,plain,
! [A: 'N_bool_fun$'] :
( ( ? [B: 'N$'] :
( ! [C: 'N$'] :
( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( C @ ( A @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ? [B: 'N$'] : ( B @ ( A @ 'fun_app$' ) ) )
& ( ? [B: 'N$'] : ( B @ ( A @ 'fun_app$' ) )
=> ? [B: 'N$'] :
( ! [C: 'N$'] :
( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( C @ ( A @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(36,axiom,
! [A: 'A_b_vec_b_vec$'] :
( ( A @ 'uminus$f' )
= ( A @ 'uuc$' @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom320) ).
thf(604,plain,
! [A: 'A_b_vec_b_vec$'] :
( ( A @ 'uminus$f' )
= ( A @ 'uuc$' @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(369,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'row_add$' ) ) @ 'fun_app$n' ) @ 'vec_nth$a' )
= ( D @ ( C @ ( B @ ( A @ 'row_add_row$b' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom442) ).
thf(2084,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'row_add$' ) ) @ 'fun_app$n' ) @ 'vec_nth$a' )
= ( D @ ( C @ ( B @ ( A @ 'row_add_row$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(399,axiom,
! [A: 'B$'] :
( ( A @ ( 'zero$d' @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom144) ).
thf(2214,plain,
! [A: 'B$'] :
( ( A @ ( 'zero$d' @ 'vec_nth$' @ 'fun_app$a' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(429,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$' ) @ 'fun_app$n' ) )
= ( C @ ( B @ ( A @ 'uxi$' ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom450) ).
thf(2383,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'mult_row$' ) @ 'fun_app$n' ) )
= ( C @ ( B @ ( A @ 'uxi$' ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(254,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ ( 'uxr$' @ 'fun_app$o' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom88) ).
thf(1574,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ ( 'uxr$' @ 'fun_app$o' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(309,axiom,
! [A: 'N$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom171) ).
thf(1806,plain,
! [A: 'N$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(130,axiom,
! [A: 'A_b_vec$'] :
( ( A @ ( 'uxs$' @ 'fun_app$k' ) )
= 'zero$d' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom90) ).
thf(1011,plain,
! [A: 'A_b_vec$'] :
( ( A @ ( 'uxs$' @ 'fun_app$k' ) )
= 'zero$d' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(125,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A = B )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom289) ).
thf(990,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(411,axiom,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxo$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom22) ).
thf(2284,plain,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxo$' ) @ 'fun_app$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)],[411]) ).
thf(238,axiom,
! [A: 'A_b_vec_a_b_vec_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvc$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ ( A @ 'uvb$' ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom41) ).
thf(1492,plain,
! [A: 'A_b_vec_a_b_vec_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvc$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ ( A @ 'uvb$' ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(261,axiom,
! [A: 'A_b_vec_b_vec$',B: 'A_b_vec_b_vec$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uxk$' ) @ 'fun_app$e' ) )
= ( C @ ( B @ 'vec_nth$d' @ 'fun_app$e' ) @ ( C @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'times$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom23) ).
thf(1603,plain,
! [A: 'A_b_vec_b_vec$',B: 'A_b_vec_b_vec$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uxk$' ) @ 'fun_app$e' ) )
= ( C @ ( B @ 'vec_nth$d' @ 'fun_app$e' ) @ ( C @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'times$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(413,axiom,
! [A: 'N$'] :
( ( A @ ( 'one$a' @ 'uminus$' @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( 'one$c' @ ( 'uminus$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom265) ).
thf(2299,plain,
! [A: 'N$'] :
( ( A @ ( 'one$a' @ 'uminus$' @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( 'one$c' @ ( 'uminus$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(348,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom350) ).
thf(1969,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(198,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_columns$a' ) ) @ 'vec_nth$b' )
= ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom242) ).
thf(1307,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_columns$a' ) ) @ 'vec_nth$b' )
= ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(232,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom353) ).
thf(1471,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(45,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$'] :
( ( B @ ( A @ 'times$d' @ 'fun_app$u' ) )
= ( B @ ( A @ 'uxm$' ) @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom484) ).
thf(631,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$'] :
( ( B @ ( A @ 'times$d' @ 'fun_app$u' ) )
= ( B @ ( A @ 'uxm$' ) @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(480,axiom,
! [A: 'A_a_fun$',B: 'A_b_vec_b_vec$',C: 'B$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvf$' ) ) @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom57) ).
thf(2605,plain,
! [A: 'A_a_fun$',B: 'A_b_vec_b_vec$',C: 'B$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvf$' ) ) @ 'fun_app$a' ) )
= ( D @ ( C @ ( B @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( A @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(378,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwj$' @ 'fun_app$d' ) )
= ( A @ 'vec_nth$a' @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).
thf(2129,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwj$' @ 'fun_app$d' ) )
= ( A @ 'vec_nth$a' @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(375,axiom,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'interchange_columns$b' ) ) @ 'vec_nth$a' )
= ( C @ ( B @ ( A @ 'interchange_columns_row$b' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom243) ).
thf(2111,plain,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'interchange_columns$b' ) ) @ 'vec_nth$a' )
= ( C @ ( B @ ( A @ 'interchange_columns_row$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(267,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom218) ).
thf(1630,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(33,axiom,
! [A: 'N$',B: 'N$',C: 'N$',D: 'A_b_vec_n_vec_n_vec$'] :
( ( ( C != B )
& ( A != B ) )
=> ( ( B @ ( C @ ( A @ ( D @ 'interchange_rows$b' ) @ 'fun_app$j' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( B @ ( D @ 'vec_nth$b' @ 'fun_app$d' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom203) ).
thf(594,plain,
! [A: 'N$',B: 'N$',C: 'N$',D: 'A_b_vec_n_vec_n_vec$'] :
( ( ( C != B )
& ( A != B ) )
=> ( ( B @ ( C @ ( A @ ( D @ 'interchange_rows$b' ) @ 'fun_app$j' ) @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( B @ ( D @ 'vec_nth$b' @ 'fun_app$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(42,axiom,
'zero$c' != 'one$b',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom154) ).
thf(621,plain,
'zero$c' != 'one$b',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(320,axiom,
! [A: 'N$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom444) ).
thf(1862,plain,
! [A: 'N$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(98,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( B @ ( C @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom184) ).
thf(848,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( B @ ( C @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(316,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom362) ).
thf(1838,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B = A )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(476,axiom,
! [A: 'A_n_vec_a_b_vec_fun$',B: 'A_n_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$g' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$f' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ ( A @ 'fun_app$v' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom118) ).
thf(2593,plain,
! [A: 'A_n_vec_a_b_vec_fun$',B: 'A_n_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$g' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$f' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ ( A @ 'fun_app$v' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(463,axiom,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'times$c' @ 'fun_app$m' ) @ 'times$c' @ 'fun_app$m' ) )
= ( C @ ( B @ 'times$c' @ 'fun_app$m' ) @ ( A @ 'times$c' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom499) ).
thf(2542,plain,
! [A: 'A$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'times$c' @ 'fun_app$m' ) @ 'times$c' @ 'fun_app$m' ) )
= ( C @ ( B @ 'times$c' @ 'fun_app$m' ) @ ( A @ 'times$c' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(409,axiom,
! [A: 'B$'] :
( ( A @ ( 'one$c' @ ( 'uminus$b' @ 'fun_app$k' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( 'one$' @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom264) ).
thf(2278,plain,
! [A: 'B$'] :
( ( A @ ( 'one$c' @ ( 'uminus$b' @ 'fun_app$k' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( 'one$' @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(211,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N_a_b_vec_n_vec_fun$'] :
( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( C @ ( B @ 'fun_app$d' ) ) )
<=> ( ( B @ 'vec_lambda$e' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom338) ).
thf(1381,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N_a_b_vec_n_vec_fun$'] :
( ( ( ( B @ 'vec_lambda$e' )
= 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$e' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(314,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom348) ).
thf(1820,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(473,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'B$',D: 'N$'] :
( ( ( D != B )
=> ( ( D @ ( C @ ( B @ ( A @ 'uwg$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'uminus$c' @ 'fun_app$m' ) @ ( B @ ( D @ ( C @ ( B @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( B @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'mult_row$' ) @ 'fun_app$n' ) @ 'row_add$' ) ) @ 'fun_app$n' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( D = B )
=> ( ( D @ ( C @ ( B @ ( A @ 'uwg$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( B @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'mult_row$' ) @ 'fun_app$n' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom44) ).
thf(2578,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'B$',D: 'N$'] :
( ( ( D != B )
=> ( ( D @ ( C @ ( B @ ( A @ 'uwg$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'uminus$c' @ 'fun_app$m' ) @ ( B @ ( D @ ( C @ ( B @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( B @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'mult_row$' ) @ 'fun_app$n' ) @ 'row_add$' ) ) @ 'fun_app$n' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( D = B )
=> ( ( D @ ( C @ ( B @ ( A @ 'uwg$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( B @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'least$' @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'mult_row$' ) @ 'fun_app$n' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(108,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom364) ).
