%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP323_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 11:39:21 AM UTC 2026
% Result : CounterSatisfiable 0.84s 0.61s
% Output : FiniteModel 0.84s
% 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_B_a_vec_set$',type,
'B_a_vec_set$': $tType ).
tff('declare_B_a_vec_set$1',type,
'fmb_B_a_vec_set$_1': 'B_a_vec_set$' ).
tff('declare_B_a_vec_set$2',type,
'fmb_B_a_vec_set$_2': 'B_a_vec_set$' ).
tff('finite_domain_B_a_vec_set$',axiom,
! [X: 'B_a_vec_set$'] :
( ( X = 'fmb_B_a_vec_set$_1' )
| ( X = 'fmb_B_a_vec_set$_2' ) ) ).
tff('distinct_domain_B_a_vec_set$',axiom,
'fmb_B_a_vec_set$_1' != 'fmb_B_a_vec_set$_2' ).
tff('declare_B_a_vec_a_vec$',type,
'B_a_vec_a_vec$': $tType ).
tff('declare_B_a_vec_a_vec$1',type,
'fmb_B_a_vec_a_vec$_1': 'B_a_vec_a_vec$' ).
tff('declare_B_a_vec_a_vec$2',type,
'fmb_B_a_vec_a_vec$_2': 'B_a_vec_a_vec$' ).
tff('finite_domain_B_a_vec_a_vec$',axiom,
! [X: 'B_a_vec_a_vec$'] :
( ( X = 'fmb_B_a_vec_a_vec$_1' )
| ( X = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('distinct_domain_B_a_vec_a_vec$',axiom,
'fmb_B_a_vec_a_vec$_1' != 'fmb_B_a_vec_a_vec$_2' ).
tff('declare_B_c_vec_set$',type,
'B_c_vec_set$': $tType ).
tff('declare_B_c_vec_set$1',type,
'fmb_B_c_vec_set$_1': 'B_c_vec_set$' ).
tff('declare_B_c_vec_set$2',type,
'fmb_B_c_vec_set$_2': 'B_c_vec_set$' ).
tff('finite_domain_B_c_vec_set$',axiom,
! [X: 'B_c_vec_set$'] :
( ( X = 'fmb_B_c_vec_set$_1' )
| ( X = 'fmb_B_c_vec_set$_2' ) ) ).
tff('distinct_domain_B_c_vec_set$',axiom,
'fmb_B_c_vec_set$_1' != 'fmb_B_c_vec_set$_2' ).
tff('declare_C_b_c_vec_bool_fun_fun$',type,
'C_b_c_vec_bool_fun_fun$': $tType ).
tff('declare_C_b_c_vec_bool_fun_fun$1',type,
'fmb_C_b_c_vec_bool_fun_fun$_1': 'C_b_c_vec_bool_fun_fun$' ).
tff('declare_C_b_c_vec_bool_fun_fun$2',type,
'fmb_C_b_c_vec_bool_fun_fun$_2': 'C_b_c_vec_bool_fun_fun$' ).
tff('finite_domain_C_b_c_vec_bool_fun_fun$',axiom,
! [X: 'C_b_c_vec_bool_fun_fun$'] :
( ( X = 'fmb_C_b_c_vec_bool_fun_fun$_1' )
| ( X = 'fmb_C_b_c_vec_bool_fun_fun$_2' ) ) ).
tff('distinct_domain_C_b_c_vec_bool_fun_fun$',axiom,
'fmb_C_b_c_vec_bool_fun_fun$_1' != 'fmb_C_b_c_vec_bool_fun_fun$_2' ).
tff('declare_B_c_vec_a_vec_a_vec_a_vec$',type,
'B_c_vec_a_vec_a_vec_a_vec$': $tType ).
tff('declare_B_c_vec_a_vec_a_vec_a_vec$1',type,
'fmb_B_c_vec_a_vec_a_vec_a_vec$_1': 'B_c_vec_a_vec_a_vec_a_vec$' ).
tff('declare_B_c_vec_a_vec_a_vec_a_vec$2',type,
'fmb_B_c_vec_a_vec_a_vec_a_vec$_2': 'B_c_vec_a_vec_a_vec_a_vec$' ).
tff('finite_domain_B_c_vec_a_vec_a_vec_a_vec$',axiom,
! [X: 'B_c_vec_a_vec_a_vec_a_vec$'] :
( ( X = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_1' )
| ( X = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' ) ) ).
tff('distinct_domain_B_c_vec_a_vec_a_vec_a_vec$',axiom,
'fmb_B_c_vec_a_vec_a_vec_a_vec$_1' != 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' ).
tff('declare_B_c_vec_a_vec_c_vec$',type,
'B_c_vec_a_vec_c_vec$': $tType ).
tff('declare_B_c_vec_a_vec_c_vec$1',type,
'fmb_B_c_vec_a_vec_c_vec$_1': 'B_c_vec_a_vec_c_vec$' ).
tff('declare_B_c_vec_a_vec_c_vec$2',type,
'fmb_B_c_vec_a_vec_c_vec$_2': 'B_c_vec_a_vec_c_vec$' ).
tff('finite_domain_B_c_vec_a_vec_c_vec$',axiom,
! [X: 'B_c_vec_a_vec_c_vec$'] :
( ( X = 'fmb_B_c_vec_a_vec_c_vec$_1' )
| ( X = 'fmb_B_c_vec_a_vec_c_vec$_2' ) ) ).
tff('distinct_domain_B_c_vec_a_vec_c_vec$',axiom,
'fmb_B_c_vec_a_vec_c_vec$_1' != 'fmb_B_c_vec_a_vec_c_vec$_2' ).
tff('declare_C_b_a_vec_c_vec_fun$',type,
'C_b_a_vec_c_vec_fun$': $tType ).
tff('declare_C_b_a_vec_c_vec_fun$1',type,
'fmb_C_b_a_vec_c_vec_fun$_1': 'C_b_a_vec_c_vec_fun$' ).
tff('declare_C_b_a_vec_c_vec_fun$2',type,
'fmb_C_b_a_vec_c_vec_fun$_2': 'C_b_a_vec_c_vec_fun$' ).
tff('finite_domain_C_b_a_vec_c_vec_fun$',axiom,
! [X: 'C_b_a_vec_c_vec_fun$'] :
( ( X = 'fmb_C_b_a_vec_c_vec_fun$_1' )
| ( X = 'fmb_C_b_a_vec_c_vec_fun$_2' ) ) ).
tff('distinct_domain_C_b_a_vec_c_vec_fun$',axiom,
'fmb_C_b_a_vec_c_vec_fun$_1' != 'fmb_C_b_a_vec_c_vec_fun$_2' ).
tff('declare_B_a_vec_a_vec_a_vec$',type,
'B_a_vec_a_vec_a_vec$': $tType ).
tff('declare_B_a_vec_a_vec_a_vec$1',type,
'fmb_B_a_vec_a_vec_a_vec$_1': 'B_a_vec_a_vec_a_vec$' ).
tff('declare_B_a_vec_a_vec_a_vec$2',type,
'fmb_B_a_vec_a_vec_a_vec$_2': 'B_a_vec_a_vec_a_vec$' ).
tff('finite_domain_B_a_vec_a_vec_a_vec$',axiom,
! [X: 'B_a_vec_a_vec_a_vec$'] :
( ( X = 'fmb_B_a_vec_a_vec_a_vec$_1' )
| ( X = 'fmb_B_a_vec_a_vec_a_vec$_2' ) ) ).
tff('distinct_domain_B_a_vec_a_vec_a_vec$',axiom,
'fmb_B_a_vec_a_vec_a_vec$_1' != 'fmb_B_a_vec_a_vec_a_vec$_2' ).
tff('declare_B_b_fun$',type,
'B_b_fun$': $tType ).
tff('declare_B_b_fun$1',type,
'fmb_B_b_fun$_1': 'B_b_fun$' ).
tff('declare_B_b_fun$2',type,
'fmb_B_b_fun$_2': 'B_b_fun$' ).
tff('finite_domain_B_b_fun$',axiom,
! [X: 'B_b_fun$'] :
( ( X = 'fmb_B_b_fun$_1' )
| ( X = 'fmb_B_b_fun$_2' ) ) ).
tff('distinct_domain_B_b_fun$',axiom,
'fmb_B_b_fun$_1' != 'fmb_B_b_fun$_2' ).
tff('declare_B_b_c_vec_fun$',type,
'B_b_c_vec_fun$': $tType ).
tff('declare_B_b_c_vec_fun$1',type,
'fmb_B_b_c_vec_fun$_1': 'B_b_c_vec_fun$' ).
tff('declare_B_b_c_vec_fun$2',type,
'fmb_B_b_c_vec_fun$_2': 'B_b_c_vec_fun$' ).
tff('finite_domain_B_b_c_vec_fun$',axiom,
! [X: 'B_b_c_vec_fun$'] :
( ( X = 'fmb_B_b_c_vec_fun$_1' )
| ( X = 'fmb_B_b_c_vec_fun$_2' ) ) ).
tff('distinct_domain_B_b_c_vec_fun$',axiom,
'fmb_B_b_c_vec_fun$_1' != 'fmb_B_b_c_vec_fun$_2' ).
tff('declare_A_b_a_vec_fun$',type,
'A_b_a_vec_fun$': $tType ).
tff('declare_A_b_a_vec_fun$1',type,
'fmb_A_b_a_vec_fun$_1': 'A_b_a_vec_fun$' ).
tff('declare_A_b_a_vec_fun$2',type,
'fmb_A_b_a_vec_fun$_2': 'A_b_a_vec_fun$' ).
tff('finite_domain_A_b_a_vec_fun$',axiom,
! [X: 'A_b_a_vec_fun$'] :
( ( X = 'fmb_A_b_a_vec_fun$_1' )
| ( X = 'fmb_A_b_a_vec_fun$_2' ) ) ).
tff('distinct_domain_A_b_a_vec_fun$',axiom,
'fmb_A_b_a_vec_fun$_1' != 'fmb_A_b_a_vec_fun$_2' ).
tff('declare_C_b_bool_fun_fun$',type,
'C_b_bool_fun_fun$': $tType ).
tff('declare_C_b_bool_fun_fun$1',type,
'fmb_C_b_bool_fun_fun$_1': 'C_b_bool_fun_fun$' ).
tff('declare_C_b_bool_fun_fun$2',type,
'fmb_C_b_bool_fun_fun$_2': 'C_b_bool_fun_fun$' ).
tff('finite_domain_C_b_bool_fun_fun$',axiom,
! [X: 'C_b_bool_fun_fun$'] :
( ( X = 'fmb_C_b_bool_fun_fun$_1' )
| ( X = 'fmb_C_b_bool_fun_fun$_2' ) ) ).
tff('distinct_domain_C_b_bool_fun_fun$',axiom,
'fmb_C_b_bool_fun_fun$_1' != 'fmb_C_b_bool_fun_fun$_2' ).
tff('declare_B_c_vec_bool_fun$',type,
'B_c_vec_bool_fun$': $tType ).
tff('declare_B_c_vec_bool_fun$1',type,
'fmb_B_c_vec_bool_fun$_1': 'B_c_vec_bool_fun$' ).
tff('declare_B_c_vec_bool_fun$2',type,
'fmb_B_c_vec_bool_fun$_2': 'B_c_vec_bool_fun$' ).
tff('finite_domain_B_c_vec_bool_fun$',axiom,
! [X: 'B_c_vec_bool_fun$'] :
( ( X = 'fmb_B_c_vec_bool_fun$_1' )
| ( X = 'fmb_B_c_vec_bool_fun$_2' ) ) ).
tff('distinct_domain_B_c_vec_bool_fun$',axiom,
'fmb_B_c_vec_bool_fun$_1' != 'fmb_B_c_vec_bool_fun$_2' ).
tff('declare_A_b_bool_fun_fun$',type,
'A_b_bool_fun_fun$': $tType ).
tff('declare_A_b_bool_fun_fun$1',type,
'fmb_A_b_bool_fun_fun$_1': 'A_b_bool_fun_fun$' ).
tff('declare_A_b_bool_fun_fun$2',type,
'fmb_A_b_bool_fun_fun$_2': 'A_b_bool_fun_fun$' ).
tff('finite_domain_A_b_bool_fun_fun$',axiom,
! [X: 'A_b_bool_fun_fun$'] :
( ( X = 'fmb_A_b_bool_fun_fun$_1' )
| ( X = 'fmb_A_b_bool_fun_fun$_2' ) ) ).
tff('distinct_domain_A_b_bool_fun_fun$',axiom,
'fmb_A_b_bool_fun_fun$_1' != 'fmb_A_b_bool_fun_fun$_2' ).
tff('declare_C_b_a_vec_fun$',type,
'C_b_a_vec_fun$': $tType ).
tff('declare_C_b_a_vec_fun$1',type,
'fmb_C_b_a_vec_fun$_1': 'C_b_a_vec_fun$' ).
tff('declare_C_b_a_vec_fun$2',type,
'fmb_C_b_a_vec_fun$_2': 'C_b_a_vec_fun$' ).
tff('finite_domain_C_b_a_vec_fun$',axiom,
! [X: 'C_b_a_vec_fun$'] :
( ( X = 'fmb_C_b_a_vec_fun$_1' )
| ( X = 'fmb_C_b_a_vec_fun$_2' ) ) ).
tff('distinct_domain_C_b_a_vec_fun$',axiom,
'fmb_C_b_a_vec_fun$_1' != 'fmb_C_b_a_vec_fun$_2' ).
tff('declare_B_c_vec_a_vec_b_c_vec_fun$',type,
'B_c_vec_a_vec_b_c_vec_fun$': $tType ).
tff('declare_B_c_vec_a_vec_b_c_vec_fun$1',type,
'fmb_B_c_vec_a_vec_b_c_vec_fun$_1': 'B_c_vec_a_vec_b_c_vec_fun$' ).
