%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP341_10 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 : Tue Sep 29 11:39:24 AM UTC 2026
% Result : Satisfiable 2.17s 0.95s
% Output : FiniteModel 2.17s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
tff('declare_$i1',type,
'fmb_$i_1': $i ).
tff('finite_domain_$i',axiom,
! [X: $i] : ( X = 'fmb_$i_1' ) ).
tff('declare_A_n_vec_n_vec_set_set$',type,
'A_n_vec_n_vec_set_set$': $tType ).
tff('declare_A_n_vec_n_vec_set_set$1',type,
'fmb_A_n_vec_n_vec_set_set$_1': 'A_n_vec_n_vec_set_set$' ).
tff('declare_A_n_vec_n_vec_set_set$2',type,
'fmb_A_n_vec_n_vec_set_set$_2': 'A_n_vec_n_vec_set_set$' ).
tff('declare_A_n_vec_n_vec_set_set$3',type,
'fmb_A_n_vec_n_vec_set_set$_3': 'A_n_vec_n_vec_set_set$' ).
tff('finite_domain_A_n_vec_n_vec_set_set$',axiom,
! [X: 'A_n_vec_n_vec_set_set$'] :
( ( X = 'fmb_A_n_vec_n_vec_set_set$_1' )
| ( X = 'fmb_A_n_vec_n_vec_set_set$_2' )
| ( X = 'fmb_A_n_vec_n_vec_set_set$_3' ) ) ).
tff('distinct_domain_A_n_vec_n_vec_set_set$',axiom,
( ( 'fmb_A_n_vec_n_vec_set_set$_1' != 'fmb_A_n_vec_n_vec_set_set$_2' )
& ( 'fmb_A_n_vec_n_vec_set_set$_1' != 'fmb_A_n_vec_n_vec_set_set$_3' )
& ( 'fmb_A_n_vec_n_vec_set_set$_2' != 'fmb_A_n_vec_n_vec_set_set$_3' ) ) ).
tff('declare_A_set_set$',type,
'A_set_set$': $tType ).
tff('declare_A_set_set$1',type,
'fmb_A_set_set$_1': 'A_set_set$' ).
tff('declare_A_set_set$2',type,
'fmb_A_set_set$_2': 'A_set_set$' ).
tff('declare_A_set_set$3',type,
'fmb_A_set_set$_3': 'A_set_set$' ).
tff('finite_domain_A_set_set$',axiom,
! [X: 'A_set_set$'] :
( ( X = 'fmb_A_set_set$_1' )
| ( X = 'fmb_A_set_set$_2' )
| ( X = 'fmb_A_set_set$_3' ) ) ).
tff('distinct_domain_A_set_set$',axiom,
( ( 'fmb_A_set_set$_1' != 'fmb_A_set_set$_2' )
& ( 'fmb_A_set_set$_1' != 'fmb_A_set_set$_3' )
& ( 'fmb_A_set_set$_2' != 'fmb_A_set_set$_3' ) ) ).
tff('declare_A_n_vec_set$',type,
'A_n_vec_set$': $tType ).
tff('declare_A_n_vec_set$1',type,
'fmb_A_n_vec_set$_1': 'A_n_vec_set$' ).
tff('finite_domain_A_n_vec_set$',axiom,
! [X: 'A_n_vec_set$'] : ( X = 'fmb_A_n_vec_set$_1' ) ).
tff('declare_A_n_vec_n_vec_bool_fun$',type,
'A_n_vec_n_vec_bool_fun$': $tType ).
tff('declare_A_n_vec_n_vec_bool_fun$1',type,
'fmb_A_n_vec_n_vec_bool_fun$_1': 'A_n_vec_n_vec_bool_fun$' ).
tff('declare_A_n_vec_n_vec_bool_fun$2',type,
'fmb_A_n_vec_n_vec_bool_fun$_2': 'A_n_vec_n_vec_bool_fun$' ).
tff('declare_A_n_vec_n_vec_bool_fun$3',type,
'fmb_A_n_vec_n_vec_bool_fun$_3': 'A_n_vec_n_vec_bool_fun$' ).
tff('finite_domain_A_n_vec_n_vec_bool_fun$',axiom,
! [X: 'A_n_vec_n_vec_bool_fun$'] :
( ( X = 'fmb_A_n_vec_n_vec_bool_fun$_1' )
| ( X = 'fmb_A_n_vec_n_vec_bool_fun$_2' )
| ( X = 'fmb_A_n_vec_n_vec_bool_fun$_3' ) ) ).
tff('distinct_domain_A_n_vec_n_vec_bool_fun$',axiom,
( ( 'fmb_A_n_vec_n_vec_bool_fun$_1' != 'fmb_A_n_vec_n_vec_bool_fun$_2' )
& ( 'fmb_A_n_vec_n_vec_bool_fun$_1' != 'fmb_A_n_vec_n_vec_bool_fun$_3' )
& ( 'fmb_A_n_vec_n_vec_bool_fun$_2' != 'fmb_A_n_vec_n_vec_bool_fun$_3' ) ) ).
tff('declare_A_n_vec_n_vec$',type,
'A_n_vec_n_vec$': $tType ).
tff('declare_A_n_vec_n_vec$1',type,
'fmb_A_n_vec_n_vec$_1': 'A_n_vec_n_vec$' ).
tff('declare_A_n_vec_n_vec$2',type,
'fmb_A_n_vec_n_vec$_2': 'A_n_vec_n_vec$' ).
tff('finite_domain_A_n_vec_n_vec$',axiom,
! [X: 'A_n_vec_n_vec$'] :
( ( X = 'fmb_A_n_vec_n_vec$_1' )
| ( X = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('distinct_domain_A_n_vec_n_vec$',axiom,
'fmb_A_n_vec_n_vec$_1' != 'fmb_A_n_vec_n_vec$_2' ).
tff('declare_Nat$',type,
'Nat$': $tType ).
tff('declare_Nat$1',type,
'fmb_Nat$_1': 'Nat$' ).
tff('declare_Nat$2',type,
'fmb_Nat$_2': 'Nat$' ).
tff('declare_Nat$3',type,
'fmb_Nat$_3': 'Nat$' ).
tff('finite_domain_Nat$',axiom,
! [X: 'Nat$'] :
( ( X = 'fmb_Nat$_1' )
| ( X = 'fmb_Nat$_2' )
| ( X = 'fmb_Nat$_3' ) ) ).
tff('distinct_domain_Nat$',axiom,
( ( 'fmb_Nat$_1' != 'fmb_Nat$_2' )
& ( 'fmb_Nat$_1' != 'fmb_Nat$_3' )
& ( 'fmb_Nat$_2' != 'fmb_Nat$_3' ) ) ).
tff('declare_A_n_vec_n_vec_set$',type,
'A_n_vec_n_vec_set$': $tType ).
tff('declare_A_n_vec_n_vec_set$1',type,
'fmb_A_n_vec_n_vec_set$_1': 'A_n_vec_n_vec_set$' ).
tff('declare_A_n_vec_n_vec_set$2',type,
'fmb_A_n_vec_n_vec_set$_2': 'A_n_vec_n_vec_set$' ).
tff('declare_A_n_vec_n_vec_set$3',type,
'fmb_A_n_vec_n_vec_set$_3': 'A_n_vec_n_vec_set$' ).
tff('finite_domain_A_n_vec_n_vec_set$',axiom,
! [X: 'A_n_vec_n_vec_set$'] :
( ( X = 'fmb_A_n_vec_n_vec_set$_1' )
| ( X = 'fmb_A_n_vec_n_vec_set$_2' )
| ( X = 'fmb_A_n_vec_n_vec_set$_3' ) ) ).
tff('distinct_domain_A_n_vec_n_vec_set$',axiom,
( ( 'fmb_A_n_vec_n_vec_set$_1' != 'fmb_A_n_vec_n_vec_set$_2' )
& ( 'fmb_A_n_vec_n_vec_set$_1' != 'fmb_A_n_vec_n_vec_set$_3' )
& ( 'fmb_A_n_vec_n_vec_set$_2' != 'fmb_A_n_vec_n_vec_set$_3' ) ) ).
tff('declare_N$',type,
'N$': $tType ).
tff('declare_N$1',type,
'fmb_N$_1': 'N$' ).