thf(890,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(275,axiom,
! [A: 'N_bool_fun$'] :
( ? [B: 'N$'] : ( B @ ( A @ 'fun_app$' ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom195) ).
thf(1667,plain,
! [A: 'N_bool_fun$'] :
( ? [B: 'N$'] : ( B @ ( A @ 'fun_app$' ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(392,axiom,
! [A: 'A$'] :
( ( A @ ( 'one$' @ 'times$c' @ 'fun_app$m' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom465) ).
thf(2180,plain,
! [A: 'A$'] :
( ( A @ ( 'one$' @ 'times$c' @ 'fun_app$m' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(358,axiom,
! [A: tlbool,B: 'A_n_vec$',C: 'A_n_vec$',D: 'N$'] :
( ( ( A != tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( C @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( C @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ) )
& ( ( A = tltrue )
=> ( ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( C @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( A = tltrue )
=> ( ( D @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom166) ).
thf(2025,plain,
! [A: tlbool,B: 'A_n_vec$',C: 'A_n_vec$',D: 'N$'] :
( ( ( A != tltrue )
=> ( ( A = tltrue )
=> ( ( D @ ( C @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) )
& ( ( A = tltrue )
=> ( ( A != tltrue )
=> ( ( D @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( C @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(146,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( B != A )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom361) ).
thf(1080,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( B != A )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B != A )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(484,axiom,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'A$',D: 'B$',E: 'B$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxd$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxd$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ 'times$c' @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom81) ).
thf(2632,plain,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'A$',D: 'B$',E: 'B$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxd$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxd$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ 'times$c' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(88,axiom,
! [A: 'A_a_b_vec_n_vec_fun$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$i' ) )
= ( B @ ( A @ 'uvq$' ) @ 'vec_lambda$h' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom407) ).
thf(799,plain,
! [A: 'A_a_b_vec_n_vec_fun$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$i' ) )
= ( B @ ( A @ 'uvq$' ) @ 'vec_lambda$h' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(336,axiom,
! [A: 'N$'] :
( ( A @ ( 'uvv$' @ 'fun_app$d' ) )
= 'zero$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom91) ).
thf(1909,plain,
! [A: 'N$'] :
( ( A @ ( 'uvv$' @ 'fun_app$d' ) )
= 'zero$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(166,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( A = B )
<=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom138) ).
thf(1162,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( C @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(72,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uui$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( A @ 'uuh$' ) ) ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom69) ).
thf(726,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uui$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( A @ 'uuh$' ) ) ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(116,axiom,
! [A: 'A_a_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvh$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom52) ).
thf(932,plain,
! [A: 'A_a_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvh$' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(344,axiom,
! [A: 'N_bool_fun$'] :
( ? [B: 'N$'] :
( ! [C: 'N$'] :
( ( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) )
=> ( C = B ) )
& ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom192) ).
thf(1952,plain,
! [A: 'N_bool_fun$'] :
( ? [B: 'N$'] :
( ! [C: 'N$'] :
( ( ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) )
=> ( C = B ) )
& ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( A @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(425,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxb$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxb$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( C @ 'times$c' @ 'fun_app$m' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom79) ).
thf(2365,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'A$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxb$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uxb$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( C @ 'times$c' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(423,axiom,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$',D: 'N$',E: 'B$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uun$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uun$' ) ) ) @ 'fun_app$a' ) )
= ( B @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uun$' ) ) ) @ 'fun_app$a' ) )
= ( C @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom76) ).
thf(2350,plain,
! [A: 'A_b_vec_n_vec$',B: 'B$',C: 'B$',D: 'N$',E: 'B$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uun$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uun$' ) ) ) @ 'fun_app$a' ) )
= ( B @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uun$' ) ) ) @ 'fun_app$a' ) )
= ( C @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(184,axiom,
! [A: 'A_a_b_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uva$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ ( A @ 'uuz$' ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom42) ).
thf(1245,plain,
! [A: 'A_a_b_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uva$' ) @ 'fun_app$d' ) )
= ( C @ ( B @ ( A @ 'uuz$' ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(169,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom281) ).
thf(1176,plain,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(128,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> $false )
& ( A != B ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom303) ).
thf(1000,plain,
! [A: 'N$',B: 'N$'] :
~ ( ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(233,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ ( 'uxw$' @ 'fun_app$o' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom83) ).
thf(1477,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ ( 'uxw$' @ 'fun_app$o' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(283,axiom,
! [A: 'A_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwt$' ) @ 'fun_app$l' ) )
= ( B @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom30) ).
thf(1694,plain,
! [A: 'A_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwt$' ) @ 'fun_app$l' ) )
= ( B @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(54,axiom,
! [A: 'A_n_vec$'] :
( ( 'zero$c' = A )
<=> ( A = 'zero$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom149) ).
thf(658,plain,
! [A: 'A_n_vec$'] :
( ( ( A = 'zero$c' )
=> ( 'zero$c' = A ) )
& ( ( 'zero$c' = A )
=> ( A = 'zero$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(12,axiom,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom343) ).
thf(521,plain,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(167,axiom,
! [A: 'N$',B: 'N_bool_fun$'] :
( ( B @ 'least$' @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom397) ).
thf(1171,plain,
! [A: 'N$',B: 'N_bool_fun$'] :
( ( B @ 'least$' @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(124,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom363) ).
thf(983,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ~ ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(368,axiom,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$',C: 'N$'] :
( ( ( C != 'i$' )
=> ( ( C @ ( B @ ( A @ 'uua$' ) @ 'fun_app$b' ) )
= ( C @ ( 'j$' @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'uminus$c' @ 'fun_app$m' ) @ ( 'i$' @ ( C @ ( B @ 'row_add$' ) ) @ 'fun_app$n' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( C = 'i$' )
=> ( ( C @ ( B @ ( A @ 'uua$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19) ).
thf(2075,plain,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$',C: 'N$'] :
( ( ( C != 'i$' )
=> ( ( C @ ( B @ ( A @ 'uua$' ) @ 'fun_app$b' ) )
= ( C @ ( 'j$' @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'uminus$c' @ 'fun_app$m' ) @ ( 'i$' @ ( C @ ( B @ 'row_add$' ) ) @ 'fun_app$n' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( C = 'i$' )
=> ( ( C @ ( B @ ( A @ 'uua$' ) @ 'fun_app$b' ) )
= ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(437,axiom,
! [A: 'A_b_vec$',B: 'B$'] :
( ( B @ ( A @ 'uuf$' @ 'fun_app$a' ) )
= ( B @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom14) ).
thf(2418,plain,
! [A: 'A_b_vec$',B: 'B$'] :
( ( B @ ( A @ 'uuf$' @ 'fun_app$a' ) )
= ( B @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(177,axiom,
! [A: tlbool] :
( ( A = tlfalse )
| ( A = tltrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_503) ).
thf(1213,plain,
! [A: tlbool] :
( ( A = tlfalse )
| ( A = tltrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(93,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom387) ).
thf(827,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(246,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( B = A )
| ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom384) ).
thf(1528,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( B = A )
| ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B = A )
| ~ ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(482,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$a' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom112) ).
thf(2620,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$a' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(103,axiom,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuk$' ) ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( B @ ( A @ 'uuj$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom68) ).
thf(868,plain,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuk$' ) ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( B @ ( A @ 'uuj$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(99,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom307) ).
thf(851,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(152,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom351) ).
thf(1102,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(366,axiom,
! [A: 'A_b_vec$'] :
( ( 'zero$d' = A )
<=> ( A = 'zero$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom152) ).
thf(2054,plain,
! [A: 'A_b_vec$'] :
( ( ( A = 'zero$d' )
=> ( 'zero$d' = A ) )
& ( ( 'zero$d' = A )
=> ( A = 'zero$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(373,axiom,
! [A: 'A$'] :
( ( A @ ( 'uxy$' @ 'fun_app$m' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom86) ).
thf(2096,plain,
! [A: 'A$'] :
( ( A @ ( 'uxy$' @ 'fun_app$m' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(15,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ 'columnvector$f' )
= ( A @ 'uwy$' @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom438) ).
thf(531,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ 'columnvector$f' )
= ( A @ 'uwy$' @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(335,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom302) ).
thf(1905,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(191,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uum$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ ( A @ 'uul$' ) ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom67) ).
thf(1277,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uum$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ ( A @ 'uul$' ) ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(443,axiom,
( ( 'j$' @ ( 'n$' @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom148) ).