tff('declare_B_c_vec_a_vec_b_c_vec_fun$2',type,
'fmb_B_c_vec_a_vec_b_c_vec_fun$_2': 'B_c_vec_a_vec_b_c_vec_fun$' ).
tff('finite_domain_B_c_vec_a_vec_b_c_vec_fun$',axiom,
! [X: 'B_c_vec_a_vec_b_c_vec_fun$'] :
( ( X = 'fmb_B_c_vec_a_vec_b_c_vec_fun$_1' )
| ( X = 'fmb_B_c_vec_a_vec_b_c_vec_fun$_2' ) ) ).
tff('distinct_domain_B_c_vec_a_vec_b_c_vec_fun$',axiom,
'fmb_B_c_vec_a_vec_b_c_vec_fun$_1' != 'fmb_B_c_vec_a_vec_b_c_vec_fun$_2' ).
tff('declare_B_c_vec_b_fun$',type,
'B_c_vec_b_fun$': $tType ).
tff('declare_B_c_vec_b_fun$1',type,
'fmb_B_c_vec_b_fun$_1': 'B_c_vec_b_fun$' ).
tff('declare_B_c_vec_b_fun$2',type,
'fmb_B_c_vec_b_fun$_2': 'B_c_vec_b_fun$' ).
tff('finite_domain_B_c_vec_b_fun$',axiom,
! [X: 'B_c_vec_b_fun$'] :
( ( X = 'fmb_B_c_vec_b_fun$_1' )
| ( X = 'fmb_B_c_vec_b_fun$_2' ) ) ).
tff('distinct_domain_B_c_vec_b_fun$',axiom,
'fmb_B_c_vec_b_fun$_1' != 'fmb_B_c_vec_b_fun$_2' ).
tff('declare_B_a_vec$',type,
'B_a_vec$': $tType ).
tff('declare_B_a_vec$1',type,
'fmb_B_a_vec$_1': 'B_a_vec$' ).
tff('declare_B_a_vec$2',type,
'fmb_B_a_vec$_2': 'B_a_vec$' ).
tff('finite_domain_B_a_vec$',axiom,
! [X: 'B_a_vec$'] :
( ( X = 'fmb_B_a_vec$_1' )
| ( X = 'fmb_B_a_vec$_2' ) ) ).
tff('distinct_domain_B_a_vec$',axiom,
'fmb_B_a_vec$_1' != 'fmb_B_a_vec$_2' ).
tff('declare_A_b_a_vec_bool_fun_fun$',type,
'A_b_a_vec_bool_fun_fun$': $tType ).
tff('declare_A_b_a_vec_bool_fun_fun$1',type,
'fmb_A_b_a_vec_bool_fun_fun$_1': 'A_b_a_vec_bool_fun_fun$' ).
tff('declare_A_b_a_vec_bool_fun_fun$2',type,
'fmb_A_b_a_vec_bool_fun_fun$_2': 'A_b_a_vec_bool_fun_fun$' ).
tff('finite_domain_A_b_a_vec_bool_fun_fun$',axiom,
! [X: 'A_b_a_vec_bool_fun_fun$'] :
( ( X = 'fmb_A_b_a_vec_bool_fun_fun$_1' )
| ( X = 'fmb_A_b_a_vec_bool_fun_fun$_2' ) ) ).
tff('distinct_domain_A_b_a_vec_bool_fun_fun$',axiom,
'fmb_A_b_a_vec_bool_fun_fun$_1' != 'fmb_A_b_a_vec_bool_fun_fun$_2' ).
tff('declare_B_c_vec_a_vec$',type,
'B_c_vec_a_vec$': $tType ).
tff('declare_B_c_vec_a_vec$1',type,
'fmb_B_c_vec_a_vec$_1': 'B_c_vec_a_vec$' ).
tff('declare_B_c_vec_a_vec$2',type,
'fmb_B_c_vec_a_vec$_2': 'B_c_vec_a_vec$' ).
tff('finite_domain_B_c_vec_a_vec$',axiom,
! [X: 'B_c_vec_a_vec$'] :
( ( X = 'fmb_B_c_vec_a_vec$_1' )
| ( X = 'fmb_B_c_vec_a_vec$_2' ) ) ).
tff('distinct_domain_B_c_vec_a_vec$',axiom,
'fmb_B_c_vec_a_vec$_1' != 'fmb_B_c_vec_a_vec$_2' ).
tff('declare_C_b_a_vec_bool_fun_fun$',type,
'C_b_a_vec_bool_fun_fun$': $tType ).
tff('declare_C_b_a_vec_bool_fun_fun$1',type,
'fmb_C_b_a_vec_bool_fun_fun$_1': 'C_b_a_vec_bool_fun_fun$' ).
tff('declare_C_b_a_vec_bool_fun_fun$2',type,
'fmb_C_b_a_vec_bool_fun_fun$_2': 'C_b_a_vec_bool_fun_fun$' ).
tff('finite_domain_C_b_a_vec_bool_fun_fun$',axiom,
! [X: 'C_b_a_vec_bool_fun_fun$'] :
( ( X = 'fmb_C_b_a_vec_bool_fun_fun$_1' )
| ( X = 'fmb_C_b_a_vec_bool_fun_fun$_2' ) ) ).
tff('distinct_domain_C_b_a_vec_bool_fun_fun$',axiom,
'fmb_C_b_a_vec_bool_fun_fun$_1' != 'fmb_C_b_a_vec_bool_fun_fun$_2' ).
tff('declare_B$',type,
'B$': $tType ).
tff('declare_B$1',type,
'fmb_B$_1': 'B$' ).
tff('declare_B$2',type,
'fmb_B$_2': 'B$' ).
tff('finite_domain_B$',axiom,
! [X: 'B$'] :
( ( X = 'fmb_B$_1' )
| ( X = 'fmb_B$_2' ) ) ).
tff('distinct_domain_B$',axiom,
'fmb_B$_1' != 'fmb_B$_2' ).
tff('declare_C$',type,
'C$': $tType ).
tff('declare_C$1',type,
'fmb_C$_1': 'C$' ).
tff('finite_domain_C$',axiom,
! [X: 'C$'] : ( X = 'fmb_C$_1' ) ).
tff('declare_B_c_vec_a_vec_set$',type,
'B_c_vec_a_vec_set$': $tType ).
tff('declare_B_c_vec_a_vec_set$1',type,
'fmb_B_c_vec_a_vec_set$_1': 'B_c_vec_a_vec_set$' ).
tff('declare_B_c_vec_a_vec_set$2',type,
'fmb_B_c_vec_a_vec_set$_2': 'B_c_vec_a_vec_set$' ).
tff('finite_domain_B_c_vec_a_vec_set$',axiom,
! [X: 'B_c_vec_a_vec_set$'] :
( ( X = 'fmb_B_c_vec_a_vec_set$_1' )
| ( X = 'fmb_B_c_vec_a_vec_set$_2' ) ) ).
tff('distinct_domain_B_c_vec_a_vec_set$',axiom,
'fmb_B_c_vec_a_vec_set$_1' != 'fmb_B_c_vec_a_vec_set$_2' ).
tff('declare_C_b_fun$',type,
'C_b_fun$': $tType ).
tff('declare_C_b_fun$1',type,
'fmb_C_b_fun$_1': 'C_b_fun$' ).
tff('declare_C_b_fun$2',type,
'fmb_C_b_fun$_2': 'C_b_fun$' ).
tff('finite_domain_C_b_fun$',axiom,
! [X: 'C_b_fun$'] :
( ( X = 'fmb_C_b_fun$_1' )
| ( X = 'fmb_C_b_fun$_2' ) ) ).
tff('distinct_domain_C_b_fun$',axiom,
'fmb_C_b_fun$_1' != 'fmb_C_b_fun$_2' ).
tff('declare_B_c_vec_b_c_vec_fun$',type,
'B_c_vec_b_c_vec_fun$': $tType ).
tff('declare_B_c_vec_b_c_vec_fun$1',type,
'fmb_B_c_vec_b_c_vec_fun$_1': 'B_c_vec_b_c_vec_fun$' ).
tff('declare_B_c_vec_b_c_vec_fun$2',type,
'fmb_B_c_vec_b_c_vec_fun$_2': 'B_c_vec_b_c_vec_fun$' ).
tff('finite_domain_B_c_vec_b_c_vec_fun$',axiom,
! [X: 'B_c_vec_b_c_vec_fun$'] :
( ( X = 'fmb_B_c_vec_b_c_vec_fun$_1' )
| ( X = 'fmb_B_c_vec_b_c_vec_fun$_2' ) ) ).
tff('distinct_domain_B_c_vec_b_c_vec_fun$',axiom,
'fmb_B_c_vec_b_c_vec_fun$_1' != 'fmb_B_c_vec_b_c_vec_fun$_2' ).
tff('declare_C_b_c_vec_fun$',type,
'C_b_c_vec_fun$': $tType ).
tff('declare_C_b_c_vec_fun$1',type,
'fmb_C_b_c_vec_fun$_1': 'C_b_c_vec_fun$' ).
tff('declare_C_b_c_vec_fun$2',type,
'fmb_C_b_c_vec_fun$_2': 'C_b_c_vec_fun$' ).
tff('finite_domain_C_b_c_vec_fun$',axiom,
! [X: 'C_b_c_vec_fun$'] :
( ( X = 'fmb_C_b_c_vec_fun$_1' )
| ( X = 'fmb_C_b_c_vec_fun$_2' ) ) ).
tff('distinct_domain_C_b_c_vec_fun$',axiom,
'fmb_C_b_c_vec_fun$_1' != 'fmb_C_b_c_vec_fun$_2' ).
tff('declare_B_a_vec_c_vec$',type,
'B_a_vec_c_vec$': $tType ).
tff('declare_B_a_vec_c_vec$1',type,
'fmb_B_a_vec_c_vec$_1': 'B_a_vec_c_vec$' ).
tff('declare_B_a_vec_c_vec$2',type,
'fmb_B_a_vec_c_vec$_2': 'B_a_vec_c_vec$' ).
tff('finite_domain_B_a_vec_c_vec$',axiom,
! [X: 'B_a_vec_c_vec$'] :
( ( X = 'fmb_B_a_vec_c_vec$_1' )
| ( X = 'fmb_B_a_vec_c_vec$_2' ) ) ).
tff('distinct_domain_B_a_vec_c_vec$',axiom,
'fmb_B_a_vec_c_vec$_1' != 'fmb_B_a_vec_c_vec$_2' ).
tff('declare_B_c_vec_c_vec_a_vec$',type,
'B_c_vec_c_vec_a_vec$': $tType ).
tff('declare_B_c_vec_c_vec_a_vec$1',type,
'fmb_B_c_vec_c_vec_a_vec$_1': 'B_c_vec_c_vec_a_vec$' ).
tff('declare_B_c_vec_c_vec_a_vec$2',type,
'fmb_B_c_vec_c_vec_a_vec$_2': 'B_c_vec_c_vec_a_vec$' ).
tff('finite_domain_B_c_vec_c_vec_a_vec$',axiom,
! [X: 'B_c_vec_c_vec_a_vec$'] :
( ( X = 'fmb_B_c_vec_c_vec_a_vec$_1' )
| ( X = 'fmb_B_c_vec_c_vec_a_vec$_2' ) ) ).
tff('distinct_domain_B_c_vec_c_vec_a_vec$',axiom,
'fmb_B_c_vec_c_vec_a_vec$_1' != 'fmb_B_c_vec_c_vec_a_vec$_2' ).
tff(declare_tlbool,type,
tlbool: $tType ).
tff(declare_tlbool1,type,
fmb_tlbool_1: tlbool ).
tff(declare_tlbool2,type,
fmb_tlbool_2: tlbool ).
tff(finite_domain_tlbool,axiom,
! [X: tlbool] :
( ( X = fmb_tlbool_1 )
| ( X = fmb_tlbool_2 ) ) ).
tff(distinct_domain_tlbool,axiom,
fmb_tlbool_1 != fmb_tlbool_2 ).
tff('declare_A_b_c_vec_fun$',type,
'A_b_c_vec_fun$': $tType ).
tff('declare_A_b_c_vec_fun$1',type,
'fmb_A_b_c_vec_fun$_1': 'A_b_c_vec_fun$' ).
tff('declare_A_b_c_vec_fun$2',type,
'fmb_A_b_c_vec_fun$_2': 'A_b_c_vec_fun$' ).
tff('finite_domain_A_b_c_vec_fun$',axiom,
! [X: 'A_b_c_vec_fun$'] :
( ( X = 'fmb_A_b_c_vec_fun$_1' )
| ( X = 'fmb_A_b_c_vec_fun$_2' ) ) ).
tff('distinct_domain_A_b_c_vec_fun$',axiom,
'fmb_A_b_c_vec_fun$_1' != 'fmb_A_b_c_vec_fun$_2' ).
tff('declare_A_b_c_vec_a_vec_a_vec_bool_fun_fun$',type,
'A_b_c_vec_a_vec_a_vec_bool_fun_fun$': $tType ).
tff('declare_A_b_c_vec_a_vec_a_vec_bool_fun_fun$1',type,
'fmb_A_b_c_vec_a_vec_a_vec_bool_fun_fun$_1': 'A_b_c_vec_a_vec_a_vec_bool_fun_fun$' ).
tff('declare_A_b_c_vec_a_vec_a_vec_bool_fun_fun$2',type,
'fmb_A_b_c_vec_a_vec_a_vec_bool_fun_fun$_2': 'A_b_c_vec_a_vec_a_vec_bool_fun_fun$' ).
tff('finite_domain_A_b_c_vec_a_vec_a_vec_bool_fun_fun$',axiom,
! [X: 'A_b_c_vec_a_vec_a_vec_bool_fun_fun$'] :
( ( X = 'fmb_A_b_c_vec_a_vec_a_vec_bool_fun_fun$_1' )
| ( X = 'fmb_A_b_c_vec_a_vec_a_vec_bool_fun_fun$_2' ) ) ).