tff('finite_domain_N$',axiom,
! [X: 'N$'] : ( X = 'fmb_N$_1' ) ).
tff('declare_Num$',type,
'Num$': $tType ).
tff('declare_Num$1',type,
'fmb_Num$_1': 'Num$' ).
tff('finite_domain_Num$',axiom,
! [X: 'Num$'] : ( X = 'fmb_Num$_1' ) ).
tff('declare_Num_set$',type,
'Num_set$': $tType ).
tff('declare_Num_set$1',type,
'fmb_Num_set$_1': 'Num_set$' ).
tff('declare_Num_set$2',type,
'fmb_Num_set$_2': 'Num_set$' ).
tff('declare_Num_set$3',type,
'fmb_Num_set$_3': 'Num_set$' ).
tff('finite_domain_Num_set$',axiom,
! [X: 'Num_set$'] :
( ( X = 'fmb_Num_set$_1' )
| ( X = 'fmb_Num_set$_2' )
| ( X = 'fmb_Num_set$_3' ) ) ).
tff('distinct_domain_Num_set$',axiom,
( ( 'fmb_Num_set$_1' != 'fmb_Num_set$_2' )
& ( 'fmb_Num_set$_1' != 'fmb_Num_set$_3' )
& ( 'fmb_Num_set$_2' != 'fmb_Num_set$_3' ) ) ).
tff(declare_tlbool,type,
tlbool: $tType ).
tff(declare_tlbool1,type,
fmb_tlbool_1: tlbool ).
tff(declare_tlbool2,type,
fmb_tlbool_2: tlbool ).
tff(finite_domain_tlbool,axiom,
! [X: tlbool] :
( ( X = fmb_tlbool_1 )
| ( X = fmb_tlbool_2 ) ) ).
tff(distinct_domain_tlbool,axiom,
fmb_tlbool_1 != fmb_tlbool_2 ).
tff('declare_A_bool_fun$',type,
'A_bool_fun$': $tType ).
tff('declare_A_bool_fun$1',type,
'fmb_A_bool_fun$_1': 'A_bool_fun$' ).
tff('declare_A_bool_fun$2',type,
'fmb_A_bool_fun$_2': 'A_bool_fun$' ).
tff('declare_A_bool_fun$3',type,
'fmb_A_bool_fun$_3': 'A_bool_fun$' ).
tff('finite_domain_A_bool_fun$',axiom,
! [X: 'A_bool_fun$'] :
( ( X = 'fmb_A_bool_fun$_1' )
| ( X = 'fmb_A_bool_fun$_2' )
| ( X = 'fmb_A_bool_fun$_3' ) ) ).
tff('distinct_domain_A_bool_fun$',axiom,
( ( 'fmb_A_bool_fun$_1' != 'fmb_A_bool_fun$_2' )
& ( 'fmb_A_bool_fun$_1' != 'fmb_A_bool_fun$_3' )
& ( 'fmb_A_bool_fun$_2' != 'fmb_A_bool_fun$_3' ) ) ).
tff('declare_A_set$',type,
'A_set$': $tType ).
tff('declare_A_set$1',type,
'fmb_A_set$_1': 'A_set$' ).
tff('finite_domain_A_set$',axiom,
! [X: 'A_set$'] : ( X = 'fmb_A_set$_1' ) ).
tff('declare_A_n_vec_set_set$',type,
'A_n_vec_set_set$': $tType ).
tff('declare_A_n_vec_set_set$1',type,
'fmb_A_n_vec_set_set$_1': 'A_n_vec_set_set$' ).
tff('declare_A_n_vec_set_set$2',type,
'fmb_A_n_vec_set_set$_2': 'A_n_vec_set_set$' ).
tff('declare_A_n_vec_set_set$3',type,
'fmb_A_n_vec_set_set$_3': 'A_n_vec_set_set$' ).
tff('finite_domain_A_n_vec_set_set$',axiom,
! [X: 'A_n_vec_set_set$'] :
( ( X = 'fmb_A_n_vec_set_set$_1' )
| ( X = 'fmb_A_n_vec_set_set$_2' )
| ( X = 'fmb_A_n_vec_set_set$_3' ) ) ).
tff('distinct_domain_A_n_vec_set_set$',axiom,
( ( 'fmb_A_n_vec_set_set$_1' != 'fmb_A_n_vec_set_set$_2' )
& ( 'fmb_A_n_vec_set_set$_1' != 'fmb_A_n_vec_set_set$_3' )
& ( 'fmb_A_n_vec_set_set$_2' != 'fmb_A_n_vec_set_set$_3' ) ) ).
tff('declare_A$',type,
'A$': $tType ).
tff('declare_A$1',type,
'fmb_A$_1': 'A$' ).
tff('declare_A$2',type,
'fmb_A$_2': 'A$' ).
tff('finite_domain_A$',axiom,
! [X: 'A$'] :
( ( X = 'fmb_A$_1' )
| ( X = 'fmb_A$_2' ) ) ).
tff('distinct_domain_A$',axiom,
'fmb_A$_1' != 'fmb_A$_2' ).
tff('declare_A_n_vec$',type,
'A_n_vec$': $tType ).
tff('declare_A_n_vec$1',type,
'fmb_A_n_vec$_1': 'A_n_vec$' ).
tff('declare_A_n_vec$2',type,
'fmb_A_n_vec$_2': 'A_n_vec$' ).
tff('finite_domain_A_n_vec$',axiom,
! [X: 'A_n_vec$'] :
( ( X = 'fmb_A_n_vec$_1' )
| ( X = 'fmb_A_n_vec$_2' ) ) ).
tff('distinct_domain_A_n_vec$',axiom,
'fmb_A_n_vec$_1' != 'fmb_A_n_vec$_2' ).
tff('declare_A_a_fun$',type,
'A_a_fun$': $tType ).
tff('declare_A_a_fun$1',type,
'fmb_A_a_fun$_1': 'A_a_fun$' ).
tff('declare_A_a_fun$2',type,
'fmb_A_a_fun$_2': 'A_a_fun$' ).
tff('declare_A_a_fun$3',type,
'fmb_A_a_fun$_3': 'A_a_fun$' ).
tff('finite_domain_A_a_fun$',axiom,
! [X: 'A_a_fun$'] :
( ( X = 'fmb_A_a_fun$_1' )
| ( X = 'fmb_A_a_fun$_2' )
| ( X = 'fmb_A_a_fun$_3' ) ) ).
tff('distinct_domain_A_a_fun$',axiom,
( ( 'fmb_A_a_fun$_1' != 'fmb_A_a_fun$_2' )
& ( 'fmb_A_a_fun$_1' != 'fmb_A_a_fun$_3' )
& ( 'fmb_A_a_fun$_2' != 'fmb_A_a_fun$_3' ) ) ).
tff('declare_A_n_vec_n_vec_n_vec$',type,
'A_n_vec_n_vec_n_vec$': $tType ).
tff('declare_A_n_vec_n_vec_n_vec$1',type,
'fmb_A_n_vec_n_vec_n_vec$_1': 'A_n_vec_n_vec_n_vec$' ).
tff('declare_A_n_vec_n_vec_n_vec$2',type,
'fmb_A_n_vec_n_vec_n_vec$_2': 'A_n_vec_n_vec_n_vec$' ).
tff('finite_domain_A_n_vec_n_vec_n_vec$',axiom,
! [X: 'A_n_vec_n_vec_n_vec$'] :
( ( X = 'fmb_A_n_vec_n_vec_n_vec$_1' )
| ( X = 'fmb_A_n_vec_n_vec_n_vec$_2' ) ) ).
tff('distinct_domain_A_n_vec_n_vec_n_vec$',axiom,
'fmb_A_n_vec_n_vec_n_vec$_1' != 'fmb_A_n_vec_n_vec_n_vec$_2' ).
tff('declare_A_n_vec_bool_fun$',type,
'A_n_vec_bool_fun$': $tType ).
tff('declare_A_n_vec_bool_fun$1',type,
'fmb_A_n_vec_bool_fun$_1': 'A_n_vec_bool_fun$' ).
tff('declare_A_n_vec_bool_fun$2',type,
'fmb_A_n_vec_bool_fun$_2': 'A_n_vec_bool_fun$' ).
tff('declare_A_n_vec_bool_fun$3',type,
'fmb_A_n_vec_bool_fun$_3': 'A_n_vec_bool_fun$' ).