thf(2449,plain,
( ( 'j$' @ ( 'n$' @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(470,axiom,
! [A: 'A_a_b_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$b' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$t' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom113) ).
thf(2564,plain,
! [A: 'A_a_b_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$b' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) @ ( A @ 'fun_app$t' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(20,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom318) ).
thf(553,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( 'one$d' = A )
<=> ( A = 'one$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom160) ).
thf(490,plain,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( ( A = 'one$d' )
=> ( 'one$d' = A ) )
& ( ( 'one$d' = A )
=> ( A = 'one$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(257,axiom,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uus$' ) ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).
thf(1583,plain,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uus$' ) ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(51,axiom,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom344) ).
thf(648,plain,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(3,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$d' ) )
= ( B @ ( A @ 'uvo$' ) @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom406) ).
thf(487,plain,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$d' ) )
= ( B @ ( A @ 'uvo$' ) @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(471,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N_a_b_vec_fun$'] :
( ! [C: 'N$'] :
( ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( B @ 'fun_app$b' ) ) )
<=> ( ( B @ 'vec_lambda$a' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom340) ).
thf(2567,plain,
! [A: 'A_b_vec_n_vec$',B: 'N_a_b_vec_fun$'] :
( ( ( ( B @ 'vec_lambda$a' )
= A )
=> ! [C: 'N$'] :
( ( 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$b' ) ) )
=> ( ( B @ 'vec_lambda$a' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(296,axiom,
! [A: tlbool,B: 'A_b_vec_n_vec_n_vec$',C: 'A_b_vec_n_vec_n_vec$',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$d' ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom164) ).
thf(1748,plain,
! [A: tlbool,B: 'A_b_vec_n_vec_n_vec$',C: 'A_b_vec_n_vec_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)],[296]) ).
thf(13,axiom,
! [A: 'A_a_b_vec_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvq$' ) @ 'fun_app$j' ) )
= ( C @ ( B @ ( A @ 'uvp$' ) ) @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom34) ).
thf(525,plain,
! [A: 'A_a_b_vec_n_vec_fun$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvq$' ) @ 'fun_app$j' ) )
= ( C @ ( B @ ( A @ 'uvp$' ) ) @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(69,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$',C: 'A_b_vec_n_vec_n_vec$'] :
( ( C @ ( B @ ( A @ 'times$d' @ 'fun_app$u' ) @ 'times$d' @ 'fun_app$u' ) )
= ( C @ ( B @ 'times$d' @ 'fun_app$u' ) @ ( A @ 'times$d' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom498) ).
thf(712,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$',C: 'A_b_vec_n_vec_n_vec$'] :
( ( C @ ( B @ ( A @ 'times$d' @ 'fun_app$u' ) @ 'times$d' @ 'fun_app$u' ) )
= ( C @ ( B @ 'times$d' @ 'fun_app$u' ) @ ( A @ 'times$d' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(61,axiom,
! [A: 'A_n_vec_n_vec$'] :
( ( A @ 'vec_nth$c' @ 'vec_lambda$d' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom255) ).
thf(690,plain,
! [A: 'A_n_vec_n_vec$'] :
( ( A @ 'vec_nth$c' @ 'vec_lambda$d' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(48,axiom,
( 'zero$a'
= ( 'uvv$' @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom412) ).
thf(640,plain,
( 'zero$a'
= ( 'uvv$' @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(143,axiom,
! [A: 'N_bool_fun$',B: 'N_bool_fun$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
& ? [C: 'N$'] : ( C @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( B @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom196) ).
thf(1070,plain,
! [A: 'N_bool_fun$',B: 'N_bool_fun$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ 'fun_app$' ) ) )
& ? [C: 'N$'] : ( C @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( B @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(67,axiom,
( 'one$d'
= ( 'uwb$' @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom418) ).
thf(707,plain,
( 'one$d'
= ( 'uwb$' @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(394,axiom,
! [A: 'A_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uud$' @ 'fun_app$l' ) )
= ( B @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).
thf(2192,plain,
! [A: 'A_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uud$' @ 'fun_app$l' ) )
= ( B @ ( A @ 'vec_nth$e' @ 'fun_app$l' ) @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(356,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom268) ).
thf(2012,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(305,axiom,
! [A: 'N$'] :
( ( A @ ( 'one$e' @ 'uminus$e' @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( 'one$b' @ 'uminus$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom262) ).
thf(1780,plain,
! [A: 'N$'] :
( ( A @ ( 'one$e' @ 'uminus$e' @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( 'one$b' @ 'uminus$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(430,axiom,
! [A: 'B$'] :
( ( A @ ( 'uvu$' @ 'fun_app$a' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).
thf(2386,plain,
! [A: 'B$'] :
( ( A @ ( 'uvu$' @ 'fun_app$a' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(66,axiom,
( 'zero$c'
= ( 'uvr$' @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom408) ).
thf(705,plain,
( 'zero$c'
= ( 'uvr$' @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(164,axiom,
! [A: 'N_a_n_vec_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$d' @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( B @ ( A @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom249) ).
thf(1156,plain,
! [A: 'N_a_n_vec_fun$',B: 'N$'] :
( ( B @ ( A @ 'vec_lambda$d' @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( B @ ( A @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(235,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'gauss_Jordan_in_ij$a' ) ) )
= ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom420) ).
thf(1484,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'gauss_Jordan_in_ij$a' ) ) )
= ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(386,axiom,
! [A: 'A$'] :
( ( A @ ( 'uxt$' @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).
thf(2160,plain,
! [A: 'A$'] :
( ( A @ ( 'uxt$' @ 'fun_app$m' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(240,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$b' ) @ 'fun_app$j' ) @ 'vec_nth$b' )
= ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom200) ).
thf(1499,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$b' ) @ 'fun_app$j' ) @ 'vec_nth$b' )
= ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(57,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( B @ ( A @ 'interchange_rows$b' ) @ 'fun_app$j' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom197) ).
thf(673,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( B @ ( A @ 'interchange_rows$b' ) @ 'fun_app$j' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(352,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom375) ).
thf(1987,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(87,axiom,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( ( B @ ( A @ 'fun_app$' ) )
& ? [C: 'N$'] :
( ! [D: 'N$'] :
( ( ! [E: 'N$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D = C ) )
& ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) ) )
=> ( B @ ( A @ 'least$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom191) ).
thf(791,plain,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( ( B @ ( A @ 'fun_app$' ) )
& ? [C: 'N$'] :
( ! [D: 'N$'] :
( ( ! [E: 'N$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D = C ) )
& ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( C @ ( A @ 'fun_app$' ) ) ) )
=> ( B @ ( A @ 'least$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(6,axiom,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom345) ).
thf(502,plain,
! [A: 'N$',B: 'N$',C: 'N_n_fun$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( C @ 'fun_app$ag' ) @ ( E @ ( C @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( B @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( A @ ( C @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(187,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( C @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom181) ).
thf(1262,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( C @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(421,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uul$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uul$' ) ) ) @ 'fun_app$b' ) )
= ( B @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uul$' ) ) ) @ 'fun_app$b' ) )
= ( C @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom74) ).
thf(2337,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uul$' ) ) ) @ 'fun_app$b' ) )
= ( E @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uul$' ) ) ) @ 'fun_app$b' ) )
= ( B @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uul$' ) ) ) @ 'fun_app$b' ) )
= ( C @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(299,axiom,
! [A: 'N$'] :
( ( A @ ( 'one$e' @ 'vec_nth$c' @ 'fun_app$f' ) )
= 'one$b' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom107) ).
thf(1763,plain,
! [A: 'N$'] :
( ( A @ ( 'one$e' @ 'vec_nth$c' @ 'fun_app$f' ) )
= 'one$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(419,axiom,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$',D: 'B$',E: 'B$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( C @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom73) ).
thf(2322,plain,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'B$',D: 'B$',E: 'B$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( C @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(312,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B = A )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom317) ).
thf(1813,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(196,axiom,
! [A: 'N$'] :
( ( A @ ( 'zero$c' @ 'vec_nth$e' @ 'fun_app$l' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom143) ).
thf(1300,plain,
! [A: 'N$'] :
( ( A @ ( 'zero$c' @ 'vec_nth$e' @ 'fun_app$l' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(247,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A != B ) )
=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom378) ).
thf(1538,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A != B ) )
=> ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(449,axiom,
! [A: 'A_b_vec$',B: 'A_b_vec$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'times$b' @ 'fun_app$k' ) @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) @ ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) @ 'times$c' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom474) ).
thf(2486,plain,
! [A: 'A_b_vec$',B: 'A_b_vec$',C: 'B$'] :
( ( 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$c' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(464,axiom,
! [A: 'A_b_vec_a_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$c' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$r' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom114) ).
thf(2545,plain,
! [A: 'A_b_vec_a_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$c' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$r' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(478,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ 'vec_nth$a' @ 'vec_lambda$a' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom334) ).