tff('distinct_domain_A_b_c_vec_a_vec_a_vec_bool_fun_fun$',axiom,
'fmb_A_b_c_vec_a_vec_a_vec_bool_fun_fun$_1' != 'fmb_A_b_c_vec_a_vec_a_vec_bool_fun_fun$_2' ).
tff('declare_A_b_c_vec_a_vec_fun$',type,
'A_b_c_vec_a_vec_fun$': $tType ).
tff('declare_A_b_c_vec_a_vec_fun$1',type,
'fmb_A_b_c_vec_a_vec_fun$_1': 'A_b_c_vec_a_vec_fun$' ).
tff('declare_A_b_c_vec_a_vec_fun$2',type,
'fmb_A_b_c_vec_a_vec_fun$_2': 'A_b_c_vec_a_vec_fun$' ).
tff('finite_domain_A_b_c_vec_a_vec_fun$',axiom,
! [X: 'A_b_c_vec_a_vec_fun$'] :
( ( X = 'fmb_A_b_c_vec_a_vec_fun$_1' )
| ( X = 'fmb_A_b_c_vec_a_vec_fun$_2' ) ) ).
tff('distinct_domain_A_b_c_vec_a_vec_fun$',axiom,
'fmb_A_b_c_vec_a_vec_fun$_1' != 'fmb_A_b_c_vec_a_vec_fun$_2' ).
tff('declare_A_b_c_vec_a_vec_a_vec_fun$',type,
'A_b_c_vec_a_vec_a_vec_fun$': $tType ).
tff('declare_A_b_c_vec_a_vec_a_vec_fun$1',type,
'fmb_A_b_c_vec_a_vec_a_vec_fun$_1': 'A_b_c_vec_a_vec_a_vec_fun$' ).
tff('declare_A_b_c_vec_a_vec_a_vec_fun$2',type,
'fmb_A_b_c_vec_a_vec_a_vec_fun$_2': 'A_b_c_vec_a_vec_a_vec_fun$' ).
tff('finite_domain_A_b_c_vec_a_vec_a_vec_fun$',axiom,
! [X: 'A_b_c_vec_a_vec_a_vec_fun$'] :
( ( X = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_1' )
| ( X = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_2' ) ) ).
tff('distinct_domain_A_b_c_vec_a_vec_a_vec_fun$',axiom,
'fmb_A_b_c_vec_a_vec_a_vec_fun$_1' != 'fmb_A_b_c_vec_a_vec_a_vec_fun$_2' ).
tff('declare_B_a_vec_a_vec_c_vec$',type,
'B_a_vec_a_vec_c_vec$': $tType ).
tff('declare_B_a_vec_a_vec_c_vec$1',type,
'fmb_B_a_vec_a_vec_c_vec$_1': 'B_a_vec_a_vec_c_vec$' ).
tff('declare_B_a_vec_a_vec_c_vec$2',type,
'fmb_B_a_vec_a_vec_c_vec$_2': 'B_a_vec_a_vec_c_vec$' ).
tff('finite_domain_B_a_vec_a_vec_c_vec$',axiom,
! [X: 'B_a_vec_a_vec_c_vec$'] :
( ( X = 'fmb_B_a_vec_a_vec_c_vec$_1' )
| ( X = 'fmb_B_a_vec_a_vec_c_vec$_2' ) ) ).
tff('distinct_domain_B_a_vec_a_vec_c_vec$',axiom,
'fmb_B_a_vec_a_vec_c_vec$_1' != 'fmb_B_a_vec_a_vec_c_vec$_2' ).
tff('declare_A_b_c_vec_bool_fun_fun$',type,
'A_b_c_vec_bool_fun_fun$': $tType ).
tff('declare_A_b_c_vec_bool_fun_fun$1',type,
'fmb_A_b_c_vec_bool_fun_fun$_1': 'A_b_c_vec_bool_fun_fun$' ).
tff('declare_A_b_c_vec_bool_fun_fun$2',type,
'fmb_A_b_c_vec_bool_fun_fun$_2': 'A_b_c_vec_bool_fun_fun$' ).
tff('finite_domain_A_b_c_vec_bool_fun_fun$',axiom,
! [X: 'A_b_c_vec_bool_fun_fun$'] :
( ( X = 'fmb_A_b_c_vec_bool_fun_fun$_1' )
| ( X = 'fmb_A_b_c_vec_bool_fun_fun$_2' ) ) ).
tff('distinct_domain_A_b_c_vec_bool_fun_fun$',axiom,
'fmb_A_b_c_vec_bool_fun_fun$_1' != 'fmb_A_b_c_vec_bool_fun_fun$_2' ).
tff('declare_A_b_c_vec_a_vec_bool_fun_fun$',type,
'A_b_c_vec_a_vec_bool_fun_fun$': $tType ).
tff('declare_A_b_c_vec_a_vec_bool_fun_fun$1',type,
'fmb_A_b_c_vec_a_vec_bool_fun_fun$_1': 'A_b_c_vec_a_vec_bool_fun_fun$' ).
tff('declare_A_b_c_vec_a_vec_bool_fun_fun$2',type,
'fmb_A_b_c_vec_a_vec_bool_fun_fun$_2': 'A_b_c_vec_a_vec_bool_fun_fun$' ).
tff('finite_domain_A_b_c_vec_a_vec_bool_fun_fun$',axiom,
! [X: 'A_b_c_vec_a_vec_bool_fun_fun$'] :
( ( X = 'fmb_A_b_c_vec_a_vec_bool_fun_fun$_1' )
| ( X = 'fmb_A_b_c_vec_a_vec_bool_fun_fun$_2' ) ) ).
tff('distinct_domain_A_b_c_vec_a_vec_bool_fun_fun$',axiom,
'fmb_A_b_c_vec_a_vec_bool_fun_fun$_1' != 'fmb_A_b_c_vec_a_vec_bool_fun_fun$_2' ).
tff('declare_B_c_vec_a_vec_a_vec$',type,
'B_c_vec_a_vec_a_vec$': $tType ).
tff('declare_B_c_vec_a_vec_a_vec$1',type,
'fmb_B_c_vec_a_vec_a_vec$_1': 'B_c_vec_a_vec_a_vec$' ).
tff('declare_B_c_vec_a_vec_a_vec$2',type,
'fmb_B_c_vec_a_vec_a_vec$_2': 'B_c_vec_a_vec_a_vec$' ).
tff('finite_domain_B_c_vec_a_vec_a_vec$',axiom,
! [X: 'B_c_vec_a_vec_a_vec$'] :
( ( X = 'fmb_B_c_vec_a_vec_a_vec$_1' )
| ( X = 'fmb_B_c_vec_a_vec_a_vec$_2' ) ) ).
tff('distinct_domain_B_c_vec_a_vec_a_vec$',axiom,
'fmb_B_c_vec_a_vec_a_vec$_1' != 'fmb_B_c_vec_a_vec_a_vec$_2' ).
tff('declare_A_b_fun$',type,
'A_b_fun$': $tType ).
tff('declare_A_b_fun$1',type,
'fmb_A_b_fun$_1': 'A_b_fun$' ).
tff('declare_A_b_fun$2',type,
'fmb_A_b_fun$_2': 'A_b_fun$' ).
tff('finite_domain_A_b_fun$',axiom,
! [X: 'A_b_fun$'] :
( ( X = 'fmb_A_b_fun$_1' )
| ( X = 'fmb_A_b_fun$_2' ) ) ).
tff('distinct_domain_A_b_fun$',axiom,
'fmb_A_b_fun$_1' != 'fmb_A_b_fun$_2' ).
tff('declare_B_set$',type,
'B_set$': $tType ).
tff('declare_B_set$1',type,
'fmb_B_set$_1': 'B_set$' ).
tff('declare_B_set$2',type,
'fmb_B_set$_2': 'B_set$' ).
tff('finite_domain_B_set$',axiom,
! [X: 'B_set$'] :
( ( X = 'fmb_B_set$_1' )
| ( X = 'fmb_B_set$_2' ) ) ).
tff('distinct_domain_B_set$',axiom,
'fmb_B_set$_1' != 'fmb_B_set$_2' ).
tff('declare_B_c_vec_b_c_vec_a_vec_fun$',type,
'B_c_vec_b_c_vec_a_vec_fun$': $tType ).
tff('declare_B_c_vec_b_c_vec_a_vec_fun$1',type,
'fmb_B_c_vec_b_c_vec_a_vec_fun$_1': 'B_c_vec_b_c_vec_a_vec_fun$' ).
tff('declare_B_c_vec_b_c_vec_a_vec_fun$2',type,
'fmb_B_c_vec_b_c_vec_a_vec_fun$_2': 'B_c_vec_b_c_vec_a_vec_fun$' ).
tff('finite_domain_B_c_vec_b_c_vec_a_vec_fun$',axiom,
! [X: 'B_c_vec_b_c_vec_a_vec_fun$'] :
( ( X = 'fmb_B_c_vec_b_c_vec_a_vec_fun$_1' )
| ( X = 'fmb_B_c_vec_b_c_vec_a_vec_fun$_2' ) ) ).
tff('distinct_domain_B_c_vec_b_c_vec_a_vec_fun$',axiom,
'fmb_B_c_vec_b_c_vec_a_vec_fun$_1' != 'fmb_B_c_vec_b_c_vec_a_vec_fun$_2' ).
tff('declare_A$',type,
'A$': $tType ).
tff('declare_A$1',type,
'fmb_A$_1': 'A$' ).
tff('finite_domain_A$',axiom,
! [X: 'A$'] : ( X = 'fmb_A$_1' ) ).
tff('declare_B_set_set$',type,
'B_set_set$': $tType ).
tff('declare_B_set_set$1',type,
'fmb_B_set_set$_1': 'B_set_set$' ).
tff('declare_B_set_set$2',type,
'fmb_B_set_set$_2': 'B_set_set$' ).
tff('finite_domain_B_set_set$',axiom,
! [X: 'B_set_set$'] :
( ( X = 'fmb_B_set_set$_1' )
| ( X = 'fmb_B_set_set$_2' ) ) ).
tff('distinct_domain_B_set_set$',axiom,
'fmb_B_set_set$_1' != 'fmb_B_set_set$_2' ).
tff('declare_B_c_vec_a_vec_a_vec_set$',type,
'B_c_vec_a_vec_a_vec_set$': $tType ).
tff('declare_B_c_vec_a_vec_a_vec_set$1',type,
'fmb_B_c_vec_a_vec_a_vec_set$_1': 'B_c_vec_a_vec_a_vec_set$' ).
tff('declare_B_c_vec_a_vec_a_vec_set$2',type,
'fmb_B_c_vec_a_vec_a_vec_set$_2': 'B_c_vec_a_vec_a_vec_set$' ).
tff('finite_domain_B_c_vec_a_vec_a_vec_set$',axiom,
! [X: 'B_c_vec_a_vec_a_vec_set$'] :
( ( X = 'fmb_B_c_vec_a_vec_a_vec_set$_1' )
| ( X = 'fmb_B_c_vec_a_vec_a_vec_set$_2' ) ) ).
tff('distinct_domain_B_c_vec_a_vec_a_vec_set$',axiom,
'fmb_B_c_vec_a_vec_a_vec_set$_1' != 'fmb_B_c_vec_a_vec_a_vec_set$_2' ).
tff('declare_B_c_vec_c_vec$',type,
'B_c_vec_c_vec$': $tType ).
tff('declare_B_c_vec_c_vec$1',type,
'fmb_B_c_vec_c_vec$_1': 'B_c_vec_c_vec$' ).
tff('declare_B_c_vec_c_vec$2',type,
'fmb_B_c_vec_c_vec$_2': 'B_c_vec_c_vec$' ).
tff('finite_domain_B_c_vec_c_vec$',axiom,
! [X: 'B_c_vec_c_vec$'] :
( ( X = 'fmb_B_c_vec_c_vec$_1' )
| ( X = 'fmb_B_c_vec_c_vec$_2' ) ) ).
tff('distinct_domain_B_c_vec_c_vec$',axiom,
'fmb_B_c_vec_c_vec$_1' != 'fmb_B_c_vec_c_vec$_2' ).
tff('declare_B_a_vec_c_vec_a_vec$',type,
'B_a_vec_c_vec_a_vec$': $tType ).
tff('declare_B_a_vec_c_vec_a_vec$1',type,
'fmb_B_a_vec_c_vec_a_vec$_1': 'B_a_vec_c_vec_a_vec$' ).
tff('declare_B_a_vec_c_vec_a_vec$2',type,
'fmb_B_a_vec_c_vec_a_vec$_2': 'B_a_vec_c_vec_a_vec$' ).
tff('finite_domain_B_a_vec_c_vec_a_vec$',axiom,
! [X: 'B_a_vec_c_vec_a_vec$'] :
( ( X = 'fmb_B_a_vec_c_vec_a_vec$_1' )
| ( X = 'fmb_B_a_vec_c_vec_a_vec$_2' ) ) ).
tff('distinct_domain_B_a_vec_c_vec_a_vec$',axiom,
'fmb_B_a_vec_c_vec_a_vec$_1' != 'fmb_B_a_vec_c_vec_a_vec$_2' ).
tff('declare_B_c_vec_a_vec_a_vec_bool_fun$',type,
'B_c_vec_a_vec_a_vec_bool_fun$': $tType ).
tff('declare_B_c_vec_a_vec_a_vec_bool_fun$1',type,
'fmb_B_c_vec_a_vec_a_vec_bool_fun$_1': 'B_c_vec_a_vec_a_vec_bool_fun$' ).
tff('declare_B_c_vec_a_vec_a_vec_bool_fun$2',type,
'fmb_B_c_vec_a_vec_a_vec_bool_fun$_2': 'B_c_vec_a_vec_a_vec_bool_fun$' ).