tff('finite_domain_A_n_vec_bool_fun$',axiom,
! [X: 'A_n_vec_bool_fun$'] :
( ( X = 'fmb_A_n_vec_bool_fun$_1' )
| ( X = 'fmb_A_n_vec_bool_fun$_2' )
| ( X = 'fmb_A_n_vec_bool_fun$_3' ) ) ).
tff('distinct_domain_A_n_vec_bool_fun$',axiom,
( ( 'fmb_A_n_vec_bool_fun$_1' != 'fmb_A_n_vec_bool_fun$_2' )
& ( 'fmb_A_n_vec_bool_fun$_1' != 'fmb_A_n_vec_bool_fun$_3' )
& ( 'fmb_A_n_vec_bool_fun$_2' != 'fmb_A_n_vec_bool_fun$_3' ) ) ).
tff('declare_N_a_n_vec_n_vec_fun$',type,
'N_a_n_vec_n_vec_fun$': $tType ).
tff('declare_N_a_n_vec_n_vec_fun$1',type,
'fmb_N_a_n_vec_n_vec_fun$_1': 'N_a_n_vec_n_vec_fun$' ).
tff('declare_N_a_n_vec_n_vec_fun$2',type,
'fmb_N_a_n_vec_n_vec_fun$_2': 'N_a_n_vec_n_vec_fun$' ).
tff('declare_N_a_n_vec_n_vec_fun$3',type,
'fmb_N_a_n_vec_n_vec_fun$_3': 'N_a_n_vec_n_vec_fun$' ).
tff('finite_domain_N_a_n_vec_n_vec_fun$',axiom,
! [X: 'N_a_n_vec_n_vec_fun$'] :
( ( X = 'fmb_N_a_n_vec_n_vec_fun$_1' )
| ( X = 'fmb_N_a_n_vec_n_vec_fun$_2' )
| ( X = 'fmb_N_a_n_vec_n_vec_fun$_3' ) ) ).
tff('distinct_domain_N_a_n_vec_n_vec_fun$',axiom,
( ( 'fmb_N_a_n_vec_n_vec_fun$_1' != 'fmb_N_a_n_vec_n_vec_fun$_2' )
& ( 'fmb_N_a_n_vec_n_vec_fun$_1' != 'fmb_N_a_n_vec_n_vec_fun$_3' )
& ( 'fmb_N_a_n_vec_n_vec_fun$_2' != 'fmb_N_a_n_vec_n_vec_fun$_3' ) ) ).
tff('declare_invertible$',type,
'invertible$': 'A_n_vec_n_vec_bool_fun$' ).
tff('invertible$_definition',axiom,
'invertible$' = 'fmb_A_n_vec_n_vec_bool_fun$_1' ).
tff('declare_zero$d',type,
'zero$d': 'A_set$' ).
tff('zero$d_definition',axiom,
'zero$d' = 'fmb_A_set$_1' ).
tff('declare_zero$c',type,
'zero$c': 'A_n_vec$' ).
tff('zero$c_definition',axiom,
'zero$c' = 'fmb_A_n_vec$_1' ).
tff('declare_zero$f',type,
'zero$f': 'A_n_vec_set$' ).
tff('zero$f_definition',axiom,
'zero$f' = 'fmb_A_n_vec_set$_1' ).
tff('declare_one$',type,
'one$': 'A$' ).
tff('one$_definition',axiom,
'one$' = 'fmb_A$_1' ).
tff('declare_zero$b',type,
'zero$b': 'A_n_vec_n_vec_n_vec$' ).
tff('zero$b_definition',axiom,
'zero$b' = 'fmb_A_n_vec_n_vec_n_vec$_1' ).
tff(declare_tltrue,type,
tltrue: tlbool ).
tff(tltrue_definition,axiom,
tltrue = fmb_tlbool_1 ).
tff('declare_one$b',type,
'one$b': 'A_n_vec_n_vec$' ).
tff('one$b_definition',axiom,
'one$b' = 'fmb_A_n_vec_n_vec$_1' ).
tff('declare_a$',type,
'a$': 'A_n_vec_n_vec$' ).
tff('a$_definition',axiom,
'a$' = 'fmb_A_n_vec_n_vec$_1' ).
tff('declare_reduced_row_echelon_form$',type,
'reduced_row_echelon_form$': 'A_n_vec_n_vec_bool_fun$' ).
tff('reduced_row_echelon_form$_definition',axiom,
'reduced_row_echelon_form$' = 'fmb_A_n_vec_n_vec_bool_fun$_2' ).
tff('declare_one$a',type,
'one$a': 'A_n_vec$' ).
tff('one$a_definition',axiom,
'one$a' = 'fmb_A_n_vec$_2' ).
tff('declare_zero$a',type,
'zero$a': 'A_n_vec_n_vec$' ).
tff('zero$a_definition',axiom,
'zero$a' = 'fmb_A_n_vec_n_vec$_2' ).
tff('declare_orthogonal_matrix$',type,
'orthogonal_matrix$': 'A_n_vec_n_vec_bool_fun$' ).
tff('orthogonal_matrix$_definition',axiom,
'orthogonal_matrix$' = 'fmb_A_n_vec_n_vec_bool_fun$_1' ).
tff('declare_one$c',type,
'one$c': 'A_set$' ).
tff('one$c_definition',axiom,
'one$c' = 'fmb_A_set$_1' ).
tff('declare_zero$',type,
'zero$': 'A$' ).
tff('zero$_definition',axiom,
'zero$' = 'fmb_A$_2' ).
tff(declare_tlfalse,type,
tlfalse: tlbool ).
tff(tlfalse_definition,axiom,
tlfalse = fmb_tlbool_2 ).
tff('declare_zero$e',type,
'zero$e': 'A_n_vec_n_vec_set$' ).
tff('zero$e_definition',axiom,
'zero$e' = 'fmb_A_n_vec_n_vec_set$_1' ).
tff('declare_p$',type,
'p$': 'A_n_vec_n_vec$' ).
tff('p$_definition',axiom,
'p$' = 'fmb_A_n_vec_n_vec$_1' ).
tff('declare_numeral$a',type,
'numeral$a': 'Num$' > 'A_n_vec_n_vec$' ).
tff('function_numeral$a',axiom,
'numeral$a'('fmb_Num$_1') = 'fmb_A_n_vec_n_vec$_2' ).
tff('declare_uu$',type,
'uu$': 'A_set$' > 'A_bool_fun$' ).
tff('function_uu$',axiom,
'uu$'('fmb_A_set$_1') = 'fmb_A_bool_fun$_2' ).
tff('declare_dbl_inc$a',type,
'dbl_inc$a': 'A_n_vec$' > 'A_n_vec$' ).
tff('function_dbl_inc$a',axiom,
( ( 'dbl_inc$a'('fmb_A_n_vec$_1') = 'fmb_A_n_vec$_2' )
& ( 'dbl_inc$a'('fmb_A_n_vec$_2') = 'fmb_A_n_vec$_2' ) ) ).
tff('declare_mat$',type,
'mat$': 'A$' > 'A_n_vec_n_vec$' ).
tff('function_mat$',axiom,
( ( 'mat$'('fmb_A$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'mat$'('fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_dbl_inc$',type,
'dbl_inc$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff('function_dbl_inc$',axiom,
( ( 'dbl_inc$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'dbl_inc$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_1' ) ) ).
tff('declare_uub$',type,
'uub$': 'A_n_vec_set$' > 'A_n_vec_bool_fun$' ).
tff('function_uub$',axiom,
'uub$'('fmb_A_n_vec_set$_1') = 'fmb_A_n_vec_bool_fun$_2' ).
tff('declare_matrix_vector_mult$',type,
'matrix_vector_mult$': ( 'A_n_vec_n_vec$' * 'A_n_vec$' ) > 'A_n_vec$' ).
tff('function_matrix_vector_mult$',axiom,
( ( 'matrix_vector_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_1' )
& ( 'matrix_vector_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_2' )
& ( 'matrix_vector_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_1' )
& ( 'matrix_vector_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_1' ) ) ).
tff('declare_times$d',type,
'times$d': ( 'A_n_vec_set$' * 'A_n_vec_set$' ) > 'A_n_vec_set$' ).