thf(2599,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ 'vec_nth$a' @ 'vec_lambda$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(19,axiom,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( 'zero$a' = A )
<=> ( A = 'zero$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom150) ).
thf(544,plain,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( ( A = 'zero$a' )
=> ( 'zero$a' = A ) )
& ( ( 'zero$a' = A )
=> ( A = 'zero$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(112,axiom,
! [A: 'N_a_bool_fun_fun$'] :
( ! [B: 'N$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
<=> ? [B: 'A_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) @ ( C @ ( A @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom133) ).
thf(907,plain,
! [A: 'N_a_bool_fun_fun$'] :
( ( ? [B: 'A_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) @ ( C @ ( A @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
=> ! [B: 'N$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) )
& ( ! [B: 'N$'] :
? [C: 'A$'] : ( C @ ( B @ ( A @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
=> ? [B: 'A_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$e' @ 'fun_app$l' ) @ ( C @ ( A @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(77,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) )
= ( C @ ( B @ ( A @ 'uuq$' ) ) @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom393) ).
thf(744,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) )
= ( C @ ( B @ ( A @ 'uuq$' ) ) @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(300,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( B != A )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom379) ).
thf(1766,plain,
! [A: 'N$',B: 'N$'] :
( ( ( B != A )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(332,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom390) ).
thf(1898,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(161,axiom,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$'] :
( ( B @ ( A @ 'times$' @ 'fun_app$o' ) )
= ( B @ ( A @ 'uxo$' ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom486) ).
thf(1141,plain,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$'] :
( ( B @ ( A @ 'times$' @ 'fun_app$o' ) )
= ( B @ ( A @ 'uxo$' ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(133,axiom,
! [A: 'N_bool_fun$',B: 'N$',C: 'N_bool_fun$'] :
( ( ! [D: 'N$'] :
( ( ! [E: 'N$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom190) ).
thf(1023,plain,
! [A: 'N_bool_fun$',B: 'N$',C: 'N_bool_fun$'] :
( ( ! [D: 'N$'] :
( ( ! [E: 'N$'] :
( ( E @ ( A @ 'fun_app$' ) )
=> ( E @ ( D @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( A @ 'fun_app$' ) ) )
=> ( D @ ( C @ 'fun_app$' ) ) )
& ! [D: 'N$'] :
( ( D @ ( A @ 'fun_app$' ) )
=> ( D @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( A @ 'least$' @ ( C @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(222,axiom,
! [A: 'A_b_vec$'] :
( ( A @ 'rowvector$a' )
= ( A @ 'uwi$' @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom429) ).
thf(1427,plain,
! [A: 'A_b_vec$'] :
( ( A @ 'rowvector$a' )
= ( A @ 'uwi$' @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(242,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( 'one$a' = A )
<=> ( A = 'one$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom161) ).
thf(1504,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( ( A = 'one$a' )
=> ( 'one$a' = A ) )
& ( ( 'one$a' = A )
=> ( A = 'one$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(149,axiom,
( 'uxt$'
= ( 'zero$' @ 'times$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom491) ).
thf(1094,plain,
( 'uxt$'
= ( 'zero$' @ 'times$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(288,axiom,
! [A: 'A_b_vec$'] :
( ( A @ ( 'uminus$b' @ 'fun_app$k' ) )
= ( A @ 'uuf$' @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom323) ).
thf(1717,plain,
! [A: 'A_b_vec$'] :
( ( A @ ( 'uminus$b' @ 'fun_app$k' ) )
= ( A @ 'uuf$' @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(39,axiom,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( A @ 'vec_nth$b' @ 'vec_lambda$e' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom258) ).
thf(612,plain,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( A @ 'vec_nth$b' @ 'vec_lambda$e' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(349,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' )
= ( C @ ( B @ ( A @ 'interchange_rows_row$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom201) ).
thf(1972,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) @ 'vec_nth$c' )
= ( C @ ( B @ ( A @ 'interchange_rows_row$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(139,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A = B )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom316) ).
thf(1052,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(342,axiom,
! [A: 'A_b_vec$'] :
( ( 'one$c' = A )
<=> ( A = 'one$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom162) ).
thf(1940,plain,
! [A: 'A_b_vec$'] :
( ( ( A = 'one$c' )
=> ( 'one$c' = A ) )
& ( ( 'one$c' = A )
=> ( A = 'one$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(220,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ ( 'one$a' @ 'times$' @ 'fun_app$o' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom463) ).
thf(1421,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ ( 'one$a' @ 'times$' @ 'fun_app$o' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(448,axiom,
( ! [A: 'N$'] :
( ( ( A @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( 'j$' @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom146) ).
thf(2479,plain,
~ ! [A: 'N$'] :
~ ( ( A @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( 'j$' @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(363,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom313) ).
thf(2045,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(347,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom63) ).
thf(1966,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(343,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uminus$d' @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'uminus$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom244) ).
thf(1949,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uminus$d' @ 'vec_nth$b' @ 'fun_app$d' ) )
= ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'uminus$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(313,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'gauss_Jordan_in_ij$' ) ) )
= ( C @ ( B @ ( A @ 'uwg$' ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom421) ).
thf(1817,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'gauss_Jordan_in_ij$' ) ) )
= ( C @ ( B @ ( A @ 'uwg$' ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(244,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom300) ).
thf(1517,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(178,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ ( A @ 'uul$' ) ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom425) ).
thf(1216,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ ( A @ 'uul$' ) ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(226,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A != B ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom349) ).
thf(1448,plain,
! [A: 'N$',B: 'N$'] :
( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A != B ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(415,axiom,
! [A: 'A_b_vec$',B: 'B$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwn$' ) @ 'fun_app$l' ) )
= ( B @ ( A @ 'vec_nth$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom32) ).
thf(2305,plain,
! [A: 'A_b_vec$',B: 'B$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwn$' ) @ 'fun_app$l' ) )
= ( B @ ( A @ 'vec_nth$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(401,axiom,
! [A: 'A_b_vec_a_b_vec_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvb$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).
thf(2226,plain,
! [A: 'A_b_vec_a_b_vec_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvb$' ) ) @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(322,axiom,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( ( A @ 'least$' )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom189) ).
thf(1866,plain,
! [A: 'N_bool_fun$',B: 'N$'] :
( ( ! [C: 'N$'] :
( ( C @ ( A @ 'fun_app$' ) )
=> ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( B @ ( A @ 'fun_app$' ) ) )
=> ( ( A @ 'least$' )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(431,axiom,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ 'vec_nth$a' @ 'vec_lambda$a' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom260) ).
thf(2389,plain,
! [A: 'A_b_vec_n_vec$'] :
( ( A @ 'vec_nth$a' @ 'vec_lambda$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(380,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( C @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom182) ).
thf(2135,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( C @ ( B @ ( A @ 'interchange_rows$' ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(467,axiom,
! [A: 'A$'] :
( ( A @ ( 'zero$' @ 'times$c' @ 'fun_app$m' ) )
= 'zero$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom455) ).
thf(2554,plain,
! [A: 'A$'] :
( ( A @ ( 'zero$' @ 'times$c' @ 'fun_app$m' ) )
= 'zero$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(141,axiom,
! [A: 'N_a_b_vec_n_vec_bool_fun_fun$'] :
( ! [B: 'N$'] :
? [C: 'A_b_vec_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$y' ) @ 'fun_app$x' ) )
<=> ? [B: 'A_b_vec_n_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$y' ) @ 'fun_app$x' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom131) ).
thf(1062,plain,
! [A: 'N_a_b_vec_n_vec_bool_fun_fun$'] :
( ( ? [B: 'A_b_vec_n_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$y' ) @ 'fun_app$x' ) )
=> ! [B: 'N$'] :
? [C: 'A_b_vec_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$y' ) @ 'fun_app$x' ) ) )
& ( ! [B: 'N$'] :
? [C: 'A_b_vec_n_vec$'] : ( C @ ( B @ ( A @ 'fun_app$y' ) @ 'fun_app$x' ) )
=> ? [B: 'A_b_vec_n_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(52,axiom,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( 'zero$a' @ ( A @ 'times$d' @ 'fun_app$u' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom457) ).
thf(652,plain,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( 'zero$a' @ ( A @ 'times$d' @ 'fun_app$u' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(481,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( E @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom176) ).
thf(2608,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( E @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( C @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(315,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false )
& ( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false )
& ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false )
& ( ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false )
& ( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false )
& ( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom213) ).
thf(1822,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
~ ( ~ ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ~ ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ~ ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ~ ( ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ~ ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ~ ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(85,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom306) ).
thf(786,plain,
! [A: 'N$',B: 'N$'] :
~ ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(251,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom366) ).