tff('finite_domain_B_c_vec_a_vec_a_vec_bool_fun$',axiom,
! [X: 'B_c_vec_a_vec_a_vec_bool_fun$'] :
( ( X = 'fmb_B_c_vec_a_vec_a_vec_bool_fun$_1' )
| ( X = 'fmb_B_c_vec_a_vec_a_vec_bool_fun$_2' ) ) ).
tff('distinct_domain_B_c_vec_a_vec_a_vec_bool_fun$',axiom,
'fmb_B_c_vec_a_vec_a_vec_bool_fun$_1' != 'fmb_B_c_vec_a_vec_a_vec_bool_fun$_2' ).
tff('declare_B_a_vec_bool_fun$',type,
'B_a_vec_bool_fun$': $tType ).
tff('declare_B_a_vec_bool_fun$1',type,
'fmb_B_a_vec_bool_fun$_1': 'B_a_vec_bool_fun$' ).
tff('declare_B_a_vec_bool_fun$2',type,
'fmb_B_a_vec_bool_fun$_2': 'B_a_vec_bool_fun$' ).
tff('finite_domain_B_a_vec_bool_fun$',axiom,
! [X: 'B_a_vec_bool_fun$'] :
( ( X = 'fmb_B_a_vec_bool_fun$_1' )
| ( X = 'fmb_B_a_vec_bool_fun$_2' ) ) ).
tff('distinct_domain_B_a_vec_bool_fun$',axiom,
'fmb_B_a_vec_bool_fun$_1' != 'fmb_B_a_vec_bool_fun$_2' ).
tff('declare_B_c_vec_a_vec_bool_fun$',type,
'B_c_vec_a_vec_bool_fun$': $tType ).
tff('declare_B_c_vec_a_vec_bool_fun$1',type,
'fmb_B_c_vec_a_vec_bool_fun$_1': 'B_c_vec_a_vec_bool_fun$' ).
tff('declare_B_c_vec_a_vec_bool_fun$2',type,
'fmb_B_c_vec_a_vec_bool_fun$_2': 'B_c_vec_a_vec_bool_fun$' ).
tff('finite_domain_B_c_vec_a_vec_bool_fun$',axiom,
! [X: 'B_c_vec_a_vec_bool_fun$'] :
( ( X = 'fmb_B_c_vec_a_vec_bool_fun$_1' )
| ( X = 'fmb_B_c_vec_a_vec_bool_fun$_2' ) ) ).
tff('distinct_domain_B_c_vec_a_vec_bool_fun$',axiom,
'fmb_B_c_vec_a_vec_bool_fun$_1' != 'fmb_B_c_vec_a_vec_bool_fun$_2' ).
tff('declare_B_c_vec$',type,
'B_c_vec$': $tType ).
tff('declare_B_c_vec$1',type,
'fmb_B_c_vec$_1': 'B_c_vec$' ).
tff('declare_B_c_vec$2',type,
'fmb_B_c_vec$_2': 'B_c_vec$' ).
tff('finite_domain_B_c_vec$',axiom,
! [X: 'B_c_vec$'] :
( ( X = 'fmb_B_c_vec$_1' )
| ( X = 'fmb_B_c_vec$_2' ) ) ).
tff('distinct_domain_B_c_vec$',axiom,
'fmb_B_c_vec$_1' != 'fmb_B_c_vec$_2' ).
tff('declare_B_c_vec_set_set$',type,
'B_c_vec_set_set$': $tType ).
tff('declare_B_c_vec_set_set$1',type,
'fmb_B_c_vec_set_set$_1': 'B_c_vec_set_set$' ).
tff('declare_B_c_vec_set_set$2',type,
'fmb_B_c_vec_set_set$_2': 'B_c_vec_set_set$' ).
tff('finite_domain_B_c_vec_set_set$',axiom,
! [X: 'B_c_vec_set_set$'] :
( ( X = 'fmb_B_c_vec_set_set$_1' )
| ( X = 'fmb_B_c_vec_set_set$_2' ) ) ).
tff('distinct_domain_B_c_vec_set_set$',axiom,
'fmb_B_c_vec_set_set$_1' != 'fmb_B_c_vec_set_set$_2' ).
tff('declare_B_bool_fun$',type,
'B_bool_fun$': $tType ).
tff('declare_B_bool_fun$1',type,
'fmb_B_bool_fun$_1': 'B_bool_fun$' ).
tff('declare_B_bool_fun$2',type,
'fmb_B_bool_fun$_2': 'B_bool_fun$' ).
tff('finite_domain_B_bool_fun$',axiom,
! [X: 'B_bool_fun$'] :
( ( X = 'fmb_B_bool_fun$_1' )
| ( X = 'fmb_B_bool_fun$_2' ) ) ).
tff('distinct_domain_B_bool_fun$',axiom,
'fmb_B_bool_fun$_1' != 'fmb_B_bool_fun$_2' ).
tff('declare_B_c_vec_a_vec_set_set$',type,
'B_c_vec_a_vec_set_set$': $tType ).
tff('declare_B_c_vec_a_vec_set_set$1',type,
'fmb_B_c_vec_a_vec_set_set$_1': 'B_c_vec_a_vec_set_set$' ).
tff('declare_B_c_vec_a_vec_set_set$2',type,
'fmb_B_c_vec_a_vec_set_set$_2': 'B_c_vec_a_vec_set_set$' ).
tff('finite_domain_B_c_vec_a_vec_set_set$',axiom,
! [X: 'B_c_vec_a_vec_set_set$'] :
( ( X = 'fmb_B_c_vec_a_vec_set_set$_1' )
| ( X = 'fmb_B_c_vec_a_vec_set_set$_2' ) ) ).
tff('distinct_domain_B_c_vec_a_vec_set_set$',axiom,
'fmb_B_c_vec_a_vec_set_set$_1' != 'fmb_B_c_vec_a_vec_set_set$_2' ).
tff('declare_vec$c',type,
'vec$c': 'B_c_vec_b_c_vec_a_vec_fun$' ).
tff('vec$c_definition',axiom,
'vec$c' = 'fmb_B_c_vec_b_c_vec_a_vec_fun$_1' ).
tff('declare_q$',type,
'q$': 'B$' ).
tff('q$_definition',axiom,
'q$' = 'fmb_B$_1' ).
tff('declare_b$',type,
'b$': 'A$' ).
tff('b$_definition',axiom,
'b$' = 'fmb_A$_1' ).
tff(declare_tltrue,type,
tltrue: tlbool ).
tff(tltrue_definition,axiom,
tltrue = fmb_tlbool_1 ).
tff('declare_a$',type,
'a$': 'B_c_vec_a_vec$' ).
tff('a$_definition',axiom,
'a$' = 'fmb_B_c_vec_a_vec$_1' ).
tff('declare_a$a',type,
'a$a': 'A$' ).
tff('a$a_definition',axiom,
'a$a' = 'fmb_A$_1' ).
tff('declare_vec$b',type,
'vec$b': 'B_b_c_vec_fun$' ).
tff('vec$b_definition',axiom,
'vec$b' = 'fmb_B_b_c_vec_fun$_1' ).
tff(declare_tlfalse,type,
tlfalse: tlbool ).
tff(tlfalse_definition,axiom,
tlfalse = fmb_tlbool_2 ).
tff('declare_interchange_rows$',type,
'interchange_rows$': ( 'B_a_vec_a_vec$' * 'A$' * 'A$' ) > 'B_a_vec_a_vec$' ).
tff('function_interchange_rows$',axiom,
( ( 'interchange_rows$'('fmb_B_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_B_a_vec_a_vec$_1' )
& ( 'interchange_rows$'('fmb_B_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_vec$g',type,
'vec$g': 'B_c_vec$' > 'B_c_vec_c_vec$' ).
tff('function_vec$g',axiom,
( ( 'vec$g'('fmb_B_c_vec$_1') = 'fmb_B_c_vec_c_vec$_2' )
& ( 'vec$g'('fmb_B_c_vec$_2') = 'fmb_B_c_vec_c_vec$_1' ) ) ).
tff('declare_fun_app$r',type,
'fun_app$r': ( 'A_b_a_vec_bool_fun_fun$' * 'A$' ) > 'B_a_vec_bool_fun$' ).
tff('function_fun_app$r',axiom,
( ( 'fun_app$r'('fmb_A_b_a_vec_bool_fun_fun$_1','fmb_A$_1') = 'fmb_B_a_vec_bool_fun$_2' )
& ( 'fun_app$r'('fmb_A_b_a_vec_bool_fun_fun$_2','fmb_A$_1') = 'fmb_B_a_vec_bool_fun$_2' ) ) ).
tff('declare_map_matrix$g',type,
'map_matrix$g': ( 'B_b_fun$' * 'B_a_vec_a_vec$' ) > 'B_a_vec_a_vec$' ).
tff('function_map_matrix$g',axiom,
( ( 'map_matrix$g'('fmb_B_b_fun$_1','fmb_B_a_vec_a_vec$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'map_matrix$g'('fmb_B_b_fun$_1','fmb_B_a_vec_a_vec$_2') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'map_matrix$g'('fmb_B_b_fun$_2','fmb_B_a_vec_a_vec$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'map_matrix$g'('fmb_B_b_fun$_2','fmb_B_a_vec_a_vec$_2') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_times$j',type,
'times$j': ( 'B_c_vec_a_vec_a_vec_set$' * 'B_c_vec_a_vec_a_vec_set$' ) > 'B_c_vec_a_vec_a_vec_set$' ).
tff('function_times$j',axiom,
( ( 'times$j'('fmb_B_c_vec_a_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'times$j'('fmb_B_c_vec_a_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'times$j'('fmb_B_c_vec_a_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'times$j'('fmb_B_c_vec_a_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' ) ) ).
tff('declare_transpose_row$f',type,
'transpose_row$f': ( 'B_c_vec_c_vec_a_vec$' * 'C$' ) > 'B_c_vec_a_vec$' ).
tff('function_transpose_row$f',axiom,
( ( 'transpose_row$f'('fmb_B_c_vec_c_vec_a_vec$_1','fmb_C$_1') = 'fmb_B_c_vec_a_vec$_2' )
& ( 'transpose_row$f'('fmb_B_c_vec_c_vec_a_vec$_2','fmb_C$_1') = 'fmb_B_c_vec_a_vec$_2' ) ) ).
tff('declare_vector_scalar_mult$b',type,
'vector_scalar_mult$b': ( 'B_a_vec$' * 'B_a_vec_c_vec$' ) > 'B_a_vec_c_vec$' ).
tff('function_vector_scalar_mult$b',axiom,
( ( 'vector_scalar_mult$b'('fmb_B_a_vec$_1','fmb_B_a_vec_c_vec$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'vector_scalar_mult$b'('fmb_B_a_vec$_1','fmb_B_a_vec_c_vec$_2') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'vector_scalar_mult$b'('fmb_B_a_vec$_2','fmb_B_a_vec_c_vec$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'vector_scalar_mult$b'('fmb_B_a_vec$_2','fmb_B_a_vec_c_vec$_2') = 'fmb_B_a_vec_c_vec$_2' ) ) ).
tff('declare_elt_set_plus$d',type,
'elt_set_plus$d': ( 'B_set$' * 'B_set_set$' ) > 'B_set_set$' ).
tff('function_elt_set_plus$d',axiom,
( ( 'elt_set_plus$d'('fmb_B_set$_1','fmb_B_set_set$_1') = 'fmb_B_set_set$_2' )
& ( 'elt_set_plus$d'('fmb_B_set$_1','fmb_B_set_set$_2') = 'fmb_B_set_set$_2' )
& ( 'elt_set_plus$d'('fmb_B_set$_2','fmb_B_set_set$_1') = 'fmb_B_set_set$_2' )
& ( 'elt_set_plus$d'('fmb_B_set$_2','fmb_B_set_set$_2') = 'fmb_B_set_set$_2' ) ) ).
tff('declare_transpose_row$d',type,
'transpose_row$d': 'B_a_vec_a_vec$' > 'A_b_a_vec_fun$' ).
tff('function_transpose_row$d',axiom,
( ( 'transpose_row$d'('fmb_B_a_vec_a_vec$_1') = 'fmb_A_b_a_vec_fun$_2' )
& ( 'transpose_row$d'('fmb_B_a_vec_a_vec$_2') = 'fmb_A_b_a_vec_fun$_1' ) ) ).
tff('declare_vec_nth$b',type,
'vec_nth$b': 'B_c_vec_c_vec$' > 'C_b_c_vec_fun$' ).
tff('function_vec_nth$b',axiom,
( ( 'vec_nth$b'('fmb_B_c_vec_c_vec$_1') = 'fmb_C_b_c_vec_fun$_2' )
& ( 'vec_nth$b'('fmb_B_c_vec_c_vec$_2') = 'fmb_C_b_c_vec_fun$_1' ) ) ).
tff('declare_interchange_rows$d',type,
'interchange_rows$d': ( 'B_c_vec_a_vec_a_vec$' * 'A$' ) > 'A_b_c_vec_a_vec_a_vec_fun$' ).
tff('function_interchange_rows$d',axiom,
( ( 'interchange_rows$d'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_2' )
& ( 'interchange_rows$d'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_1' ) ) ).
tff('declare_row_add_row$',type,
'row_add_row$': ( 'B_c_vec_a_vec$' * 'A$' * 'A$' * 'B$' ) > 'A_b_c_vec_fun$' ).
tff('function_row_add_row$',axiom,
( ( 'row_add_row$'('fmb_B_c_vec_a_vec$_1','fmb_A$_1','fmb_A$_1','fmb_B$_1') = 'fmb_A_b_c_vec_fun$_2' )
& ( 'row_add_row$'('fmb_B_c_vec_a_vec$_1','fmb_A$_1','fmb_A$_1','fmb_B$_2') = 'fmb_A_b_c_vec_fun$_2' )
& ( 'row_add_row$'('fmb_B_c_vec_a_vec$_2','fmb_A$_1','fmb_A$_1','fmb_B$_1') = 'fmb_A_b_c_vec_fun$_2' )
& ( 'row_add_row$'('fmb_B_c_vec_a_vec$_2','fmb_A$_1','fmb_A$_1','fmb_B$_2') = 'fmb_A_b_c_vec_fun$_2' ) ) ).