tff('function_times$d',axiom,
'times$d'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set$_1') = 'fmb_A_n_vec_set$_1' ).
tff('declare_vector_matrix_mult$a',type,
'vector_matrix_mult$a': ( 'A_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec$' ).
tff('function_vector_matrix_mult$a',axiom,
( ( 'vector_matrix_mult$a'('fmb_A_n_vec$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec$_1' )
& ( 'vector_matrix_mult$a'('fmb_A_n_vec$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec$_1' )
& ( 'vector_matrix_mult$a'('fmb_A_n_vec$_2','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec$_2' )
& ( 'vector_matrix_mult$a'('fmb_A_n_vec$_2','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec$_1' ) ) ).
tff('declare_axis$',type,
'axis$': ( 'N$' * 'A_n_vec$' ) > 'A_n_vec_n_vec$' ).
tff('function_axis$',axiom,
( ( 'axis$'('fmb_N$_1','fmb_A_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'axis$'('fmb_N$_1','fmb_A_n_vec$_2') = 'fmb_A_n_vec_n_vec$_1' ) ) ).
tff('declare_columnvector$',type,
'columnvector$': 'A_n_vec$' > 'A_n_vec_n_vec$' ).
tff('function_columnvector$',axiom,
( ( 'columnvector$'('fmb_A_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'columnvector$'('fmb_A_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_gauss_Jordan$',type,
'gauss_Jordan$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff('function_gauss_Jordan$',axiom,
( ( 'gauss_Jordan$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'gauss_Jordan$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_plus$g',type,
'plus$g': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).
tff('function_plus$g',axiom,
( ( 'plus$g'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'plus$g'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'plus$g'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'plus$g'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_times$g',type,
'times$g': ( 'Num$' * 'Num$' ) > 'Num$' ).
tff('function_times$g',axiom,
'times$g'('fmb_Num$_1','fmb_Num$_1') = 'fmb_Num$_1' ).
tff('declare_collect$a',type,
'collect$a': 'A_n_vec_n_vec_bool_fun$' > 'A_n_vec_n_vec_set$' ).
tff('function_collect$a',axiom,
( ( 'collect$a'('fmb_A_n_vec_n_vec_bool_fun$_1') = 'fmb_A_n_vec_n_vec_set$_2' )
& ( 'collect$a'('fmb_A_n_vec_n_vec_bool_fun$_2') = 'fmb_A_n_vec_n_vec_set$_3' )
& ( 'collect$a'('fmb_A_n_vec_n_vec_bool_fun$_3') = 'fmb_A_n_vec_n_vec_set$_1' ) ) ).
tff('declare_axis$a',type,
'axis$a': ( 'N$' * 'A$' ) > 'A_n_vec$' ).
tff('function_axis$a',axiom,
( ( 'axis$a'('fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec$_2' )
& ( 'axis$a'('fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec$_1' ) ) ).
tff('declare_plus$c',type,
'plus$c': ( 'A_n_vec_n_vec_set_set$' * 'A_n_vec_n_vec_set_set$' ) > 'A_n_vec_n_vec_set_set$' ).
tff('function_plus$c',axiom,
( ( 'plus$c'('fmb_A_n_vec_n_vec_set_set$_1','fmb_A_n_vec_n_vec_set_set$_1') = 'fmb_A_n_vec_n_vec_set_set$_2' )
& ( 'plus$c'('fmb_A_n_vec_n_vec_set_set$_1','fmb_A_n_vec_n_vec_set_set$_2') = 'fmb_A_n_vec_n_vec_set_set$_3' )
& ( 'plus$c'('fmb_A_n_vec_n_vec_set_set$_1','fmb_A_n_vec_n_vec_set_set$_3') = 'fmb_A_n_vec_n_vec_set_set$_3' )
& ( 'plus$c'('fmb_A_n_vec_n_vec_set_set$_2','fmb_A_n_vec_n_vec_set_set$_1') = 'fmb_A_n_vec_n_vec_set_set$_3' )
& ( 'plus$c'('fmb_A_n_vec_n_vec_set_set$_2','fmb_A_n_vec_n_vec_set_set$_2') = 'fmb_A_n_vec_n_vec_set_set$_3' )
& ( 'plus$c'('fmb_A_n_vec_n_vec_set_set$_2','fmb_A_n_vec_n_vec_set_set$_3') = 'fmb_A_n_vec_n_vec_set_set$_3' )
& ( 'plus$c'('fmb_A_n_vec_n_vec_set_set$_3','fmb_A_n_vec_n_vec_set_set$_1') = 'fmb_A_n_vec_n_vec_set_set$_3' )
& ( 'plus$c'('fmb_A_n_vec_n_vec_set_set$_3','fmb_A_n_vec_n_vec_set_set$_2') = 'fmb_A_n_vec_n_vec_set_set$_3' )
& ( 'plus$c'('fmb_A_n_vec_n_vec_set_set$_3','fmb_A_n_vec_n_vec_set_set$_3') = 'fmb_A_n_vec_n_vec_set_set$_3' ) ) ).
tff('declare_plus$i',type,
'plus$i': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec_n_vec$' ).
tff('function_plus$i',axiom,
( ( 'plus$i'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_1' )
& ( 'plus$i'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_2' )
& ( 'plus$i'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_2' )
& ( 'plus$i'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_1' ) ) ).
tff('declare_vec$a',type,
'vec$a': 'A_n_vec$' > 'A_n_vec_n_vec$' ).
tff('function_vec$a',axiom,
( ( 'vec$a'('fmb_A_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'vec$a'('fmb_A_n_vec$_2') = 'fmb_A_n_vec_n_vec$_1' ) ) ).
tff('declare_times$a',type,
'times$a': ( 'A_n_vec$' * 'A_n_vec$' ) > 'A_n_vec$' ).
tff('function_times$a',axiom,
( ( 'times$a'('fmb_A_n_vec$_1','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_1' )
& ( 'times$a'('fmb_A_n_vec$_1','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_1' )
& ( 'times$a'('fmb_A_n_vec$_2','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_1' )
& ( 'times$a'('fmb_A_n_vec$_2','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_2' ) ) ).
tff('declare_times$',type,
'times$': ( 'A$' * 'A$' ) > 'A$' ).
tff('function_times$',axiom,
( ( 'times$'('fmb_A$_1','fmb_A$_1') = 'fmb_A$_1' )
& ( 'times$'('fmb_A$_1','fmb_A$_2') = 'fmb_A$_2' )
& ( 'times$'('fmb_A$_2','fmb_A$_1') = 'fmb_A$_2' )
& ( 'times$'('fmb_A$_2','fmb_A$_2') = 'fmb_A$_2' ) ) ).
tff('declare_collect$',type,
'collect$': 'A_bool_fun$' > 'A_set$' ).
tff('function_collect$',axiom,
( ( 'collect$'('fmb_A_bool_fun$_1') = 'fmb_A_set$_1' )
& ( 'collect$'('fmb_A_bool_fun$_2') = 'fmb_A_set$_1' )
& ( 'collect$'('fmb_A_bool_fun$_3') = 'fmb_A_set$_1' ) ) ).
tff('declare_matrix_inv$',type,
'matrix_inv$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff('function_matrix_inv$',axiom,
( ( 'matrix_inv$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'matrix_inv$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_equivalent_matrices$',type,
'equivalent_matrices$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_bool_fun$' ).
tff('function_equivalent_matrices$',axiom,
( ( 'equivalent_matrices$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_bool_fun$_1' )
& ( 'equivalent_matrices$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_bool_fun$_3' ) ) ).
tff('declare_plus$a',type,
'plus$a': ( 'A_set_set$' * 'A_set_set$' ) > 'A_set_set$' ).
tff('function_plus$a',axiom,
( ( 'plus$a'('fmb_A_set_set$_1','fmb_A_set_set$_1') = 'fmb_A_set_set$_2' )
& ( 'plus$a'('fmb_A_set_set$_1','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' )
& ( 'plus$a'('fmb_A_set_set$_1','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' )
& ( 'plus$a'('fmb_A_set_set$_2','fmb_A_set_set$_1') = 'fmb_A_set_set$_3' )
& ( 'plus$a'('fmb_A_set_set$_2','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' )
& ( 'plus$a'('fmb_A_set_set$_2','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' )
& ( 'plus$a'('fmb_A_set_set$_3','fmb_A_set_set$_1') = 'fmb_A_set_set$_3' )
& ( 'plus$a'('fmb_A_set_set$_3','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' )
& ( 'plus$a'('fmb_A_set_set$_3','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' ) ) ).