thf(1558,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A != B )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(31,axiom,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( 'one$d' @ ( A @ 'times$d' @ 'fun_app$u' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom467) ).
thf(588,plain,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( 'one$d' @ ( A @ 'times$d' @ 'fun_app$u' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(64,axiom,
! [A: 'A_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwh$' @ 'fun_app$f' ) )
= ( A @ 'vec_nth$e' @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).
thf(699,plain,
! [A: 'A_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwh$' @ 'fun_app$f' ) )
= ( A @ 'vec_nth$e' @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(134,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom269) ).
thf(1030,plain,
! [A: 'N$',B: 'N$'] :
~ ( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(281,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwy$' @ 'fun_app$d' ) )
= ( B @ ( A @ 'uwx$' ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
thf(1689,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uwy$' @ 'fun_app$d' ) )
= ( B @ ( A @ 'uwx$' ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(55,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvo$' ) @ 'fun_app$f' ) )
= ( C @ ( B @ ( A @ 'uvn$' ) ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom35) ).
thf(667,plain,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uvo$' ) @ 'fun_app$f' ) )
= ( C @ ( B @ ( A @ 'uvn$' ) ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(393,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'B$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'fun_app$' ) )
<=> ( ( D @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( C @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom47) ).
thf(2183,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'B$',D: 'N$'] :
( ( ( ( D @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( C @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) )
=> ( D @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'fun_app$' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uwf$' ) ) @ 'fun_app$' ) )
=> ( ( D @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( C @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(243,axiom,
! [A: 'N$',B: 'N$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom234) ).
thf(1513,plain,
! [A: 'N$',B: 'N$'] :
( ( A = B )
=> ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(273,axiom,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$',C: 'A_b_vec_n_vec$'] :
( ( C @ ( B @ ( A @ 'times$' @ 'fun_app$o' ) @ 'times$' @ 'fun_app$o' ) )
= ( C @ ( B @ 'times$' @ 'fun_app$o' ) @ ( A @ 'times$' @ 'fun_app$o' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom500) ).
thf(1661,plain,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$',C: 'A_b_vec_n_vec$'] :
( ( C @ ( B @ ( A @ 'times$' @ 'fun_app$o' ) @ 'times$' @ 'fun_app$o' ) )
= ( C @ ( B @ 'times$' @ 'fun_app$o' ) @ ( A @ 'times$' @ 'fun_app$o' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(59,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$a' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( A @ 'uuh$' ) ) ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom426) ).
thf(684,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_columns_row$a' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( A @ 'uuh$' ) ) ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(360,axiom,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom224) ).
thf(2036,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(483,axiom,
! [A: 'A_b_vec_n_vec$',B: 'A_b_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',axiom140) ).
thf(2623,plain,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$'] :
( ( ! [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)],[483]) ).
thf(438,axiom,
! [A: 'N_a_b_vec_bool_fun_fun$'] :
( ! [B: 'N$'] :
? [C: 'A_b_vec$'] : ( C @ ( B @ ( A @ 'fun_app$af' ) @ 'fun_app$ae' ) )
<=> ? [B: 'A_b_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom135) ).
thf(2421,plain,
! [A: 'N_a_b_vec_bool_fun_fun$'] :
( ( ? [B: 'A_b_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'fun_app$af' ) @ 'fun_app$ae' ) )
=> ! [B: 'N$'] :
? [C: 'A_b_vec$'] : ( C @ ( B @ ( A @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
& ( ! [B: 'N$'] :
? [C: 'A_b_vec$'] : ( C @ ( B @ ( A @ 'fun_app$af' ) @ 'fun_app$ae' ) )
=> ? [B: 'A_b_vec_n_vec$'] :
! [C: 'N$'] : ( C @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ ( C @ ( A @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(145,axiom,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'A$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxe$' ) ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( B @ ( A @ 'uxd$' ) ) ) @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom60) ).
thf(1077,plain,
! [A: 'A_b_vec_b_vec$',B: 'B$',C: 'A$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxe$' ) ) @ 'fun_app$e' ) )
= ( D @ ( C @ ( B @ ( A @ 'uxd$' ) ) ) @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(424,axiom,
! [A: 'N$'] :
( ( A @ ( 'one$a' @ 'vec_nth$a' @ 'fun_app$b' ) )
= 'one$c' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom110) ).
thf(2362,plain,
! [A: 'N$'] :
( ( A @ ( 'one$a' @ 'vec_nth$a' @ 'fun_app$b' ) )
= 'one$c' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(426,axiom,
! [A: 'A_b_vec$',B: 'B$'] :
( ( B @ ( A @ 'uwi$' @ 'fun_app$e' ) )
= ( A @ 'vec_nth$' @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).
thf(2374,plain,
! [A: 'A_b_vec$',B: 'B$'] :
( ( B @ ( A @ 'uwi$' @ 'fun_app$e' ) )
= ( A @ 'vec_nth$' @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(412,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'B$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom72) ).
thf(2287,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'B$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( D @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) ) @ 'fun_app$a' ) )
= ( E @ ( C @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(303,axiom,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom372) ).
thf(1774,plain,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(414,axiom,
! [A: 'N$'] :
( ( A @ ( 'uvx$' @ 'fun_app$l' ) )
= 'one$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom101) ).
thf(2302,plain,
! [A: 'N$'] :
( ( A @ ( 'uvx$' @ 'fun_app$l' ) )
= 'one$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(192,axiom,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom315) ).
thf(1280,plain,
! [A: 'N$',B: 'N$'] :
( ( A @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
| ( A = B )
| ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(279,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxj$' ) @ 'fun_app$f' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'times$a' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21) ).
thf(1678,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uxj$' ) @ 'fun_app$f' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'times$a' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(94,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom217) ).
thf(833,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(90,axiom,
! [A: 'A_n_vec$'] :
( ( 'zero$c' @ ( A @ 'times$a' @ 'fun_app$p' ) )
= 'zero$c' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom456) ).
thf(818,plain,
! [A: 'A_n_vec$'] :
( ( 'zero$c' @ ( A @ 'times$a' @ 'fun_app$p' ) )
= 'zero$c' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(259,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom220) ).
thf(1593,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( ( A = B )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(197,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom276) ).
thf(1303,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( C @ ( B @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A = B ) )
=> ( C @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(297,axiom,
! [A: 'A_b_vec$'] :
( ( A @ ( 'uxx$' @ 'fun_app$k' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom85) ).
thf(1757,plain,
! [A: 'A_b_vec$'] :
( ( A @ ( 'uxx$' @ 'fun_app$k' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(234,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom215) ).
thf(1480,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( B = C )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( C @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(75,axiom,
! [A: 'N_n_bool_fun_fun$',B: 'N$',C: 'N$'] :
( ( ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ! [D: 'N$',E: 'N$'] :
( ( E @ ( D @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ) )
=> ( C @ ( B @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom222) ).
thf(735,plain,
! [A: 'N_n_bool_fun_fun$',B: 'N$',C: 'N$'] :
( ( ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ! [D: 'N$',E: 'N$'] :
( ( E @ ( D @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ) )
=> ( C @ ( B @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(119,axiom,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( A @ 'vec_nth$e' )
= ( B @ 'vec_nth$e' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom128) ).
thf(950,plain,
! [A: 'A_n_vec$',B: 'A_n_vec$'] :
( ( ( A = B )
=> ( ( A @ 'vec_nth$e' )
= ( B @ 'vec_nth$e' ) ) )
& ( ( ( A @ 'vec_nth$e' )
= ( B @ 'vec_nth$e' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(95,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A = B ) )
=> ( A @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom293) ).
thf(835,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A = B ) )
=> ( A @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(474,axiom,
! [A: 'N$'] :
( ( A @ ( 'one$b' @ 'vec_nth$e' @ 'fun_app$l' ) )
= 'one$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom108) ).
thf(2587,plain,
! [A: 'N$'] :
( ( A @ ( 'one$b' @ 'vec_nth$e' @ 'fun_app$l' ) )
= 'one$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(185,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'A_b_vec$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxg$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ ( A @ 'uxf$' ) ) ) @ 'vec_lambda$a' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom59) ).
thf(1248,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'A_b_vec$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxg$' ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( B @ ( A @ 'uxf$' ) ) ) @ 'vec_lambda$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(365,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A = B ) )
=> ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom227) ).
thf(2050,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A = B ) )
=> ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(24,axiom,
! [A: 'A_b_vec_a_b_vec_fun$',B: 'A_b_vec_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$f' ) )
= ( B @ ( A @ 'uvc$' ) @ 'vec_lambda$e' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom400) ).
thf(564,plain,
! [A: 'A_b_vec_a_b_vec_fun$',B: 'A_b_vec_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$f' ) )
= ( B @ ( A @ 'uvc$' ) @ 'vec_lambda$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(353,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( ( B != A )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom385) ).