tff('declare_fun_app$g',type,
'fun_app$g': ( 'A_b_fun$' * 'A$' ) > 'B$' ).
tff('function_fun_app$g',axiom,
( ( 'fun_app$g'('fmb_A_b_fun$_1','fmb_A$_1') = 'fmb_B$_1' )
& ( 'fun_app$g'('fmb_A_b_fun$_2','fmb_A$_1') = 'fmb_B$_2' ) ) ).
tff('declare_vector_scalar_mult$c',type,
'vector_scalar_mult$c': ( 'B_c_vec$' * 'B_c_vec_c_vec$' ) > 'B_c_vec_c_vec$' ).
tff('function_vector_scalar_mult$c',axiom,
( ( 'vector_scalar_mult$c'('fmb_B_c_vec$_1','fmb_B_c_vec_c_vec$_1') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'vector_scalar_mult$c'('fmb_B_c_vec$_1','fmb_B_c_vec_c_vec$_2') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'vector_scalar_mult$c'('fmb_B_c_vec$_2','fmb_B_c_vec_c_vec$_1') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'vector_scalar_mult$c'('fmb_B_c_vec$_2','fmb_B_c_vec_c_vec$_2') = 'fmb_B_c_vec_c_vec$_1' ) ) ).
tff('declare_vec$e',type,
'vec$e': 'B_c_vec_a_vec_a_vec$' > 'B_c_vec_a_vec_a_vec_a_vec$' ).
tff('function_vec$e',axiom,
( ( 'vec$e'('fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'vec$e'('fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_1' ) ) ).
tff('declare_vector_scalar_mult$e',type,
'vector_scalar_mult$e': ( 'B_c_vec_a_vec$' * 'B_c_vec_a_vec_a_vec$' ) > 'B_c_vec_a_vec_a_vec$' ).
tff('function_vector_scalar_mult$e',axiom,
( ( 'vector_scalar_mult$e'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'vector_scalar_mult$e'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'vector_scalar_mult$e'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'vector_scalar_mult$e'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' ) ) ).
tff('declare_columnvector_row$',type,
'columnvector_row$': ( 'B_c_vec_a_vec$' * 'A$' ) > 'B_c_vec_a_vec$' ).
tff('function_columnvector_row$',axiom,
( ( 'columnvector_row$'('fmb_B_c_vec_a_vec$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'columnvector_row$'('fmb_B_c_vec_a_vec$_2','fmb_A$_1') = 'fmb_B_c_vec_a_vec$_2' ) ) ).
tff('declare_fun_app$t',type,
'fun_app$t': ( 'A_b_c_vec_a_vec_a_vec_bool_fun_fun$' * 'A$' ) > 'B_c_vec_a_vec_a_vec_bool_fun$' ).
tff('function_fun_app$t',axiom,
( ( 'fun_app$t'('fmb_A_b_c_vec_a_vec_a_vec_bool_fun_fun$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec_bool_fun$_2' )
& ( 'fun_app$t'('fmb_A_b_c_vec_a_vec_a_vec_bool_fun_fun$_2','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec_bool_fun$_2' ) ) ).
tff('declare_vec_nth$l',type,
'vec_nth$l': ( 'B_a_vec_a_vec_c_vec$' * 'C$' ) > 'B_a_vec_a_vec$' ).
tff('function_vec_nth$l',axiom,
( ( 'vec_nth$l'('fmb_B_a_vec_a_vec_c_vec$_1','fmb_C$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'vec_nth$l'('fmb_B_a_vec_a_vec_c_vec$_2','fmb_C$_1') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_elt_set_times$',type,
'elt_set_times$': ( 'B_a_vec$' * 'B_a_vec_set$' ) > 'B_a_vec_set$' ).
tff('function_elt_set_times$',axiom,
( ( 'elt_set_times$'('fmb_B_a_vec$_1','fmb_B_a_vec_set$_1') = 'fmb_B_a_vec_set$_2' )
& ( 'elt_set_times$'('fmb_B_a_vec$_1','fmb_B_a_vec_set$_2') = 'fmb_B_a_vec_set$_2' )
& ( 'elt_set_times$'('fmb_B_a_vec$_2','fmb_B_a_vec_set$_1') = 'fmb_B_a_vec_set$_2' )
& ( 'elt_set_times$'('fmb_B_a_vec$_2','fmb_B_a_vec_set$_2') = 'fmb_B_a_vec_set$_2' ) ) ).
tff('declare_plus$o',type,
'plus$o': ( 'B_set$' * 'B_set$' ) > 'B_set$' ).
tff('function_plus$o',axiom,
( ( 'plus$o'('fmb_B_set$_1','fmb_B_set$_1') = 'fmb_B_set$_2' )
& ( 'plus$o'('fmb_B_set$_1','fmb_B_set$_2') = 'fmb_B_set$_2' )
& ( 'plus$o'('fmb_B_set$_2','fmb_B_set$_1') = 'fmb_B_set$_2' )
& ( 'plus$o'('fmb_B_set$_2','fmb_B_set$_2') = 'fmb_B_set$_2' ) ) ).
tff('declare_interchange_columns_row$d',type,
'interchange_columns_row$d': ( 'B_c_vec_a_vec_a_vec$' * 'A$' * 'A$' ) > 'A_b_c_vec_a_vec_fun$' ).
tff('function_interchange_columns_row$d',axiom,
( ( 'interchange_columns_row$d'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_fun$_2' )
& ( 'interchange_columns_row$d'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_fun$_1' ) ) ).
tff('declare_interchange_columns$a',type,
'interchange_columns$a': ( 'B_c_vec_a_vec_a_vec_a_vec$' * 'A$' * 'A$' ) > 'B_c_vec_a_vec_a_vec_a_vec$' ).
tff('function_interchange_columns$a',axiom,
( ( 'interchange_columns$a'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_1' )
& ( 'interchange_columns$a'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' ) ) ).
tff('declare_vector_scalar_mult$d',type,
'vector_scalar_mult$d': 'B$' > 'B_c_vec_b_c_vec_fun$' ).
tff('function_vector_scalar_mult$d',axiom,
( ( 'vector_scalar_mult$d'('fmb_B$_1') = 'fmb_B_c_vec_b_c_vec_fun$_2' )
& ( 'vector_scalar_mult$d'('fmb_B$_2') = 'fmb_B_c_vec_b_c_vec_fun$_2' ) ) ).
tff('declare_map_matrix$c',type,
'map_matrix$c': ( 'B_c_vec_b_c_vec_fun$' * 'B_c_vec_a_vec_a_vec$' ) > 'B_c_vec_a_vec_a_vec$' ).
tff('function_map_matrix$c',axiom,
( ( 'map_matrix$c'('fmb_B_c_vec_b_c_vec_fun$_1','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'map_matrix$c'('fmb_B_c_vec_b_c_vec_fun$_1','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'map_matrix$c'('fmb_B_c_vec_b_c_vec_fun$_2','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'map_matrix$c'('fmb_B_c_vec_b_c_vec_fun$_2','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' ) ) ).
tff('declare_map_matrix$',type,
'map_matrix$': ( 'B_b_fun$' * 'B_c_vec_a_vec$' ) > 'B_c_vec_a_vec$' ).
tff('function_map_matrix$',axiom,
( ( 'map_matrix$'('fmb_B_b_fun$_1','fmb_B_c_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'map_matrix$'('fmb_B_b_fun$_1','fmb_B_c_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'map_matrix$'('fmb_B_b_fun$_2','fmb_B_c_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'map_matrix$'('fmb_B_b_fun$_2','fmb_B_c_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec$_1' ) ) ).
tff('declare_vec_nth$a',type,
'vec_nth$a': 'B_c_vec$' > 'C_b_fun$' ).
tff('function_vec_nth$a',axiom,
( ( 'vec_nth$a'('fmb_B_c_vec$_1') = 'fmb_C_b_fun$_2' )
& ( 'vec_nth$a'('fmb_B_c_vec$_2') = 'fmb_C_b_fun$_1' ) ) ).
tff('declare_plus$m',type,
'plus$m': ( 'B_c_vec_a_vec_set$' * 'B_c_vec_a_vec_set$' ) > 'B_c_vec_a_vec_set$' ).
tff('function_plus$m',axiom,
( ( 'plus$m'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'plus$m'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'plus$m'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'plus$m'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_set$_2' ) ) ).
tff('declare_collect$',type,
'collect$': 'B_c_vec_bool_fun$' > 'B_c_vec_set$' ).
tff('function_collect$',axiom,
( ( 'collect$'('fmb_B_c_vec_bool_fun$_1') = 'fmb_B_c_vec_set$_2' )
& ( 'collect$'('fmb_B_c_vec_bool_fun$_2') = 'fmb_B_c_vec_set$_1' ) ) ).
tff('declare_map_matrix$a',type,
'map_matrix$a': ( 'B_b_c_vec_fun$' * 'B_a_vec_a_vec$' ) > 'B_c_vec_a_vec_a_vec$' ).
tff('function_map_matrix$a',axiom,
( ( 'map_matrix$a'('fmb_B_b_c_vec_fun$_1','fmb_B_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_2' )
& ( 'map_matrix$a'('fmb_B_b_c_vec_fun$_1','fmb_B_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'map_matrix$a'('fmb_B_b_c_vec_fun$_2','fmb_B_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_2' )
& ( 'map_matrix$a'('fmb_B_b_c_vec_fun$_2','fmb_B_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' ) ) ).
tff('declare_vec_nth$d',type,
'vec_nth$d': 'B_c_vec_a_vec_a_vec_a_vec$' > 'A_b_c_vec_a_vec_a_vec_fun$' ).
tff('function_vec_nth$d',axiom,
( ( 'vec_nth$d'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1') = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_1' )
& ( 'vec_nth$d'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2') = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_2' ) ) ).
tff('declare_times$c',type,
'times$c': ( 'B_a_vec_a_vec$' * 'B_a_vec_a_vec$' ) > 'B_a_vec_a_vec$' ).
tff('function_times$c',axiom,
( ( 'times$c'('fmb_B_a_vec_a_vec$_1','fmb_B_a_vec_a_vec$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'times$c'('fmb_B_a_vec_a_vec$_1','fmb_B_a_vec_a_vec$_2') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'times$c'('fmb_B_a_vec_a_vec$_2','fmb_B_a_vec_a_vec$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'times$c'('fmb_B_a_vec_a_vec$_2','fmb_B_a_vec_a_vec$_2') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_times$e',type,
'times$e': ( 'B_c_vec_a_vec_a_vec_a_vec$' * 'B_c_vec_a_vec_a_vec_a_vec$' ) > 'B_c_vec_a_vec_a_vec_a_vec$' ).
tff('function_times$e',axiom,
( ( 'times$e'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'times$e'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'times$e'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'times$e'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' ) ) ).
tff('declare_plus$k',type,
'plus$k': ( 'B_c_vec_set$' * 'B_c_vec_set$' ) > 'B_c_vec_set$' ).
tff('function_plus$k',axiom,
( ( 'plus$k'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set$_1') = 'fmb_B_c_vec_set$_2' )
& ( 'plus$k'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set$_2') = 'fmb_B_c_vec_set$_2' )
& ( 'plus$k'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set$_1') = 'fmb_B_c_vec_set$_2' )
& ( 'plus$k'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set$_2') = 'fmb_B_c_vec_set$_2' ) ) ).
tff('declare_plus$j',type,
'plus$j': ( 'B_c_vec_a_vec_a_vec_set$' * 'B_c_vec_a_vec_a_vec_set$' ) > 'B_c_vec_a_vec_a_vec_set$' ).
tff('function_plus$j',axiom,
( ( 'plus$j'('fmb_B_c_vec_a_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'plus$j'('fmb_B_c_vec_a_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'plus$j'('fmb_B_c_vec_a_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'plus$j'('fmb_B_c_vec_a_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' ) ) ).
tff('declare_transpose$e',type,
'transpose$e': 'B_a_vec_c_vec$' > 'B_c_vec_a_vec$' ).
tff('function_transpose$e',axiom,
( ( 'transpose$e'('fmb_B_a_vec_c_vec$_1') = 'fmb_B_c_vec_a_vec$_2' )
& ( 'transpose$e'('fmb_B_a_vec_c_vec$_2') = 'fmb_B_c_vec_a_vec$_1' ) ) ).
tff('declare_transpose$',type,
'transpose$': 'B_a_vec_a_vec$' > 'B_a_vec_a_vec$' ).
tff('function_transpose$',axiom,
( ( 'transpose$'('fmb_B_a_vec_a_vec$_1') = 'fmb_B_a_vec_a_vec$_1' )
& ( 'transpose$'('fmb_B_a_vec_a_vec$_2') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_fun_app$w',type,
'fun_app$w': ( 'C_b_bool_fun_fun$' * 'C$' ) > 'B_bool_fun$' ).
tff('function_fun_app$w',axiom,
( ( 'fun_app$w'('fmb_C_b_bool_fun_fun$_1','fmb_C$_1') = 'fmb_B_bool_fun$_2' )
& ( 'fun_app$w'('fmb_C_b_bool_fun_fun$_2','fmb_C$_1') = 'fmb_B_bool_fun$_2' ) ) ).
tff('declare_fun_app$z',type,
'fun_app$z': ( 'A_b_c_vec_bool_fun_fun$' * 'A$' ) > 'B_c_vec_bool_fun$' ).
tff('function_fun_app$z',axiom,
( ( 'fun_app$z'('fmb_A_b_c_vec_bool_fun_fun$_1','fmb_A$_1') = 'fmb_B_c_vec_bool_fun$_2' )
& ( 'fun_app$z'('fmb_A_b_c_vec_bool_fun_fun$_2','fmb_A$_1') = 'fmb_B_c_vec_bool_fun$_2' ) ) ).