tff('declare_plus$',type,
'plus$': ( 'A_set$' * 'A_set$' ) > 'A_set$' ).
tff('function_plus$',axiom,
'plus$'('fmb_A_set$_1','fmb_A_set$_1') = 'fmb_A_set$_1' ).
tff('declare_plus$h',type,
'plus$h': ( 'A$' * 'A$' ) > 'A$' ).
tff('function_plus$h',axiom,
( ( 'plus$h'('fmb_A$_1','fmb_A$_1') = 'fmb_A$_2' )
& ( 'plus$h'('fmb_A$_1','fmb_A$_2') = 'fmb_A$_1' )
& ( 'plus$h'('fmb_A$_2','fmb_A$_1') = 'fmb_A$_1' )
& ( 'plus$h'('fmb_A$_2','fmb_A$_2') = 'fmb_A$_2' ) ) ).
tff('declare_row_add$',type,
'row_add$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' ) > 'A_n_vec_n_vec$' ).
tff('function_row_add$',axiom,
( ( 'row_add$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'row_add$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'row_add$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'row_add$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_numeral$',type,
'numeral$': 'Num$' > 'A_n_vec$' ).
tff('function_numeral$',axiom,
'numeral$'('fmb_Num$_1') = 'fmb_A_n_vec$_2' ).
tff('declare_rowvector$',type,
'rowvector$': 'A_n_vec$' > 'A_n_vec_n_vec$' ).
tff('function_rowvector$',axiom,
( ( 'rowvector$'('fmb_A_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'rowvector$'('fmb_A_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_gauss_Jordan_upt_k$',type,
'gauss_Jordan_upt_k$': ( 'A_n_vec_n_vec$' * 'Nat$' ) > 'A_n_vec_n_vec$' ).
tff('function_gauss_Jordan_upt_k$',axiom,
( ( 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_1','fmb_Nat$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_1','fmb_Nat$_2') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_1','fmb_Nat$_3') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_2','fmb_Nat$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_2','fmb_Nat$_2') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'gauss_Jordan_upt_k$'('fmb_A_n_vec_n_vec$_2','fmb_Nat$_3') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_mat$a',type,
'mat$a': 'A_n_vec$' > 'A_n_vec_n_vec_n_vec$' ).
tff('function_mat$a',axiom,
( ( 'mat$a'('fmb_A_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_2' )
& ( 'mat$a'('fmb_A_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_2' ) ) ).
tff('declare_collect$b',type,
'collect$b': 'A_n_vec_bool_fun$' > 'A_n_vec_set$' ).
tff('function_collect$b',axiom,
( ( 'collect$b'('fmb_A_n_vec_bool_fun$_1') = 'fmb_A_n_vec_set$_1' )
& ( 'collect$b'('fmb_A_n_vec_bool_fun$_2') = 'fmb_A_n_vec_set$_1' )
& ( 'collect$b'('fmb_A_n_vec_bool_fun$_3') = 'fmb_A_n_vec_set$_1' ) ) ).
tff('declare_mult_column$',type,
'mult_column$': ( 'A_n_vec_n_vec$' * 'N$' * 'A$' ) > 'A_n_vec_n_vec$' ).
tff('function_mult_column$',axiom,
( ( 'mult_column$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'mult_column$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'mult_column$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'mult_column$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_column_add$',type,
'column_add$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' ) > 'A_n_vec_n_vec$' ).
tff('function_column_add$',axiom,
( ( 'column_add$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'column_add$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'column_add$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'column_add$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_plus$b',type,
'plus$b': ( 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$' ) > 'A_n_vec_n_vec_set$' ).
tff('function_plus$b',axiom,
( ( 'plus$b'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_1' )
& ( 'plus$b'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_2' )
& ( 'plus$b'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_3' )
& ( 'plus$b'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_2' )
& ( 'plus$b'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_1' )
& ( 'plus$b'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_3' )
& ( 'plus$b'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_3' )
& ( 'plus$b'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_3' )
& ( 'plus$b'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_3' ) ) ).
tff('declare_divide$',type,
'divide$': 'A$' > 'A_a_fun$' ).
tff('function_divide$',axiom,
( ( 'divide$'('fmb_A$_1') = 'fmb_A_a_fun$_2' )
& ( 'divide$'('fmb_A$_2') = 'fmb_A_a_fun$_1' ) ) ).
tff('declare_matrix_matrix_mult$',type,
'matrix_matrix_mult$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).
tff('function_matrix_matrix_mult$',axiom,
( ( 'matrix_matrix_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'matrix_matrix_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'matrix_matrix_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'matrix_matrix_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_transpose$',type,
'transpose$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff('function_transpose$',axiom,
( ( 'transpose$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'transpose$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_fun_app$d',type,
'fun_app$d': ( 'A_a_fun$' * 'A$' ) > 'A$' ).
tff('function_fun_app$d',axiom,
( ( 'fun_app$d'('fmb_A_a_fun$_1','fmb_A$_1') = 'fmb_A$_2' )
& ( 'fun_app$d'('fmb_A_a_fun$_1','fmb_A$_2') = 'fmb_A$_2' )
& ( 'fun_app$d'('fmb_A_a_fun$_2','fmb_A$_1') = 'fmb_A$_1' )
& ( 'fun_app$d'('fmb_A_a_fun$_2','fmb_A$_2') = 'fmb_A$_2' )
& ( 'fun_app$d'('fmb_A_a_fun$_3','fmb_A$_1') = 'fmb_A$_2' )
& ( 'fun_app$d'('fmb_A_a_fun$_3','fmb_A$_2') = 'fmb_A$_2' ) ) ).
tff('declare_uua$',type,
'uua$': 'A_n_vec_n_vec_set$' > 'A_n_vec_n_vec_bool_fun$' ).
tff('function_uua$',axiom,
( ( 'uua$'('fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_bool_fun$_3' )
& ( 'uua$'('fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_bool_fun$_1' )
& ( 'uua$'('fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_bool_fun$_2' ) ) ).
tff('declare_matrix_vector_mult$a',type,
'matrix_vector_mult$a': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).
tff('function_matrix_vector_mult$a',axiom,
( ( 'matrix_vector_mult$a'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'matrix_vector_mult$a'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'matrix_vector_mult$a'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'matrix_vector_mult$a'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_column$',type,
'column$': ( 'N$' * 'A_n_vec_n_vec$' ) > 'A_n_vec$' ).
tff('function_column$',axiom,
( ( 'column$'('fmb_N$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec$_2' )
& ( 'column$'('fmb_N$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec$_1' ) ) ).
tff('declare_vec$',type,
'vec$': 'A$' > 'A_n_vec$' ).
tff('function_vec$',axiom,
( ( 'vec$'('fmb_A$_1') = 'fmb_A_n_vec$_2' )
& ( 'vec$'('fmb_A$_2') = 'fmb_A_n_vec$_1' ) ) ).
tff('declare_times$b',type,
'times$b': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).
tff('function_times$b',axiom,
( ( 'times$b'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'times$b'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'times$b'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'times$b'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_plus$d',type,
'plus$d': ( 'A_n_vec$' * 'A_n_vec$' ) > 'A_n_vec$' ).
tff('function_plus$d',axiom,
( ( 'plus$d'('fmb_A_n_vec$_1','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_1' )
& ( 'plus$d'('fmb_A_n_vec$_1','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_2' )
& ( 'plus$d'('fmb_A_n_vec$_2','fmb_A_n_vec$_1') = 'fmb_A_n_vec$_2' )
& ( 'plus$d'('fmb_A_n_vec$_2','fmb_A_n_vec$_2') = 'fmb_A_n_vec$_1' ) ) ).
tff('declare_fun_app$c',type,
'fun_app$c': ( 'N_a_n_vec_n_vec_fun$' * 'N$' ) > 'A_n_vec_n_vec$' ).
tff('function_fun_app$c',axiom,
( ( 'fun_app$c'('fmb_N_a_n_vec_n_vec_fun$_1','fmb_N$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'fun_app$c'('fmb_N_a_n_vec_n_vec_fun$_2','fmb_N$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'fun_app$c'('fmb_N_a_n_vec_n_vec_fun$_3','fmb_N$_1') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_numeral$b',type,
'numeral$b': 'Num$' > 'A$' ).