thf(1989,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( B != A )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( B != A )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(239,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A = C )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom228) ).
thf(1495,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A = C )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(420,axiom,
! [A: 'A_b_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uminus$' @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ ( 'uminus$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom248) ).
thf(2334,plain,
! [A: 'A_b_vec_n_vec$',B: 'N$'] :
( ( B @ ( A @ 'uminus$' @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( B @ ( A @ 'vec_nth$a' @ 'fun_app$b' ) @ ( 'uminus$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(7,axiom,
( 'zero$f'
= ( 'uvt$' @ 'vec_lambda$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom410) ).
thf(506,plain,
( 'zero$f'
= ( 'uvt$' @ 'vec_lambda$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(140,axiom,
! [A: 'N$',B: 'N$'] :
( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom383) ).
thf(1056,plain,
! [A: 'N$',B: 'N$'] :
( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ~ ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(433,axiom,
! [A: 'N$',B: 'A_b_vec_n_vec$',C: 'A_b_vec_n_vec$'] :
( ( ( ( 'j$' @ ( 'i$' @ ( 'a$' @ 'gauss_Jordan_in_ij$' ) ) )
= ( C @ ( B @ 'uua$' ) @ 'vec_lambda$a' ) )
& ( C
= ( 'j$' @ ( 'i$' @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( 'i$' @ ( B @ 'mult_row$' ) @ 'fun_app$n' ) ) )
& ( B
= ( A @ ( 'i$' @ ( 'a$' @ 'interchange_rows$' ) @ 'fun_app$d' ) ) )
& ( A @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( 'j$' @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( ( 'uu$' @ 'least$' )
= A ) )
=> 'thesis$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom240) ).
thf(2404,plain,
! [A: 'N$',B: 'A_b_vec_n_vec$',C: 'A_b_vec_n_vec$'] :
( ( ( ( 'j$' @ ( 'i$' @ ( 'a$' @ 'gauss_Jordan_in_ij$' ) ) )
= ( C @ ( B @ 'uua$' ) @ 'vec_lambda$a' ) )
& ( C
= ( 'j$' @ ( 'i$' @ ( B @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) @ ( 'one$' @ 'divide$' @ 'fun_app$m' ) @ ( 'i$' @ ( B @ 'mult_row$' ) @ 'fun_app$n' ) ) )
& ( B
= ( A @ ( 'i$' @ ( 'a$' @ 'interchange_rows$' ) @ 'fun_app$d' ) ) )
& ( A @ ( 'i$' @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( ( 'j$' @ ( A @ ( 'a$' @ 'vec_nth$a' @ 'fun_app$b' ) @ 'vec_nth$' @ 'fun_app$a' ) )
!= 'zero$' )
& ( ( 'uu$' @ 'least$' )
= A ) )
=> 'thesis$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(120,axiom,
! [A: 'N_bool_fun$',B: 'N$'] :
( ! [C: 'N$'] :
( ! [D: 'N$'] :
( ( D @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( D @ ( A @ 'fun_app$' ) ) )
=> ( C @ ( A @ 'fun_app$' ) ) )
=> ( B @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom273) ).
thf(960,plain,
! [A: 'N_bool_fun$',B: 'N$'] :
( ! [C: 'N$'] :
( ! [D: 'N$'] :
( ( D @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( D @ ( A @ 'fun_app$' ) ) )
=> ( C @ ( A @ 'fun_app$' ) ) )
=> ( B @ ( A @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(63,axiom,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$a' ) )
= ( B @ ( A @ 'uve$' ) @ 'vec_lambda$d' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom401) ).
thf(696,plain,
! [A: 'A_a_fun$',B: 'A_n_vec_n_vec$'] :
( ( B @ ( A @ 'map_matrix$a' ) )
= ( B @ ( A @ 'uve$' ) @ 'vec_lambda$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(367,axiom,
! [A: 'N$',B: 'N$'] :
( ( A = B )
<=> ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom225) ).
thf(2063,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(225,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuh$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuh$' ) ) ) @ 'fun_app$l' ) )
= ( B @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuh$' ) ) ) @ 'fun_app$l' ) )
= ( C @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom75) ).
thf(1436,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( E != B )
=> ( ( ( E != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuh$' ) ) ) @ 'fun_app$l' ) )
= ( E @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) )
& ( ( E = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuh$' ) ) ) @ 'fun_app$l' ) )
= ( B @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ) )
& ( ( E = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'uuh$' ) ) ) @ 'fun_app$l' ) )
= ( C @ ( D @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(319,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwp$' ) @ 'fun_app$f' ) )
= ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom27) ).
thf(1859,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'uwp$' ) @ 'fun_app$f' ) )
= ( B @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(135,axiom,
! [A: 'A_n_vec_a_fun$',B: 'A_n_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$d' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$f' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ ( A @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom115) ).
thf(1033,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$d' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( D @ ( C @ ( B @ 'vec_nth$f' ) @ 'vec_nth$c' @ 'fun_app$f' ) @ ( A @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(286,axiom,
! [A: 'N$'] :
~ ( A @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom310) ).
thf(1710,plain,
! [A: 'N$'] :
~ ( A @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(404,axiom,
! [A: 'A_b_vec$',B: 'A_b_vec$'] :
( ( A = B )
<=> ! [C: 'B$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom139) ).
thf(2241,plain,
! [A: 'A_b_vec$',B: 'A_b_vec$'] :
( ( ! [C: 'B$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: 'B$'] :
( ( C @ ( A @ 'vec_nth$' @ 'fun_app$a' ) )
= ( C @ ( B @ 'vec_nth$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(28,axiom,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A
= ( C @ ( B @ 'fun_app$ag' ) ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom308) ).
thf(575,plain,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A
= ( C @ ( B @ 'fun_app$ag' ) ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(102,axiom,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A
= ( C @ ( B @ 'fun_app$ag' ) ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom236) ).
thf(860,plain,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( A
= ( C @ ( B @ 'fun_app$ag' ) ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(407,axiom,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$'] :
( ( ( A @ 'vec_nth$a' )
= ( B @ 'vec_nth$a' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom130) ).
thf(2265,plain,
! [A: 'A_b_vec_n_vec$',B: 'A_b_vec_n_vec$'] :
( ( ( 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)],[407]) ).
thf(14,axiom,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( A @ ( 'zero$a' @ 'times$d' @ 'fun_app$u' ) )
= 'zero$a' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom452) ).
thf(528,plain,
! [A: 'A_b_vec_n_vec_n_vec$'] :
( ( A @ ( 'zero$a' @ 'times$d' @ 'fun_app$u' ) )
= 'zero$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(339,axiom,
! [A: 'N$',B: 'N$'] :
( ( A = B )
<=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom212) ).
thf(1923,plain,
! [A: 'N$',B: 'N$'] :
( ( ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(454,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( E @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( E @ ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( E @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom173) ).
thf(2507,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$',E: 'N$'] :
( ( ( D != B )
=> ( ( ( D != C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( E @ ( D @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) )
& ( ( D = C )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( E @ ( B @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ) )
& ( ( D = B )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$' ) ) @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( E @ ( C @ ( A @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(334,axiom,
! [A: 'N$'] :
~ ( A @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom290) ).
thf(1902,plain,
! [A: 'N$'] :
~ ( A @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(327,axiom,
! [A: 'N$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom170) ).
thf(1885,plain,
! [A: 'N$'] : ( A @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(104,axiom,
! [A: 'A_n_vec$'] :
( ( 'one$b' @ ( A @ 'times$a' @ 'fun_app$p' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom466) ).
thf(871,plain,
! [A: 'A_n_vec$'] :
( ( 'one$b' @ ( A @ 'times$a' @ 'fun_app$p' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(43,axiom,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom311) ).
thf(624,plain,
! [A: 'N$',B: 'N_n_fun$',C: 'N$',D: 'N$'] :
( ( ! [E: 'N$',F: 'N$'] :
( ( F @ ( E @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( F @ ( B @ 'fun_app$ag' ) @ ( E @ ( B @ 'fun_app$ag' ) @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( D @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( C @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( D @ ( B @ 'fun_app$ag' ) @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(96,axiom,
! [A: 'A_b_vec$'] :
( ( 'zero$d' @ ( A @ 'times$b' @ 'fun_app$k' ) )
= 'zero$d' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom459) ).
thf(839,plain,
! [A: 'A_b_vec$'] :
( ( 'zero$d' @ ( A @ 'times$b' @ 'fun_app$k' ) )
= 'zero$d' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(462,axiom,
! [A: 'A_b_vec$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uwv$' ) @ 'fun_app$a' ) )
= ( B @ ( A @ 'vec_nth$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom33) ).
thf(2539,plain,
! [A: 'A_b_vec$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uwv$' ) @ 'fun_app$a' ) )
= ( B @ ( A @ 'vec_nth$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(287,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom301) ).