tff('declare_interchange_rows$e',type,
'interchange_rows$e': ( 'B_c_vec_a_vec$' * 'A$' ) > 'A_b_c_vec_a_vec_fun$' ).
tff('function_interchange_rows$e',axiom,
( ( 'interchange_rows$e'('fmb_B_c_vec_a_vec$_1','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_fun$_2' )
& ( 'interchange_rows$e'('fmb_B_c_vec_a_vec$_2','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_fun$_1' ) ) ).
tff('declare_elt_set_times$c',type,
'elt_set_times$c': ( 'B_c_vec_a_vec_set$' * 'B_c_vec_a_vec_set_set$' ) > 'B_c_vec_a_vec_set_set$' ).
tff('function_elt_set_times$c',axiom,
( ( 'elt_set_times$c'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set_set$_1') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'elt_set_times$c'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set_set$_2') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'elt_set_times$c'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set_set$_1') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'elt_set_times$c'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set_set$_2') = 'fmb_B_c_vec_a_vec_set_set$_2' ) ) ).
tff('declare_vec_nth$j',type,
'vec_nth$j': ( 'B_a_vec_a_vec_a_vec$' * 'A$' ) > 'B_a_vec_a_vec$' ).
tff('function_vec_nth$j',axiom,
( ( 'vec_nth$j'('fmb_B_a_vec_a_vec_a_vec$_1','fmb_A$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'vec_nth$j'('fmb_B_a_vec_a_vec_a_vec$_2','fmb_A$_1') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_map_matrix$d',type,
'map_matrix$d': ( 'B_c_vec_a_vec_b_c_vec_fun$' * 'B_c_vec_a_vec_a_vec_a_vec$' ) > 'B_c_vec_a_vec_a_vec$' ).
tff('function_map_matrix$d',axiom,
( ( 'map_matrix$d'('fmb_B_c_vec_a_vec_b_c_vec_fun$_1','fmb_B_c_vec_a_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'map_matrix$d'('fmb_B_c_vec_a_vec_b_c_vec_fun$_1','fmb_B_c_vec_a_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'map_matrix$d'('fmb_B_c_vec_a_vec_b_c_vec_fun$_2','fmb_B_c_vec_a_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'map_matrix$d'('fmb_B_c_vec_a_vec_b_c_vec_fun$_2','fmb_B_c_vec_a_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' ) ) ).
tff('declare_plus$p',type,
'plus$p': ( 'B_set_set$' * 'B_set_set$' ) > 'B_set_set$' ).
tff('function_plus$p',axiom,
( ( 'plus$p'('fmb_B_set_set$_1','fmb_B_set_set$_1') = 'fmb_B_set_set$_2' )
& ( 'plus$p'('fmb_B_set_set$_1','fmb_B_set_set$_2') = 'fmb_B_set_set$_2' )
& ( 'plus$p'('fmb_B_set_set$_2','fmb_B_set_set$_1') = 'fmb_B_set_set$_2' )
& ( 'plus$p'('fmb_B_set_set$_2','fmb_B_set_set$_2') = 'fmb_B_set_set$_2' ) ) ).
tff('declare_row_add_row$b',type,
'row_add_row$b': ( 'B_c_vec_a_vec_a_vec_a_vec$' * 'A$' * 'A$' * 'B_c_vec_a_vec$' * 'A$' ) > 'B_c_vec_a_vec_a_vec$' ).
tff('function_row_add_row$b',axiom,
( ( 'row_add_row$b'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1','fmb_B_c_vec_a_vec$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'row_add_row$b'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1','fmb_B_c_vec_a_vec$_2','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'row_add_row$b'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1','fmb_B_c_vec_a_vec$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'row_add_row$b'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1','fmb_B_c_vec_a_vec$_2','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' ) ) ).
tff('declare_plus$l',type,
'plus$l': ( 'B_c_vec_set_set$' * 'B_c_vec_set_set$' ) > 'B_c_vec_set_set$' ).
tff('function_plus$l',axiom,
( ( 'plus$l'('fmb_B_c_vec_set_set$_1','fmb_B_c_vec_set_set$_1') = 'fmb_B_c_vec_set_set$_2' )
& ( 'plus$l'('fmb_B_c_vec_set_set$_1','fmb_B_c_vec_set_set$_2') = 'fmb_B_c_vec_set_set$_2' )
& ( 'plus$l'('fmb_B_c_vec_set_set$_2','fmb_B_c_vec_set_set$_1') = 'fmb_B_c_vec_set_set$_2' )
& ( 'plus$l'('fmb_B_c_vec_set_set$_2','fmb_B_c_vec_set_set$_2') = 'fmb_B_c_vec_set_set$_2' ) ) ).
tff('declare_fun_app$m',type,
'fun_app$m': ( 'B_c_vec_b_fun$' * 'B_c_vec$' ) > 'B$' ).
tff('function_fun_app$m',axiom,
( ( 'fun_app$m'('fmb_B_c_vec_b_fun$_1','fmb_B_c_vec$_1') = 'fmb_B$_1' )
& ( 'fun_app$m'('fmb_B_c_vec_b_fun$_1','fmb_B_c_vec$_2') = 'fmb_B$_1' )
& ( 'fun_app$m'('fmb_B_c_vec_b_fun$_2','fmb_B_c_vec$_1') = 'fmb_B$_1' )
& ( 'fun_app$m'('fmb_B_c_vec_b_fun$_2','fmb_B_c_vec$_2') = 'fmb_B$_1' ) ) ).
tff('declare_vec$f',type,
'vec$f': 'B_a_vec$' > 'B_a_vec_c_vec$' ).
tff('function_vec$f',axiom,
( ( 'vec$f'('fmb_B_a_vec$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'vec$f'('fmb_B_a_vec$_2') = 'fmb_B_a_vec_c_vec$_1' ) ) ).
tff('declare_transpose_row$',type,
'transpose_row$': 'B_c_vec_a_vec$' > 'C_b_a_vec_fun$' ).
tff('function_transpose_row$',axiom,
( ( 'transpose_row$'('fmb_B_c_vec_a_vec$_1') = 'fmb_C_b_a_vec_fun$_2' )
& ( 'transpose_row$'('fmb_B_c_vec_a_vec$_2') = 'fmb_C_b_a_vec_fun$_1' ) ) ).
tff('declare_elt_set_times$e',type,
'elt_set_times$e': ( 'B$' * 'B_set$' ) > 'B_set$' ).
tff('function_elt_set_times$e',axiom,
( ( 'elt_set_times$e'('fmb_B$_1','fmb_B_set$_1') = 'fmb_B_set$_2' )
& ( 'elt_set_times$e'('fmb_B$_1','fmb_B_set$_2') = 'fmb_B_set$_2' )
& ( 'elt_set_times$e'('fmb_B$_2','fmb_B_set$_1') = 'fmb_B_set$_2' )
& ( 'elt_set_times$e'('fmb_B$_2','fmb_B_set$_2') = 'fmb_B_set$_2' ) ) ).
tff('declare_interchange_columns_row$a',type,
'interchange_columns_row$a': ( 'B_c_vec_a_vec_a_vec_a_vec$' * 'A$' * 'A$' ) > 'A_b_c_vec_a_vec_a_vec_fun$' ).
tff('function_interchange_columns_row$a',axiom,
( ( 'interchange_columns_row$a'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_1' )
& ( 'interchange_columns_row$a'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_2' ) ) ).
tff('declare_vec$a',type,
'vec$a': 'B_c_vec_a_vec$' > 'B_c_vec_a_vec_a_vec$' ).
tff('function_vec$a',axiom,
( ( 'vec$a'('fmb_B_c_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'vec$a'('fmb_B_c_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_2' ) ) ).
tff('declare_transpose_row$e',type,
'transpose_row$e': 'B_c_vec_a_vec_a_vec_a_vec$' > 'A_b_c_vec_a_vec_a_vec_fun$' ).
tff('function_transpose_row$e',axiom,
( ( 'transpose_row$e'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1') = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_1' )
& ( 'transpose_row$e'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2') = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_2' ) ) ).
tff('declare_plus$g',type,
'plus$g': ( 'B_a_vec_c_vec$' * 'B_a_vec_c_vec$' ) > 'B_a_vec_c_vec$' ).
tff('function_plus$g',axiom,
( ( 'plus$g'('fmb_B_a_vec_c_vec$_1','fmb_B_a_vec_c_vec$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'plus$g'('fmb_B_a_vec_c_vec$_1','fmb_B_a_vec_c_vec$_2') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'plus$g'('fmb_B_a_vec_c_vec$_2','fmb_B_a_vec_c_vec$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'plus$g'('fmb_B_a_vec_c_vec$_2','fmb_B_a_vec_c_vec$_2') = 'fmb_B_a_vec_c_vec$_2' ) ) ).
tff('declare_fun_app$aa',type,
'fun_app$aa': ( 'C_b_a_vec_c_vec_fun$' * 'C$' ) > 'B_a_vec_c_vec$' ).
tff('function_fun_app$aa',axiom,
( ( 'fun_app$aa'('fmb_C_b_a_vec_c_vec_fun$_1','fmb_C$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'fun_app$aa'('fmb_C_b_a_vec_c_vec_fun$_2','fmb_C$_1') = 'fmb_B_a_vec_c_vec$_1' ) ) ).
tff('declare_interchange_columns$',type,
'interchange_columns$': ( 'B_a_vec_a_vec$' * 'A$' * 'A$' ) > 'B_a_vec_a_vec$' ).
tff('function_interchange_columns$',axiom,
( ( 'interchange_columns$'('fmb_B_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_B_a_vec_a_vec$_1' )
& ( 'interchange_columns$'('fmb_B_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_columnvector_row$a',type,
'columnvector_row$a': ( 'B_c_vec$' * 'C$' ) > 'B_c_vec$' ).
tff('function_columnvector_row$a',axiom,
( ( 'columnvector_row$a'('fmb_B_c_vec$_1','fmb_C$_1') = 'fmb_B_c_vec$_1' )
& ( 'columnvector_row$a'('fmb_B_c_vec$_2','fmb_C$_1') = 'fmb_B_c_vec$_2' ) ) ).
tff('declare_interchange_columns$d',type,
'interchange_columns$d': ( 'B_c_vec_a_vec_a_vec$' * 'A$' * 'A$' ) > 'B_c_vec_a_vec_a_vec$' ).
tff('function_interchange_columns$d',axiom,
( ( 'interchange_columns$d'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'interchange_columns$d'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec$_2' ) ) ).
tff('declare_interchange_columns_row$e',type,
'interchange_columns_row$e': ( 'B_c_vec_a_vec$' * 'C$' * 'C$' ) > 'A_b_c_vec_fun$' ).
tff('function_interchange_columns_row$e',axiom,
( ( 'interchange_columns_row$e'('fmb_B_c_vec_a_vec$_1','fmb_C$_1','fmb_C$_1') = 'fmb_A_b_c_vec_fun$_2' )
& ( 'interchange_columns_row$e'('fmb_B_c_vec_a_vec$_2','fmb_C$_1','fmb_C$_1') = 'fmb_A_b_c_vec_fun$_1' ) ) ).
tff('declare_interchange_columns$c',type,
'interchange_columns$c': ( 'B_a_vec_c_vec$' * 'A$' * 'A$' ) > 'B_a_vec_c_vec$' ).
tff('function_interchange_columns$c',axiom,
( ( 'interchange_columns$c'('fmb_B_a_vec_c_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_B_a_vec_c_vec$_1' )
& ( 'interchange_columns$c'('fmb_B_a_vec_c_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_B_a_vec_c_vec$_2' ) ) ).
tff('declare_plus$c',type,
'plus$c': ( 'B_a_vec_a_vec$' * 'B_a_vec_a_vec$' ) > 'B_a_vec_a_vec$' ).
tff('function_plus$c',axiom,
( ( 'plus$c'('fmb_B_a_vec_a_vec$_1','fmb_B_a_vec_a_vec$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'plus$c'('fmb_B_a_vec_a_vec$_1','fmb_B_a_vec_a_vec$_2') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'plus$c'('fmb_B_a_vec_a_vec$_2','fmb_B_a_vec_a_vec$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'plus$c'('fmb_B_a_vec_a_vec$_2','fmb_B_a_vec_a_vec$_2') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_interchange_columns_row$b',type,
'interchange_columns_row$b': ( 'B_a_vec_a_vec$' * 'A$' * 'A$' ) > 'A_b_a_vec_fun$' ).
tff('function_interchange_columns_row$b',axiom,
( ( 'interchange_columns_row$b'('fmb_B_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_a_vec_fun$_2' )
& ( 'interchange_columns_row$b'('fmb_B_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_a_vec_fun$_1' ) ) ).
tff('declare_vec$d',type,
'vec$d': 'B_a_vec$' > 'B_a_vec_a_vec$' ).
tff('function_vec$d',axiom,
( ( 'vec$d'('fmb_B_a_vec$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'vec$d'('fmb_B_a_vec$_2') = 'fmb_B_a_vec_a_vec$_1' ) ) ).
tff('declare_times$i',type,
'times$i': ( 'B_a_vec_set$' * 'B_a_vec_set$' ) > 'B_a_vec_set$' ).
tff('function_times$i',axiom,
( ( 'times$i'('fmb_B_a_vec_set$_1','fmb_B_a_vec_set$_1') = 'fmb_B_a_vec_set$_2' )
& ( 'times$i'('fmb_B_a_vec_set$_1','fmb_B_a_vec_set$_2') = 'fmb_B_a_vec_set$_2' )
& ( 'times$i'('fmb_B_a_vec_set$_2','fmb_B_a_vec_set$_1') = 'fmb_B_a_vec_set$_2' )
& ( 'times$i'('fmb_B_a_vec_set$_2','fmb_B_a_vec_set$_2') = 'fmb_B_a_vec_set$_2' ) ) ).