tff('function_numeral$b',axiom,
'numeral$b'('fmb_Num$_1') = 'fmb_A$_2' ).
tff('declare_plus$e',type,
'plus$e': ( 'A_n_vec_set$' * 'A_n_vec_set$' ) > 'A_n_vec_set$' ).
tff('function_plus$e',axiom,
'plus$e'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set$_1') = 'fmb_A_n_vec_set$_1' ).
tff('declare_times$h',type,
'times$h': ( 'Num_set$' * 'Num_set$' ) > 'Num_set$' ).
tff('function_times$h',axiom,
( ( 'times$h'('fmb_Num_set$_1','fmb_Num_set$_1') = 'fmb_Num_set$_2' )
& ( 'times$h'('fmb_Num_set$_1','fmb_Num_set$_2') = 'fmb_Num_set$_3' )
& ( 'times$h'('fmb_Num_set$_1','fmb_Num_set$_3') = 'fmb_Num_set$_3' )
& ( 'times$h'('fmb_Num_set$_2','fmb_Num_set$_1') = 'fmb_Num_set$_3' )
& ( 'times$h'('fmb_Num_set$_2','fmb_Num_set$_2') = 'fmb_Num_set$_3' )
& ( 'times$h'('fmb_Num_set$_2','fmb_Num_set$_3') = 'fmb_Num_set$_3' )
& ( 'times$h'('fmb_Num_set$_3','fmb_Num_set$_1') = 'fmb_Num_set$_3' )
& ( 'times$h'('fmb_Num_set$_3','fmb_Num_set$_2') = 'fmb_Num_set$_3' )
& ( 'times$h'('fmb_Num_set$_3','fmb_Num_set$_3') = 'fmb_Num_set$_3' ) ) ).
tff('declare_similar_matrices$',type,
'similar_matrices$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_bool_fun$' ).
tff('function_similar_matrices$',axiom,
( ( 'similar_matrices$'('fmb_A_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_bool_fun$_1' )
& ( 'similar_matrices$'('fmb_A_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_bool_fun$_3' ) ) ).
tff('declare_transpose$a',type,
'transpose$a': 'A_n_vec_n_vec_n_vec$' > 'A_n_vec_n_vec_n_vec$' ).
tff('function_transpose$a',axiom,
( ( 'transpose$a'('fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_1' )
& ( 'transpose$a'('fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_2' ) ) ).
tff('declare_times$c',type,
'times$c': ( 'A_set$' * 'A_set$' ) > 'A_set$' ).
tff('function_times$c',axiom,
'times$c'('fmb_A_set$_1','fmb_A_set$_1') = 'fmb_A_set$_1' ).
tff('declare_interchange_columns$',type,
'interchange_columns$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' ) > 'A_n_vec_n_vec$' ).
tff('function_interchange_columns$',axiom,
( ( 'interchange_columns$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_N$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'interchange_columns$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_N$_1') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_vector_matrix_mult$',type,
'vector_matrix_mult$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).
tff('function_vector_matrix_mult$',axiom,
( ( 'vector_matrix_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'vector_matrix_mult$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'vector_matrix_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'vector_matrix_mult$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_mult_row$',type,
'mult_row$': ( 'A_n_vec_n_vec$' * 'N$' * 'A$' ) > 'A_n_vec_n_vec$' ).
tff('function_mult_row$',axiom,
( ( 'mult_row$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_1' )
& ( 'mult_row$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'mult_row$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_A$_1') = 'fmb_A_n_vec_n_vec$_2' )
& ( 'mult_row$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1','fmb_A$_2') = 'fmb_A_n_vec_n_vec$_2' ) ) ).
tff('declare_matrix_matrix_mult$a',type,
'matrix_matrix_mult$a': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec_n_vec$' ).
tff('function_matrix_matrix_mult$a',axiom,
( ( 'matrix_matrix_mult$a'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_1' )
& ( 'matrix_matrix_mult$a'('fmb_A_n_vec_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_1' )
& ( 'matrix_matrix_mult$a'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_1') = 'fmb_A_n_vec_n_vec_n_vec$_1' )
& ( 'matrix_matrix_mult$a'('fmb_A_n_vec_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_n_vec$_2') = 'fmb_A_n_vec_n_vec_n_vec$_2' ) ) ).
tff('declare_dbl_inc$b',type,
'dbl_inc$b': 'A$' > 'A$' ).
tff('function_dbl_inc$b',axiom,
( ( 'dbl_inc$b'('fmb_A$_1') = 'fmb_A$_1' )
& ( 'dbl_inc$b'('fmb_A$_2') = 'fmb_A$_1' ) ) ).
tff('declare_interchange_rows$',type,
'interchange_rows$': ( 'A_n_vec_n_vec$' * 'N$' ) > 'N_a_n_vec_n_vec_fun$' ).
tff('function_interchange_rows$',axiom,
( ( 'interchange_rows$'('fmb_A_n_vec_n_vec$_1','fmb_N$_1') = 'fmb_N_a_n_vec_n_vec_fun$_2' )
& ( 'interchange_rows$'('fmb_A_n_vec_n_vec$_2','fmb_N$_1') = 'fmb_N_a_n_vec_n_vec_fun$_3' ) ) ).
tff('declare_times$e',type,
'times$e': ( 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$' ) > 'A_n_vec_n_vec_set$' ).
tff('function_times$e',axiom,
( ( 'times$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_1' )
& ( 'times$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_1' )
& ( 'times$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_1' )
& ( 'times$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_1' )
& ( 'times$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_2' )
& ( 'times$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_3' )
& ( 'times$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_1') = 'fmb_A_n_vec_n_vec_set$_1' )
& ( 'times$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_2') = 'fmb_A_n_vec_n_vec_set$_3' )
& ( 'times$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_3') = 'fmb_A_n_vec_n_vec_set$_3' ) ) ).
tff('declare_times$f',type,
'times$f': ( 'A_set_set$' * 'A_set_set$' ) > 'A_set_set$' ).
tff('function_times$f',axiom,
( ( 'times$f'('fmb_A_set_set$_1','fmb_A_set_set$_1') = 'fmb_A_set_set$_3' )
& ( 'times$f'('fmb_A_set_set$_1','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' )
& ( 'times$f'('fmb_A_set_set$_1','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' )
& ( 'times$f'('fmb_A_set_set$_2','fmb_A_set_set$_1') = 'fmb_A_set_set$_3' )
& ( 'times$f'('fmb_A_set_set$_2','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' )
& ( 'times$f'('fmb_A_set_set$_2','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' )
& ( 'times$f'('fmb_A_set_set$_3','fmb_A_set_set$_1') = 'fmb_A_set_set$_3' )
& ( 'times$f'('fmb_A_set_set$_3','fmb_A_set_set$_2') = 'fmb_A_set_set$_3' )
& ( 'times$f'('fmb_A_set_set$_3','fmb_A_set_set$_3') = 'fmb_A_set_set$_3' ) ) ).
tff('declare_plus$f',type,
'plus$f': ( 'A_n_vec_set_set$' * 'A_n_vec_set_set$' ) > 'A_n_vec_set_set$' ).
tff('function_plus$f',axiom,
( ( 'plus$f'('fmb_A_n_vec_set_set$_1','fmb_A_n_vec_set_set$_1') = 'fmb_A_n_vec_set_set$_2' )
& ( 'plus$f'('fmb_A_n_vec_set_set$_1','fmb_A_n_vec_set_set$_2') = 'fmb_A_n_vec_set_set$_3' )
& ( 'plus$f'('fmb_A_n_vec_set_set$_1','fmb_A_n_vec_set_set$_3') = 'fmb_A_n_vec_set_set$_3' )
& ( 'plus$f'('fmb_A_n_vec_set_set$_2','fmb_A_n_vec_set_set$_1') = 'fmb_A_n_vec_set_set$_3' )
& ( 'plus$f'('fmb_A_n_vec_set_set$_2','fmb_A_n_vec_set_set$_2') = 'fmb_A_n_vec_set_set$_3' )
& ( 'plus$f'('fmb_A_n_vec_set_set$_2','fmb_A_n_vec_set_set$_3') = 'fmb_A_n_vec_set_set$_3' )
& ( 'plus$f'('fmb_A_n_vec_set_set$_3','fmb_A_n_vec_set_set$_1') = 'fmb_A_n_vec_set_set$_3' )
& ( 'plus$f'('fmb_A_n_vec_set_set$_3','fmb_A_n_vec_set_set$_2') = 'fmb_A_n_vec_set_set$_3' )
& ( 'plus$f'('fmb_A_n_vec_set_set$_3','fmb_A_n_vec_set_set$_3') = 'fmb_A_n_vec_set_set$_3' ) ) ).