thf(1713,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(325,axiom,
! [A: 'A_b_vec_b_vec$',B: 'B$'] :
( ( B @ ( A @ 'uuc$' @ 'fun_app$e' ) )
= ( B @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ ( 'uminus$b' @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12) ).
thf(1880,plain,
! [A: 'A_b_vec_b_vec$',B: 'B$'] :
( ( B @ ( A @ 'uuc$' @ 'fun_app$e' ) )
= ( B @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) @ ( 'uminus$b' @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(129,axiom,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom239) ).
thf(1004,plain,
! [A: 'N$',B: 'N$'] :
( ( B @ ( A @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ( ( A @ ( B @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(37,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$a' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( A @ 'uup$' ) ) ) @ 'vec_lambda$b' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom423) ).
thf(607,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'interchange_rows_row$a' ) ) @ 'fun_app$f' ) )
= ( D @ ( C @ ( B @ ( A @ 'uup$' ) ) ) @ 'vec_lambda$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(381,axiom,
! [A: 'N$'] :
( ( A @ ( 'one$b' @ 'uminus$a' @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( 'one$' @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom263) ).
thf(2138,plain,
! [A: 'N$'] :
( ( A @ ( 'one$b' @ 'uminus$a' @ 'vec_nth$e' @ 'fun_app$l' ) )
= ( 'one$' @ ( 'uminus$c' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(262,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom374) ).
thf(1606,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(117,axiom,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$e' ) @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'times$a' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom472) ).
thf(935,plain,
! [A: 'A_n_vec_n_vec$',B: 'A_n_vec_n_vec$',C: 'N$'] :
( ( C @ ( B @ ( A @ 'times$e' ) @ 'vec_nth$c' @ 'fun_app$f' ) )
= ( C @ ( B @ 'vec_nth$c' @ 'fun_app$f' ) @ ( C @ ( A @ 'vec_nth$c' @ 'fun_app$f' ) @ 'times$a' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(280,axiom,
! [A: 'A_b_vec_b_vec$',B: 'B_a_b_vec_fun$'] :
( ! [C: 'B$'] :
( ( C @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) )
= ( C @ ( B @ 'fun_app$e' ) ) )
<=> ( ( B @ 'vec_lambda$c' )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom336) ).
thf(1681,plain,
! [A: 'A_b_vec_b_vec$',B: 'B_a_b_vec_fun$'] :
( ( ( ( B @ 'vec_lambda$c' )
= A )
=> ! [C: 'B$'] :
( ( C @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) )
= ( C @ ( B @ 'fun_app$e' ) ) ) )
& ( ! [C: 'B$'] :
( ( C @ ( A @ 'vec_nth$d' @ 'fun_app$e' ) )
= ( C @ ( B @ 'fun_app$e' ) ) )
=> ( ( B @ 'vec_lambda$c' )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(440,axiom,
( 'uxy$'
= ( 'one$' @ 'times$c' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom496) ).
thf(2436,plain,
( 'uxy$'
= ( 'one$' @ 'times$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(317,axiom,
! [A: 'A_b_vec$',B: 'A_b_vec$'] :
( ( ( B @ ( A @ 'times$b' @ 'fun_app$k' ) )
!= 'zero$d' )
=> ( ( B != 'zero$d' )
& ( A != 'zero$d' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom479) ).
thf(1848,plain,
! [A: 'A_b_vec$',B: 'A_b_vec$'] :
( ( ( B @ ( A @ 'times$b' @ 'fun_app$k' ) )
!= 'zero$d' )
=> ( ( B != 'zero$d' )
& ( A != 'zero$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(441,axiom,
! [A: 'N$'] :
( ( A @ ( 'uwc$' @ 'fun_app$b' ) )
= 'one$c' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom100) ).
thf(2438,plain,
! [A: 'N$'] :
( ( A @ ( 'uwc$' @ 'fun_app$b' ) )
= 'one$c' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(218,axiom,
! [A: 'A_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom198) ).
thf(1416,plain,
! [A: 'A_n_vec_n_vec$',B: 'N$'] :
( ( B @ ( B @ ( A @ 'interchange_rows$a' ) @ 'fun_app$h' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(370,axiom,
! [A: 'A_b_vec_a_b_vec_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$f' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom117) ).
thf(2087,plain,
! [A: 'A_b_vec_a_b_vec_fun$',B: 'A_b_vec_n_vec_n_vec$',C: 'N$',D: 'N$'] :
( ( D @ ( C @ ( B @ ( A @ 'map_matrix$f' ) @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) )
= ( D @ ( C @ ( B @ 'vec_nth$b' @ 'fun_app$d' ) @ 'vec_nth$a' @ 'fun_app$b' ) @ ( A @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(337,axiom,
! [A: 'N_n_bool_fun_fun$',B: 'N$',C: 'N$'] :
( ( ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ) )
=> ( C @ ( B @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom223) ).
thf(1912,plain,
! [A: 'N_n_bool_fun_fun$',B: 'N$',C: 'N$'] :
( ( ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) )
& ! [D: 'N$',E: 'N$'] :
( ( D @ ( E @ ( 'less_eq$' @ 'fun_app$c' ) @ 'fun_app$' ) )
=> ( E @ ( D @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ) )
=> ( C @ ( B @ ( A @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(391,axiom,
! [A: 'B_a_fun$',B: 'B$'] :
( ( B @ ( A @ 'vec_lambda$' @ 'vec_nth$' @ 'fun_app$a' ) )
= ( B @ ( A @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom253) ).
thf(2177,plain,
! [A: 'B_a_fun$',B: 'B$'] :
( ( B @ ( A @ 'vec_lambda$' @ 'vec_nth$' @ 'fun_app$a' ) )
= ( B @ ( A @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(131,axiom,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom272) ).
thf(1014,plain,
! [A: 'N$',B: 'N$',C: 'N$'] :
( ( ( A @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) )
& ( B @ ( A @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) )
=> ( B @ ( C @ ( 'less$' @ 'fun_app$c' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(301,axiom,
( 'zero$d'
= ( 'uvu$' @ 'vec_lambda$' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom411) ).
thf(1769,plain,
( 'zero$d'
= ( 'uvu$' @ 'vec_lambda$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(58,axiom,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$'] :
( ( ( B @ ( A @ 'times$d' @ 'fun_app$u' ) )
!= 'zero$a' )
=> ( ( B != 'zero$a' )
& ( A != 'zero$a' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom477) ).
thf(676,plain,
! [A: 'A_b_vec_n_vec_n_vec$',B: 'A_b_vec_n_vec_n_vec$'] :
( ( ( B @ ( A @ 'times$d' @ 'fun_app$u' ) )
!= 'zero$a' )
=> ( ( B != 'zero$a' )
& ( A != 'zero$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(2649,plain,
$false,
inference(e,[status(thm)],[1322,1036,1337,1411,760,1454,2412,628,518,2427,2250,2163,645,892,1586,2452,777,555,762,1068,1808,1205,2099,2114,1793,1692,1173,994,2527,2590,1401,655,2380,2195,1608,1137,1310,715,2141,1872,1327,2476,1919,2042,1999,2316,747,913,670,2575,2548,709,973,1935,1359,1803,1265,1887,1409,1430,1985,2039,1760,2501,802,1577,2126,1132,1330,2217,702,751,853,1892,2169,1147,1319,969,1568,2158,1963,1875,2533,1741,881,1489,924,1664,789,1811,1373,1632,2259,485,1864,2034,1960,966,821,2090,591,1183,1283,687,2281,634,2530,2002,1433,1600,2392,2205,1975,1104,1697,1651,1074,512,2047,2093,1783,1736,1636,1730,534,2232,2409,1900,894,2560,1042,1580,1570,598,1502,561,1487,693,1238,1883,1274,2441,1519,2596,2132,729,1555,1296,1624,583,1159,1210,1392,842,2464,1938,1195,2211,742,874,2377,615,1111,1856,610,499,857,2498,1234,1541,1096,1672,884,1361,1292,642,1414,637,1700,2172,2349,1889,1419,1739,1461,537,1424,2455,2551,1016,1207,1612,1039,1099,2536,1451,1456,1231,1552,569,1720,1627,1114,1324,2504,1776,997,515,2519,1202,938,1241,2208,508,921,558,1895,1185,718,773,586,2144,1727,2602,2524,601,1135,1648,1251,618,2275,2149,1219,824,732,1389,2489,2016,1124,1669,572,1733,1107,1092,2557,1464,1638,1271,2308,2166,1090,2319,1356,1675,540,2521,900,2229,2415,1349,567,1144,1771,764,604,2084,2214,2383,1574,1806,1011,990,2284,1492,1603,2299,1969,1307,1471,631,2605,2129,2111,1630,594,621,1862,848,1838,2593,2542,2278,1381,1820,2578,890,1667,2180,2025,1080,2632,799,1909,1162,726,932,1952,2365,2350,1245,1176,1000,1477,1694,658,521,1171,983,2075,2418,1213,827,1528,2620,868,851,1102,2054,2096,531,1905,1277,2449,2564,553,490,1583,648,487,2567,1748,525,712,690,640,1070,707,2192,2012,1780,2386,705,1156,1484,2160,1499,673,1987,791,502,1262,2337,1763,2322,1813,1300,1538,2486,2545,2599,544,907,744,1766,1898,1141,1023,1427,1504,1094,1717,612,1972,1052,1940,1421,2479,2045,1966,1949,1817,1517,1216,1448,2305,2226,1866,2389,2135,2554,1062,652,2608,1822,786,1558,588,699,1030,1689,667,2183,1513,1661,684,2036,2623,2421,1077,2362,2374,2287,1774,2302,1280,1678,833,818,1593,1303,1757,1480,735,950,835,2587,1248,2050,564,1989,1495,2334,506,1056,2404,960,696,2063,1436,1859,1033,1710,2241,575,860,2265,528,1923,2507,1902,1885,871,624,839,2539,1713,1880,1004,607,2138,1606,935,1681,2436,1848,2438,1416,2087,1912,2177,1014,1769,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP325_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Fri Sep 25 19:07:13 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.87/1.55 % [INFO] Parsing done (568ms).