tff('declare_interchange_rows$c',type,
'interchange_rows$c': ( 'B_a_vec_c_vec$' * 'C$' ) > 'C_b_a_vec_c_vec_fun$' ).
tff('function_interchange_rows$c',axiom,
( ( 'interchange_rows$c'('fmb_B_a_vec_c_vec$_1','fmb_C$_1') = 'fmb_C_b_a_vec_c_vec_fun$_2' )
& ( 'interchange_rows$c'('fmb_B_a_vec_c_vec$_2','fmb_C$_1') = 'fmb_C_b_a_vec_c_vec_fun$_1' ) ) ).
tff('declare_vector_scalar_mult$g',type,
'vector_scalar_mult$g': ( 'B_c_vec$' * 'B_c_vec_a_vec$' ) > 'B_c_vec_a_vec$' ).
tff('function_vector_scalar_mult$g',axiom,
( ( 'vector_scalar_mult$g'('fmb_B_c_vec$_1','fmb_B_c_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'vector_scalar_mult$g'('fmb_B_c_vec$_1','fmb_B_c_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'vector_scalar_mult$g'('fmb_B_c_vec$_2','fmb_B_c_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'vector_scalar_mult$g'('fmb_B_c_vec$_2','fmb_B_c_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec$_1' ) ) ).
tff('declare_fun_app$d',type,
'fun_app$d': ( 'C_b_c_vec_fun$' * 'C$' ) > 'B_c_vec$' ).
tff('function_fun_app$d',axiom,
( ( 'fun_app$d'('fmb_C_b_c_vec_fun$_1','fmb_C$_1') = 'fmb_B_c_vec$_1' )
& ( 'fun_app$d'('fmb_C_b_c_vec_fun$_2','fmb_C$_1') = 'fmb_B_c_vec$_2' ) ) ).
tff('declare_fun_app$f',type,
'fun_app$f': ( 'A_b_c_vec_a_vec_a_vec_fun$' * 'A$' ) > 'B_c_vec_a_vec_a_vec$' ).
tff('function_fun_app$f',axiom,
( ( 'fun_app$f'('fmb_A_b_c_vec_a_vec_a_vec_fun$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec$_2' )
& ( 'fun_app$f'('fmb_A_b_c_vec_a_vec_a_vec_fun$_2','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' ) ) ).
tff('declare_transpose$c',type,
'transpose$c': 'B_c_vec_a_vec$' > 'B_a_vec_c_vec$' ).
tff('function_transpose$c',axiom,
( ( 'transpose$c'('fmb_B_c_vec_a_vec$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'transpose$c'('fmb_B_c_vec_a_vec$_2') = 'fmb_B_a_vec_c_vec$_1' ) ) ).
tff('declare_vec_nth$k',type,
'vec_nth$k': ( 'B_a_vec_c_vec_a_vec$' * 'A$' ) > 'B_a_vec_c_vec$' ).
tff('function_vec_nth$k',axiom,
( ( 'vec_nth$k'('fmb_B_a_vec_c_vec_a_vec$_1','fmb_A$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'vec_nth$k'('fmb_B_a_vec_c_vec_a_vec$_2','fmb_A$_1') = 'fmb_B_a_vec_c_vec$_2' ) ) ).
tff('declare_fun_app$u',type,
'fun_app$u': ( 'C_b_a_vec_bool_fun_fun$' * 'C$' ) > 'B_a_vec_bool_fun$' ).
tff('function_fun_app$u',axiom,
( ( 'fun_app$u'('fmb_C_b_a_vec_bool_fun_fun$_1','fmb_C$_1') = 'fmb_B_a_vec_bool_fun$_2' )
& ( 'fun_app$u'('fmb_C_b_a_vec_bool_fun_fun$_2','fmb_C$_1') = 'fmb_B_a_vec_bool_fun$_2' ) ) ).
tff('declare_transpose$d',type,
'transpose$d': 'B_c_vec_a_vec_a_vec$' > 'B_c_vec_a_vec_a_vec$' ).
tff('function_transpose$d',axiom,
( ( 'transpose$d'('fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'transpose$d'('fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_2' ) ) ).
tff('declare_columnvector_row$h',type,
'columnvector_row$h': ( 'B_a_vec_c_vec$' * 'C$' ) > 'B_a_vec_a_vec$' ).
tff('function_columnvector_row$h',axiom,
( ( 'columnvector_row$h'('fmb_B_a_vec_c_vec$_1','fmb_C$_1') = 'fmb_B_a_vec_a_vec$_1' )
& ( 'columnvector_row$h'('fmb_B_a_vec_c_vec$_2','fmb_C$_1') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_elt_set_times$a',type,
'elt_set_times$a': ( 'B_c_vec_a_vec_a_vec$' * 'B_c_vec_a_vec_a_vec_set$' ) > 'B_c_vec_a_vec_a_vec_set$' ).
tff('function_elt_set_times$a',axiom,
( ( 'elt_set_times$a'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'elt_set_times$a'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'elt_set_times$a'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'elt_set_times$a'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' ) ) ).
tff('declare_elt_set_plus$g',type,
'elt_set_plus$g': ( 'B_c_vec$' * 'B_c_vec_set$' ) > 'B_c_vec_set$' ).
tff('function_elt_set_plus$g',axiom,
( ( 'elt_set_plus$g'('fmb_B_c_vec$_1','fmb_B_c_vec_set$_1') = 'fmb_B_c_vec_set$_2' )
& ( 'elt_set_plus$g'('fmb_B_c_vec$_1','fmb_B_c_vec_set$_2') = 'fmb_B_c_vec_set$_2' )
& ( 'elt_set_plus$g'('fmb_B_c_vec$_2','fmb_B_c_vec_set$_1') = 'fmb_B_c_vec_set$_2' )
& ( 'elt_set_plus$g'('fmb_B_c_vec$_2','fmb_B_c_vec_set$_2') = 'fmb_B_c_vec_set$_2' ) ) ).
tff('declare_transpose_row$h',type,
'transpose_row$h': ( 'B_a_vec_c_vec_a_vec$' * 'C$' ) > 'B_a_vec_a_vec$' ).
tff('function_transpose_row$h',axiom,
( ( 'transpose_row$h'('fmb_B_a_vec_c_vec_a_vec$_1','fmb_C$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'transpose_row$h'('fmb_B_a_vec_c_vec_a_vec$_2','fmb_C$_1') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_map_matrix$i',type,
'map_matrix$i': ( 'B_b_c_vec_fun$' * 'B_a_vec_c_vec$' ) > 'B_c_vec_a_vec_c_vec$' ).
tff('function_map_matrix$i',axiom,
( ( 'map_matrix$i'('fmb_B_b_c_vec_fun$_1','fmb_B_a_vec_c_vec$_1') = 'fmb_B_c_vec_a_vec_c_vec$_2' )
& ( 'map_matrix$i'('fmb_B_b_c_vec_fun$_1','fmb_B_a_vec_c_vec$_2') = 'fmb_B_c_vec_a_vec_c_vec$_1' )
& ( 'map_matrix$i'('fmb_B_b_c_vec_fun$_2','fmb_B_a_vec_c_vec$_1') = 'fmb_B_c_vec_a_vec_c_vec$_2' )
& ( 'map_matrix$i'('fmb_B_b_c_vec_fun$_2','fmb_B_a_vec_c_vec$_2') = 'fmb_B_c_vec_a_vec_c_vec$_1' ) ) ).
tff('declare_fun_app$o',type,
'fun_app$o': ( 'B_c_vec_a_vec_b_c_vec_fun$' * 'B_c_vec_a_vec$' ) > 'B_c_vec$' ).
tff('function_fun_app$o',axiom,
( ( 'fun_app$o'('fmb_B_c_vec_a_vec_b_c_vec_fun$_1','fmb_B_c_vec_a_vec$_1') = 'fmb_B_c_vec$_2' )
& ( 'fun_app$o'('fmb_B_c_vec_a_vec_b_c_vec_fun$_1','fmb_B_c_vec_a_vec$_2') = 'fmb_B_c_vec$_2' )
& ( 'fun_app$o'('fmb_B_c_vec_a_vec_b_c_vec_fun$_2','fmb_B_c_vec_a_vec$_1') = 'fmb_B_c_vec$_2' )
& ( 'fun_app$o'('fmb_B_c_vec_a_vec_b_c_vec_fun$_2','fmb_B_c_vec_a_vec$_2') = 'fmb_B_c_vec$_2' ) ) ).
tff('declare_fun_app$e',type,
'fun_app$e': ( 'A_b_c_vec_a_vec_fun$' * 'A$' ) > 'B_c_vec_a_vec$' ).
tff('function_fun_app$e',axiom,
( ( 'fun_app$e'('fmb_A_b_c_vec_a_vec_fun$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec$_2' )
& ( 'fun_app$e'('fmb_A_b_c_vec_a_vec_fun$_2','fmb_A$_1') = 'fmb_B_c_vec_a_vec$_1' ) ) ).
tff('declare_columnvector_row$e',type,
'columnvector_row$e': ( 'B_c_vec_a_vec_a_vec$' * 'A$' ) > 'B_c_vec_a_vec_a_vec$' ).
tff('function_columnvector_row$e',axiom,
( ( 'columnvector_row$e'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'columnvector_row$e'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec$_2' ) ) ).
tff('declare_interchange_columns_row$c',type,
'interchange_columns_row$c': ( 'B_a_vec_c_vec$' * 'A$' * 'A$' ) > 'C_b_a_vec_fun$' ).
tff('function_interchange_columns_row$c',axiom,
( ( 'interchange_columns_row$c'('fmb_B_a_vec_c_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_C_b_a_vec_fun$_1' )
& ( 'interchange_columns_row$c'('fmb_B_a_vec_c_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_C_b_a_vec_fun$_2' ) ) ).
tff('declare_transpose$b',type,
'transpose$b': 'B_c_vec_c_vec$' > 'B_c_vec_c_vec$' ).
tff('function_transpose$b',axiom,
( ( 'transpose$b'('fmb_B_c_vec_c_vec$_1') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'transpose$b'('fmb_B_c_vec_c_vec$_2') = 'fmb_B_c_vec_c_vec$_2' ) ) ).
tff('declare_transpose_row$c',type,
'transpose_row$c': 'B_a_vec_c_vec$' > 'A_b_c_vec_fun$' ).
tff('function_transpose_row$c',axiom,
( ( 'transpose_row$c'('fmb_B_a_vec_c_vec$_1') = 'fmb_A_b_c_vec_fun$_1' )
& ( 'transpose_row$c'('fmb_B_a_vec_c_vec$_2') = 'fmb_A_b_c_vec_fun$_2' ) ) ).
tff('declare_interchange_rows_row$e',type,
'interchange_rows_row$e': ( 'B_c_vec_a_vec$' * 'A$' * 'A$' ) > 'A_b_c_vec_fun$' ).
tff('function_interchange_rows_row$e',axiom,
( ( 'interchange_rows_row$e'('fmb_B_c_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_c_vec_fun$_2' )
& ( 'interchange_rows_row$e'('fmb_B_c_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_c_vec_fun$_1' ) ) ).
tff('declare_uub$',type,
'uub$': 'B_set$' > 'B_bool_fun$' ).
tff('function_uub$',axiom,
( ( 'uub$'('fmb_B_set$_1') = 'fmb_B_bool_fun$_2' )
& ( 'uub$'('fmb_B_set$_2') = 'fmb_B_bool_fun$_1' ) ) ).
tff('declare_times$l',type,
'times$l': ( 'B_c_vec_set_set$' * 'B_c_vec_set_set$' ) > 'B_c_vec_set_set$' ).
tff('function_times$l',axiom,
( ( 'times$l'('fmb_B_c_vec_set_set$_1','fmb_B_c_vec_set_set$_1') = 'fmb_B_c_vec_set_set$_2' )
& ( 'times$l'('fmb_B_c_vec_set_set$_1','fmb_B_c_vec_set_set$_2') = 'fmb_B_c_vec_set_set$_2' )
& ( 'times$l'('fmb_B_c_vec_set_set$_2','fmb_B_c_vec_set_set$_1') = 'fmb_B_c_vec_set_set$_2' )
& ( 'times$l'('fmb_B_c_vec_set_set$_2','fmb_B_c_vec_set_set$_2') = 'fmb_B_c_vec_set_set$_2' ) ) ).
tff('declare_collect$b',type,
'collect$b': 'B_bool_fun$' > 'B_set$' ).
tff('function_collect$b',axiom,
( ( 'collect$b'('fmb_B_bool_fun$_1') = 'fmb_B_set$_2' )
& ( 'collect$b'('fmb_B_bool_fun$_2') = 'fmb_B_set$_1' ) ) ).
tff('declare_map_matrix$h',type,
'map_matrix$h': ( 'B_b_fun$' * 'B_a_vec_c_vec$' ) > 'B_a_vec_c_vec$' ).
tff('function_map_matrix$h',axiom,
( ( 'map_matrix$h'('fmb_B_b_fun$_1','fmb_B_a_vec_c_vec$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'map_matrix$h'('fmb_B_b_fun$_1','fmb_B_a_vec_c_vec$_2') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'map_matrix$h'('fmb_B_b_fun$_2','fmb_B_a_vec_c_vec$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'map_matrix$h'('fmb_B_b_fun$_2','fmb_B_a_vec_c_vec$_2') = 'fmb_B_a_vec_c_vec$_2' ) ) ).
tff('declare_times$',type,
'times$': 'B$' > 'B_b_fun$' ).
tff('function_times$',axiom,
( ( 'times$'('fmb_B$_1') = 'fmb_B_b_fun$_2' )
& ( 'times$'('fmb_B$_2') = 'fmb_B_b_fun$_2' ) ) ).
tff('declare_interchange_rows$a',type,
'interchange_rows$a': ( 'B_c_vec_a_vec_a_vec_a_vec$' * 'A$' * 'A$' ) > 'B_c_vec_a_vec_a_vec_a_vec$' ).