tff('declare_member$f',type,
'member$f': ( 'A_n_vec_set$' * 'A_n_vec_set_set$' ) > $o ).
tff('predicate_member$f',axiom,
( ~ 'member$f'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set_set$_1')
& ~ 'member$f'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set_set$_2')
& ~ 'member$f'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set_set$_3') ) ).
tff('declare_member$',type,
'member$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_set$' ) > $o ).
tff('predicate_member$',axiom,
( ~ 'member$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_set$_1')
& 'member$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_set$_2')
& 'member$'('fmb_A_n_vec_n_vec$_1','fmb_A_n_vec_n_vec_set$_3')
& 'member$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_set$_1')
& ~ 'member$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_set$_2')
& 'member$'('fmb_A_n_vec_n_vec$_2','fmb_A_n_vec_n_vec_set$_3') ) ).
tff('declare_member$e',type,
'member$e': ( 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set_set$' ) > $o ).
tff('predicate_member$e',axiom,
( ~ 'member$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set_set$_1')
& ~ 'member$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set_set$_2')
& ~ 'member$e'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set_set$_3')
& ~ 'member$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set_set$_1')
& ~ 'member$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set_set$_2')
& ~ 'member$e'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set_set$_3')
& 'member$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set_set$_1')
& 'member$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set_set$_2')
& 'member$e'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set_set$_3') ) ).
tff('declare_member$d',type,
'member$d': ( 'Num$' * 'Num_set$' ) > $o ).
tff('predicate_member$d',axiom,
( 'member$d'('fmb_Num$_1','fmb_Num_set$_1')
& 'member$d'('fmb_Num$_1','fmb_Num_set$_2')
& 'member$d'('fmb_Num$_1','fmb_Num_set$_3') ) ).
tff('declare_member$b',type,
'member$b': ( 'A$' * 'A_set$' ) > $o ).
tff('predicate_member$b',axiom,
( ~ 'member$b'('fmb_A$_1','fmb_A_set$_1')
& 'member$b'('fmb_A$_2','fmb_A_set$_1') ) ).
tff('declare_fun_app$b',type,
'fun_app$b': ( 'A_bool_fun$' * 'A$' ) > $o ).
tff('predicate_fun_app$b',axiom,
( ~ 'fun_app$b'('fmb_A_bool_fun$_1','fmb_A$_1')
& 'fun_app$b'('fmb_A_bool_fun$_1','fmb_A$_2')
& ~ 'fun_app$b'('fmb_A_bool_fun$_2','fmb_A$_1')
& 'fun_app$b'('fmb_A_bool_fun$_2','fmb_A$_2')
& ~ 'fun_app$b'('fmb_A_bool_fun$_3','fmb_A$_1')
& 'fun_app$b'('fmb_A_bool_fun$_3','fmb_A$_2') ) ).
tff('declare_less_eq$',type,
'less_eq$': ( 'A_n_vec_set$' * 'A_n_vec_set$' ) > $o ).
tff('predicate_less_eq$',axiom,
~ 'less_eq$'('fmb_A_n_vec_set$_1','fmb_A_n_vec_set$_1') ).
tff('declare_fun_app$a',type,
'fun_app$a': ( 'A_n_vec_bool_fun$' * 'A_n_vec$' ) > $o ).
tff('predicate_fun_app$a',axiom,
( ~ 'fun_app$a'('fmb_A_n_vec_bool_fun$_1','fmb_A_n_vec$_1')
& ~ 'fun_app$a'('fmb_A_n_vec_bool_fun$_1','fmb_A_n_vec$_2')
& ~ 'fun_app$a'('fmb_A_n_vec_bool_fun$_2','fmb_A_n_vec$_1')
& ~ 'fun_app$a'('fmb_A_n_vec_bool_fun$_2','fmb_A_n_vec$_2')
& ~ 'fun_app$a'('fmb_A_n_vec_bool_fun$_3','fmb_A_n_vec$_1')
& ~ 'fun_app$a'('fmb_A_n_vec_bool_fun$_3','fmb_A_n_vec$_2') ) ).
tff('declare_invertible$a',type,
'invertible$a': 'A_n_vec_n_vec_n_vec$' > $o ).
tff('predicate_invertible$a',axiom,
( ~ 'invertible$a'('fmb_A_n_vec_n_vec_n_vec$_1')
& ~ 'invertible$a'('fmb_A_n_vec_n_vec_n_vec$_2') ) ).
tff('declare_less_eq$a',type,
'less_eq$a': ( 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$' ) > $o ).
tff('predicate_less_eq$a',axiom,
( 'less_eq$a'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_1')
& ~ 'less_eq$a'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_2')
& 'less_eq$a'('fmb_A_n_vec_n_vec_set$_1','fmb_A_n_vec_n_vec_set$_3')
& ~ 'less_eq$a'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_1')
& 'less_eq$a'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_2')
& 'less_eq$a'('fmb_A_n_vec_n_vec_set$_2','fmb_A_n_vec_n_vec_set$_3')
& ~ 'less_eq$a'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_1')
& ~ 'less_eq$a'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_2')
& 'less_eq$a'('fmb_A_n_vec_n_vec_set$_3','fmb_A_n_vec_n_vec_set$_3') ) ).
tff('declare_less_eq$b',type,
'less_eq$b': ( 'A_set$' * 'A_set$' ) > $o ).
tff('predicate_less_eq$b',axiom,
'less_eq$b'('fmb_A_set$_1','fmb_A_set$_1') ).
tff('declare_member$c',type,
'member$c': ( 'A_set$' * 'A_set_set$' ) > $o ).
tff('predicate_member$c',axiom,
( ~ 'member$c'('fmb_A_set$_1','fmb_A_set_set$_1')
& ~ 'member$c'('fmb_A_set$_1','fmb_A_set_set$_2')
& ~ 'member$c'('fmb_A_set$_1','fmb_A_set_set$_3') ) ).
tff('declare_member$a',type,
'member$a': ( 'A_n_vec$' * 'A_n_vec_set$' ) > $o ).
tff('predicate_member$a',axiom,
( ~ 'member$a'('fmb_A_n_vec$_1','fmb_A_n_vec_set$_1')
& ~ 'member$a'('fmb_A_n_vec$_2','fmb_A_n_vec_set$_1') ) ).
tff('declare_fun_app$',type,
'fun_app$': ( 'A_n_vec_n_vec_bool_fun$' * 'A_n_vec_n_vec$' ) > $o ).
tff('predicate_fun_app$',axiom,
( 'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_1','fmb_A_n_vec_n_vec$_1')
& ~ 'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_1','fmb_A_n_vec_n_vec$_2')
& 'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_2','fmb_A_n_vec_n_vec$_1')
& 'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_2','fmb_A_n_vec_n_vec$_2')
& ~ 'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_3','fmb_A_n_vec_n_vec$_1')
& 'fun_app$'('fmb_A_n_vec_n_vec_bool_fun$_3','fmb_A_n_vec_n_vec$_2') ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP341_10 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/0.43 % Computer : n011.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 12:55:15 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/0.46 Running first-order model finding
% 0.17/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.17/0.95 % (2374652)Will run a generic schedule for satisfiability detection.
% 2.17/0.95 % (2374674)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2849241787:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.17/0.95 % (2374671)% WARNING: option uhcvi not known.
% 2.17/0.95 % (2374670)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1672129088_2999 on theBenchmark for (2999ds/0Mi)
% 2.17/0.95 % (2374671)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3763564321:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.17/0.95 % (2374672)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1407709601:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.17/0.95 % (2374673)dis+10_1_sil=32000:sp=arity:random_seed=2809247392:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.17/0.95 % (2374675)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3761399445:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.17/0.95 % (2374676)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2858280648:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.17/0.95 % (2374674)Instruction limit reached!