% 2.87/1.56 % [INFO] Running in sequential loop mode.
% 3.87/1.94 % [INFO] eprover registered as external prover.
% 3.87/1.95 % [INFO] Scanning for conjecture ...
% 4.33/2.18 % [INFO] Found a conjecture (or negated_conjecture) and 503 axioms. Running axiom selection ...
% 5.36/2.44 % [INFO] Axiom selection finished. Selected 482 axioms (removed 21 axioms).
% 6.84/2.84 % [INFO] Problem is typed first-order (TPTP TFF).
% 6.84/2.87 % [INFO] Type checking passed.
% 6.84/2.88 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 12.72/4.32 % [INFO] [Domain constraints] Detected constraint on tlbool
% 12.72/4.32 % [INFO] [Domain constraints] dom(tlbool) ⊆ {tltrue,tlfalse}
% 19.35/5.81 % External prover 'e' found a proof!
% 19.35/5.81 % [INFO] Killing All external provers ...
% 19.35/5.81 % Time passed: 5267ms (effective reasoning time: 4240ms)
% 19.35/5.81 % 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)>
% 19.35/5.81 % Axioms used in derivation (482): axiom326, axiom32, axiom260, axiom280, axiom127, axiom315, axiom116, axiom452, axiom491, axiom28, axiom76, axiom273, axiom61, axiom230, axiom100, axiom6, axiom54, axiom480, axiom396, axiom25, axiom369, axiom14, axiom474, axiom333, axiom221, axiom214, axiom295, axiom485, axiom322, axiom307, axiom496, axiom284, axiom423, axiom169, axiom65, axiom36, axiom203, axiom142, axiom311, axiom291, axiom441, axiom430, axiom50, axiom158, axiom131, axiom10, axiom386, axiom392, axiom337, axiom344, axiom138, axiom119, axiom210, axiom407, axiom191, axiom477, axiom17, axiom401, axiom22, axiom397, axiom412, axiom460, axiom354, axiom467, axiom257, axiom172, axiom147, axiom341, axiom173, axiom109, axiom348, axiom184, axiom329, axiom376, axiom266, axiom445, axiom42, axiom239, axiom300, axiom350, axiom372, axiom195, axiom162, axiom358, axiom161, axiom123, axiom246, axiom383, axiom2, axiom134, axiom456, axiom33, axiom150, axiom11, axiom130, axiom235, axiom98, formula_503, axiom304, axiom225, axiom473, axiom365, axiom39, axiom499, axiom330, axiom418, axiom484, axiom112, axiom251, axiom64, axiom283, axiom126, axiom427, axiom59, axiom247, axiom48, axiom217, axiom343, axiom27, axiom352, axiom411, axiom294, axiom179, axiom363, axiom314, axiom289, axiom437, axiom236, axiom151, axiom115, axiom94, axiom83, axiom101, axiom336, axiom308, axiom321, axiom35, axiom78, axiom24, axiom278, axiom272, axiom228, axiom405, axiom455, axiom475, axiom121, axiom132, axiom490, axiom56, axiom466, axiom137, axiom206, axiom143, axiom318, axiom60, axiom0, axiom240, axiom290, axiom13, axiom53, axiom359, axiom416, axiom489, axiom108, axiom395, axiom387, axiom16, axiom459, axiom400, axiom258, axiom75, axiom448, axiom385, axiom478, axiom157, axiom90, axiom168, axiom332, axiom9, axiom303, axiom366, axiom207, axiom494, axiom133, axiom80, axiom371, axiom422, axiom185, axiom472, axiom202, axiom252, axiom146, axiom97, axiom192, axiom355, axiom360, axiom391, axiom263, axiom415, axiom254, axiom444, axiom45, axiom174, axiom398, axiom382, axiom483, axiom229, axiom319, axiom347, axiom180, axiom67, axiom213, axiom450, axiom196, axiom232, axiom243, axiom426, axiom72, axiom461, axiom463, axiom310, axiom449, axiom438, axiom267, formula_504, axiom224, axiom122, axiom38, axiom419, axiom377, axiom500, axiom91, axiom1, axiom105, axiom218, axiom86, axiom163, axiom408, axiom111, axiom120, axiom297, axiom447, axiom52, axiom156, axiom279, axiom223, axiom12, axiom390, axiom331, axiom212, axiom501, axiom342, axiom381, axiom193, axiom34, axiom79, axiom152, axiom425, axiom167, axiom454, axiom190, axiom205, axiom364, axiom443, axiom41, axiom96, axiom149, axiom189, axiom375, axiom394, axiom23, axiom93, axiom227, axiom182, axiom476, axiom216, axiom286, axiom479, axiom313, axiom118, axiom275, axiom63, axiom19, axiom458, axiom102, axiom8, axiom410, axiom320, axiom30, axiom370, axiom201, axiom178, axiom259, axiom74, axiom276, axiom451, axiom85, axiom145, axiom233, axiom220, axiom302, axiom367, axiom378, axiom57, axiom471, axiom186, axiom497, axiom164, axiom374, axiom440, axiom282, axiom271, axiom287, axiom4, axiom255, axiom106, axiom153, axiom324, axiom71, axiom462, axiom15, axiom129, axiom114, axiom244, axiom136, axiom414, axiom170, axiom181, axiom482, axiom486, axiom346, axiom262, axiom68, axiom335, axiom268, axiom293, axiom175, axiom237, axiom26, axiom356, axiom298, axiom46, axiom439, axiom469, axiom110, axiom125, axiom49, axiom219, axiom197, axiom248, axiom421, axiom199, axiom166, axiom18, axiom457, axiom338, axiom242, axiom379, axiom88, axiom389, axiom226, axiom442, axiom327, axiom399, axiom66, axiom345, axiom464, axiom215, axiom204, axiom296, axiom141, axiom357, axiom274, axiom117, axiom393, axiom44, axiom222, axiom323, axiom446, axiom84, axiom269, axiom453, axiom81, axiom103, axiom231, axiom306, axiom155, axiom495, axiom253, axiom368, axiom99, axiom148, axiom128, axiom316, axiom285, axiom20, axiom349, axiom249, axiom183, axiom301, axiom211, axiom29, axiom361, axiom429, axiom177, axiom31, axiom380, axiom188, axiom264, axiom431, axiom208, axiom159, axiom402, axiom384, axiom73, axiom107, axiom417, axiom339, axiom154, axiom40, axiom265, axiom165, axiom47, axiom270, axiom113, axiom176, axiom171, axiom3, axiom305, axiom424, axiom187, axiom245, axiom288, axiom69, axiom317, axiom135, axiom277, axiom373, axiom198, axiom144, axiom312, axiom55, axiom281, axiom95, axiom70, axiom238, axiom465, axiom299, axiom351, axiom124, axiom261, axiom77, axiom413, axiom256, axiom334, axiom160, axiom43, axiom481, axiom406, axiom388, axiom420, axiom62, axiom498, axiom209, axiom21, axiom139, axiom200, axiom250, axiom58, axiom292, axiom234, axiom362, axiom51, axiom309, axiom470, axiom468, axiom492, axiom328, axiom140, axiom340, axiom194, axiom353
% 19.35/5.81 % No. of inferences in proof: 968
% 19.35/5.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5267 ms resp. 4240 ms w/o parsing
% 20.65/6.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.65/6.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------