% 2.17/0.95 % (2374674)------------------------------
% 2.17/0.95 % (2374674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.17/0.95 % (2374674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/0.95 % (2374674)CaDiCaL version: 2.1.3
% 2.17/0.95 % (2374674)Termination reason: Instruction limit
% 2.17/0.95 % (2374674)Termination phase: Saturation
% 2.17/0.95 % (2374674)Time elapsed: 0.038 s
% 2.17/0.95 % (2374674)Peak memory usage: 13 MB
% 2.17/0.95 % (2374674)Instructions burned: 119 (million)
% 2.17/0.95 % (2374703)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=527012210:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.17/0.95 % (2374673)Instruction limit reached!
% 2.17/0.95 % (2374673)------------------------------
% 2.17/0.95 % (2374673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.17/0.95 % (2374673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/0.95 % (2374673)CaDiCaL version: 2.1.3
% 2.17/0.95 % (2374673)Termination reason: Instruction limit
% 2.17/0.95 % (2374673)Termination phase: Saturation
% 2.17/0.95 % (2374673)Time elapsed: 0.060 s
% 2.17/0.95 % (2374673)Peak memory usage: 13 MB
% 2.17/0.95 % (2374673)Instructions burned: 105 (million)
% 2.17/0.95 % TRYING [1]
% 2.17/0.95 % TRYING [2]
% 2.17/0.95 % (2374675)Instruction limit reached!
% 2.17/0.95 % (2374675)------------------------------
% 2.17/0.95 % (2374675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.17/0.95 % (2374675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/0.95 % (2374675)CaDiCaL version: 2.1.3
% 2.17/0.95 % (2374675)Termination reason: Instruction limit
% 2.17/0.95 % (2374675)Termination phase: Saturation
% 2.17/0.95 % (2374675)Time elapsed: 0.076 s
% 2.17/0.95 % (2374675)Peak memory usage: 13 MB
% 2.17/0.95 % (2374675)Instructions burned: 131 (million)
% 2.17/0.95 % (2374717)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2521902568:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.17/0.95 % TRYING [3]
% 2.17/0.95 % (2374676)Instruction limit reached!
% 2.17/0.95 % (2374676)------------------------------
% 2.17/0.95 % (2374676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.17/0.95 % (2374676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/0.95 % (2374676)CaDiCaL version: 2.1.3
% 2.17/0.95 % (2374676)Termination reason: Instruction limit
% 2.17/0.95 % (2374676)Termination phase: Saturation
% 2.17/0.95 % (2374676)Time elapsed: 0.095 s
% 2.17/0.95 % (2374676)Peak memory usage: 13 MB
% 2.17/0.95 % (2374676)Instructions burned: 159 (million)
% 2.17/0.95 % (2374724)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4179381746:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.17/0.95 % Detected minimum model sizes of [1,1,1,1,1,1,1,1,1,1,1]
% 2.17/0.95 % Detected maximum model sizes of [max,max,max,max,max,max,max,max,max,max,2]
% 2.17/0.95 % TRYING [1,1,1,1,1,1,1,1,1,1,1]
% 2.17/0.95 % TRYING [1,1,1,1,1,1,1,1,1,1,2]
% 2.17/0.95 % TRYING [1,1,1,1,1,1,2,1,1,1,2]
% 2.17/0.95 % (2374734)ott-21_1_sil=16000:fs=off:random_seed=300783371:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.17/0.95 % TRYING [1,1,1,1,2,1,2,1,1,1,2]
% 2.17/0.95 % TRYING [1,1,2,1,2,1,2,1,1,1,2]
% 2.17/0.95 % TRYING [2,1,2,1,2,1,2,1,1,1,2]
% 2.17/0.95 % (2374717)Instruction limit reached!
% 2.17/0.95 % (2374717)------------------------------
% 2.17/0.95 % (2374717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.17/0.95 % (2374717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/0.95 % (2374717)CaDiCaL version: 2.1.3
% 2.17/0.95 % (2374717)Termination reason: Instruction limit
% 2.17/0.95 % (2374717)Termination phase: Saturation
% 2.17/0.95 % (2374717)Time elapsed: 0.081 s
% 2.17/0.95 % (2374717)Peak memory usage: 13 MB
% 2.17/0.95 % (2374717)Instructions burned: 131 (million)
% 2.17/0.95 % TRYING [3,1,2,1,2,1,2,1,1,1,2]
% 2.17/0.95 % (2374756)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1676984668:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.17/0.95 % TRYING [4]
% 2.17/0.95 % (2374734)Instruction limit reached!
% 2.17/0.95 % (2374734)------------------------------
% 2.17/0.95 % (2374734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.17/0.95 % (2374734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/0.95 % (2374734)CaDiCaL version: 2.1.3
% 2.17/0.95 % (2374734)Termination reason: Instruction limit
% 2.17/0.95 % (2374734)Termination phase: Saturation
% 2.17/0.95 % (2374734)Time elapsed: 0.076 s
% 2.17/0.95 % (2374734)Peak memory usage: 12 MB
% 2.17/0.95 % (2374734)Instructions burned: 181 (million)
% 2.17/0.95 % (2374703)Instruction limit reached!
% 2.17/0.95 % (2374703)------------------------------
% 2.17/0.95 % (2374703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.17/0.95 % (2374703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/0.95 % (2374703)CaDiCaL version: 2.1.3
% 2.17/0.95 % (2374703)Termination reason: Instruction limit
% 2.17/0.95 % (2374703)Termination phase: Finite model building constraint generation
% 2.17/0.95 % (2374703)Time elapsed: 0.157 s
% 2.17/0.95 % (2374703)Peak memory usage: 34 MB
% 2.17/0.95 % (2374703)Instructions burned: 721 (million)
% 2.17/0.95 % TRYING [2,1,2,1,2,1,2,1,1,2,2]
% 2.17/0.95 % (2374764)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3736086951:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.17/0.95 % (2374763)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1394441976:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.17/0.95 % TRYING [3,1,2,1,2,1,2,1,1,2,2]
% 2.17/0.95 % TRYING [2,1,2,1,2,1,3,1,1,2,2]
% 2.17/0.95 % Detected minimum model sizes of [1,1,1,1,1,1,1,1,1,1,1]
% 2.17/0.95 % Detected maximum model sizes of [max,max,max,max,max,max,max,max,max,max,2]
% 2.17/0.95 % TRYING [2,1,2,1,2,1,2,1,2,2,2]
% 2.17/0.95 % TRYING [1,1,1,1,1,1,1,1,1,1,1]
% 2.17/0.95 % TRYING [1,1,1,1,1,1,1,1,1,1,2]
% 2.17/0.95 % TRYING [1,1,1,1,1,1,2,1,1,1,2]
% 2.17/0.95 % TRYING [1,1,1,1,2,1,2,1,1,1,2]
% 2.17/0.95 % TRYING [2,1,3,1,2,1,2,1,2,2,2]
% 2.17/0.95 % TRYING [1,1,2,1,2,1,2,1,1,1,2]
% 2.17/0.95 % TRYING [2,1,4,1,2,1,2,1,2,2,2]
% 2.17/0.95 % TRYING [2,1,2,1,2,1,2,1,1,1,2]
% 2.17/0.95 % TRYING [2,1,3,1,2,1,2,1,3,2,2]
% 2.17/0.95 % Finite Model Found!
% 2.17/0.95 % SZS status Satisfiable for theBenchmark
% 2.17/0.95 % (2374670) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2374652-2374670"...
% 2.17/0.95 % (2374670)...printing done.
% 2.17/0.95 % SZS output start FiniteModel for theBenchmark
% See solution above
% 2.17/0.96 % (2374670)------------------------------
% 2.17/0.96 % (2374670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.17/0.96 % (2374670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/0.96 % (2374670)CaDiCaL version: 2.1.3
% 2.17/0.96 % (2374670)Termination reason: Satisfiable
% 2.17/0.96 % (2374670)Time elapsed: 0.439 s
% 2.17/0.96 % (2374670)Peak memory usage: 23 MB
% 2.17/0.96 % (2374670)Instructions burned: 1153 (million)
% 2.17/0.96 % (2374652)Success in time 0.481 s
% 2.17/0.96 % Vampire exiting
%------------------------------------------------------------------------------