tff('function_interchange_rows$a',axiom,
( ( 'interchange_rows$a'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_1' )
& ( 'interchange_rows$a'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' ) ) ).
tff('declare_interchange_rows_row$',type,
'interchange_rows_row$': ( 'B_c_vec_c_vec$' * 'C$' * 'C$' ) > 'C_b_c_vec_fun$' ).
tff('function_interchange_rows_row$',axiom,
( ( 'interchange_rows_row$'('fmb_B_c_vec_c_vec$_1','fmb_C$_1','fmb_C$_1') = 'fmb_C_b_c_vec_fun$_2' )
& ( 'interchange_rows_row$'('fmb_B_c_vec_c_vec$_2','fmb_C$_1','fmb_C$_1') = 'fmb_C_b_c_vec_fun$_1' ) ) ).
tff('declare_elt_set_plus$c',type,
'elt_set_plus$c': ( 'B_c_vec_a_vec_set$' * 'B_c_vec_a_vec_set_set$' ) > 'B_c_vec_a_vec_set_set$' ).
tff('function_elt_set_plus$c',axiom,
( ( 'elt_set_plus$c'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set_set$_1') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'elt_set_plus$c'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set_set$_2') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'elt_set_plus$c'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set_set$_1') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'elt_set_plus$c'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set_set$_2') = 'fmb_B_c_vec_a_vec_set_set$_2' ) ) ).
tff('declare_interchange_rows$b',type,
'interchange_rows$b': ( 'B_c_vec_c_vec$' * 'C$' * 'C$' ) > 'B_c_vec_c_vec$' ).
tff('function_interchange_rows$b',axiom,
( ( 'interchange_rows$b'('fmb_B_c_vec_c_vec$_1','fmb_C$_1','fmb_C$_1') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'interchange_rows$b'('fmb_B_c_vec_c_vec$_2','fmb_C$_1','fmb_C$_1') = 'fmb_B_c_vec_c_vec$_2' ) ) ).
tff('declare_elt_set_times$g',type,
'elt_set_times$g': ( 'B_c_vec$' * 'B_c_vec_set$' ) > 'B_c_vec_set$' ).
tff('function_elt_set_times$g',axiom,
( ( 'elt_set_times$g'('fmb_B_c_vec$_1','fmb_B_c_vec_set$_1') = 'fmb_B_c_vec_set$_2' )
& ( 'elt_set_times$g'('fmb_B_c_vec$_1','fmb_B_c_vec_set$_2') = 'fmb_B_c_vec_set$_2' )
& ( 'elt_set_times$g'('fmb_B_c_vec$_2','fmb_B_c_vec_set$_1') = 'fmb_B_c_vec_set$_2' )
& ( 'elt_set_times$g'('fmb_B_c_vec$_2','fmb_B_c_vec_set$_2') = 'fmb_B_c_vec_set$_2' ) ) ).
tff('declare_elt_set_times$f',type,
'elt_set_times$f': ( 'B_c_vec_a_vec$' * 'B_c_vec_a_vec_set$' ) > 'B_c_vec_a_vec_set$' ).
tff('function_elt_set_times$f',axiom,
( ( 'elt_set_times$f'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'elt_set_times$f'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'elt_set_times$f'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'elt_set_times$f'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_set$_2' ) ) ).
tff('declare_times$m',type,
'times$m': ( 'B_c_vec_a_vec_set$' * 'B_c_vec_a_vec_set$' ) > 'B_c_vec_a_vec_set$' ).
tff('function_times$m',axiom,
( ( 'times$m'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'times$m'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'times$m'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'times$m'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_set$_2' ) ) ).
tff('declare_plus$',type,
'plus$': 'B$' > 'B_b_fun$' ).
tff('function_plus$',axiom,
( ( 'plus$'('fmb_B$_1') = 'fmb_B_b_fun$_2' )
& ( 'plus$'('fmb_B$_2') = 'fmb_B_b_fun$_2' ) ) ).
tff('declare_elt_set_times$b',type,
'elt_set_times$b': ( 'B_c_vec_set$' * 'B_c_vec_set_set$' ) > 'B_c_vec_set_set$' ).
tff('function_elt_set_times$b',axiom,
( ( 'elt_set_times$b'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set_set$_1') = 'fmb_B_c_vec_set_set$_2' )
& ( 'elt_set_times$b'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set_set$_2') = 'fmb_B_c_vec_set_set$_2' )
& ( 'elt_set_times$b'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set_set$_1') = 'fmb_B_c_vec_set_set$_2' )
& ( 'elt_set_times$b'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set_set$_2') = 'fmb_B_c_vec_set_set$_2' ) ) ).
tff('declare_plus$f',type,
'plus$f': ( 'B_c_vec_a_vec_a_vec$' * 'B_c_vec_a_vec_a_vec$' ) > 'B_c_vec_a_vec_a_vec$' ).
tff('function_plus$f',axiom,
( ( 'plus$f'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'plus$f'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'plus$f'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'plus$f'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' ) ) ).
tff('declare_vector_scalar_mult$a',type,
'vector_scalar_mult$a': ( 'B_c_vec_a_vec_a_vec$' * 'B_c_vec_a_vec_a_vec_a_vec$' ) > 'B_c_vec_a_vec_a_vec_a_vec$' ).
tff('function_vector_scalar_mult$a',axiom,
( ( 'vector_scalar_mult$a'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'vector_scalar_mult$a'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'vector_scalar_mult$a'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'vector_scalar_mult$a'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' ) ) ).
tff('declare_fun_app$y',type,
'fun_app$y': ( 'A_b_bool_fun_fun$' * 'A$' ) > 'B_bool_fun$' ).
tff('function_fun_app$y',axiom,
( ( 'fun_app$y'('fmb_A_b_bool_fun_fun$_1','fmb_A$_1') = 'fmb_B_bool_fun$_2' )
& ( 'fun_app$y'('fmb_A_b_bool_fun_fun$_2','fmb_A$_1') = 'fmb_B_bool_fun$_2' ) ) ).
tff('declare_transpose_row$b',type,
'transpose_row$b': 'B_c_vec_c_vec$' > 'C_b_c_vec_fun$' ).
tff('function_transpose_row$b',axiom,
( ( 'transpose_row$b'('fmb_B_c_vec_c_vec$_1') = 'fmb_C_b_c_vec_fun$_2' )
& ( 'transpose_row$b'('fmb_B_c_vec_c_vec$_2') = 'fmb_C_b_c_vec_fun$_1' ) ) ).
tff('declare_map_matrix$e',type,
'map_matrix$e': ( 'B_c_vec_b_c_vec_a_vec_fun$' * 'B_c_vec_a_vec_a_vec$' ) > 'B_c_vec_a_vec_a_vec_a_vec$' ).
tff('function_map_matrix$e',axiom,
( ( 'map_matrix$e'('fmb_B_c_vec_b_c_vec_a_vec_fun$_1','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'map_matrix$e'('fmb_B_c_vec_b_c_vec_a_vec_fun$_1','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_1' )
& ( 'map_matrix$e'('fmb_B_c_vec_b_c_vec_a_vec_fun$_2','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'map_matrix$e'('fmb_B_c_vec_b_c_vec_a_vec_fun$_2','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_1' ) ) ).
tff('declare_row_add_row$c',type,
'row_add_row$c': ( 'B_a_vec_a_vec$' * 'A$' * 'A$' * 'B$' * 'A$' ) > 'B_a_vec$' ).
tff('function_row_add_row$c',axiom,
( ( 'row_add_row$c'('fmb_B_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1','fmb_B$_1','fmb_A$_1') = 'fmb_B_a_vec$_1' )
& ( 'row_add_row$c'('fmb_B_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1','fmb_B$_2','fmb_A$_1') = 'fmb_B_a_vec$_1' )
& ( 'row_add_row$c'('fmb_B_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1','fmb_B$_1','fmb_A$_1') = 'fmb_B_a_vec$_1' )
& ( 'row_add_row$c'('fmb_B_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1','fmb_B$_2','fmb_A$_1') = 'fmb_B_a_vec$_1' ) ) ).
tff('declare_interchange_rows_row$d',type,
'interchange_rows_row$d': ( 'B_c_vec_a_vec_a_vec$' * 'A$' * 'A$' ) > 'A_b_c_vec_a_vec_fun$' ).
tff('function_interchange_rows_row$d',axiom,
( ( 'interchange_rows_row$d'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_fun$_2' )
& ( 'interchange_rows_row$d'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_fun$_1' ) ) ).
tff('declare_fun_app$x',type,
'fun_app$x': ( 'A_b_c_vec_a_vec_bool_fun_fun$' * 'A$' ) > 'B_c_vec_a_vec_bool_fun$' ).
tff('function_fun_app$x',axiom,
( ( 'fun_app$x'('fmb_A_b_c_vec_a_vec_bool_fun_fun$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec_bool_fun$_2' )
& ( 'fun_app$x'('fmb_A_b_c_vec_a_vec_bool_fun_fun$_2','fmb_A$_1') = 'fmb_B_c_vec_a_vec_bool_fun$_2' ) ) ).
tff('declare_fun_app$i',type,
'fun_app$i': ( 'C_b_a_vec_fun$' * 'C$' ) > 'B_a_vec$' ).
tff('function_fun_app$i',axiom,
( ( 'fun_app$i'('fmb_C_b_a_vec_fun$_1','fmb_C$_1') = 'fmb_B_a_vec$_2' )
& ( 'fun_app$i'('fmb_C_b_a_vec_fun$_2','fmb_C$_1') = 'fmb_B_a_vec$_1' ) ) ).
tff('declare_interchange_rows_row$c',type,
'interchange_rows_row$c': ( 'B_a_vec_c_vec$' * 'C$' * 'C$' ) > 'C_b_a_vec_fun$' ).
tff('function_interchange_rows_row$c',axiom,
( ( 'interchange_rows_row$c'('fmb_B_a_vec_c_vec$_1','fmb_C$_1','fmb_C$_1') = 'fmb_C_b_a_vec_fun$_1' )
& ( 'interchange_rows_row$c'('fmb_B_a_vec_c_vec$_2','fmb_C$_1','fmb_C$_1') = 'fmb_C_b_a_vec_fun$_2' ) ) ).
tff('declare_fun_app$n',type,
'fun_app$n': ( 'B_c_vec_b_c_vec_fun$' * 'B_c_vec$' ) > 'B_c_vec$' ).
tff('function_fun_app$n',axiom,
( ( 'fun_app$n'('fmb_B_c_vec_b_c_vec_fun$_1','fmb_B_c_vec$_1') = 'fmb_B_c_vec$_2' )
& ( 'fun_app$n'('fmb_B_c_vec_b_c_vec_fun$_1','fmb_B_c_vec$_2') = 'fmb_B_c_vec$_2' )
& ( 'fun_app$n'('fmb_B_c_vec_b_c_vec_fun$_2','fmb_B_c_vec$_1') = 'fmb_B_c_vec$_2' )
& ( 'fun_app$n'('fmb_B_c_vec_b_c_vec_fun$_2','fmb_B_c_vec$_2') = 'fmb_B_c_vec$_2' ) ) ).
tff('declare_times$a',type,
'times$a': ( 'B_c_vec_a_vec$' * 'B_c_vec_a_vec$' ) > 'B_c_vec_a_vec$' ).
tff('function_times$a',axiom,
( ( 'times$a'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'times$a'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'times$a'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'times$a'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec$_1' ) ) ).
tff('declare_plus$e',type,
'plus$e': ( 'B_c_vec_a_vec_a_vec_a_vec$' * 'B_c_vec_a_vec_a_vec_a_vec$' ) > 'B_c_vec_a_vec_a_vec_a_vec$' ).
tff('function_plus$e',axiom,
( ( 'plus$e'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'plus$e'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'plus$e'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' )
& ( 'plus$e'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' ) ) ).
tff('declare_times$b',type,
'times$b': 'B_c_vec$' > 'B_c_vec_b_c_vec_fun$' ).
tff('function_times$b',axiom,
( ( 'times$b'('fmb_B_c_vec$_1') = 'fmb_B_c_vec_b_c_vec_fun$_1' )
& ( 'times$b'('fmb_B_c_vec$_2') = 'fmb_B_c_vec_b_c_vec_fun$_1' ) ) ).
tff('declare_vec_nth$g',type,
'vec_nth$g': 'B_a_vec_c_vec$' > 'C_b_a_vec_fun$' ).
tff('function_vec_nth$g',axiom,
( ( 'vec_nth$g'('fmb_B_a_vec_c_vec$_1') = 'fmb_C_b_a_vec_fun$_1' )
& ( 'vec_nth$g'('fmb_B_a_vec_c_vec$_2') = 'fmb_C_b_a_vec_fun$_2' ) ) ).
tff('declare_plus$b',type,
'plus$b': 'B_c_vec$' > 'B_c_vec_b_c_vec_fun$' ).
tff('function_plus$b',axiom,
( ( 'plus$b'('fmb_B_c_vec$_1') = 'fmb_B_c_vec_b_c_vec_fun$_2' )
& ( 'plus$b'('fmb_B_c_vec$_2') = 'fmb_B_c_vec_b_c_vec_fun$_2' ) ) ).
tff('declare_plus$a',type,
'plus$a': ( 'B_c_vec_a_vec$' * 'B_c_vec_a_vec$' ) > 'B_c_vec_a_vec$' ).
tff('function_plus$a',axiom,
( ( 'plus$a'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'plus$a'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'plus$a'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'plus$a'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec$_1' ) ) ).
tff('declare_columnvector_row$b',type,
'columnvector_row$b': ( 'B_a_vec$' * 'A$' ) > 'B_c_vec$' ).
tff('function_columnvector_row$b',axiom,
( ( 'columnvector_row$b'('fmb_B_a_vec$_1','fmb_A$_1') = 'fmb_B_c_vec$_2' )
& ( 'columnvector_row$b'('fmb_B_a_vec$_2','fmb_A$_1') = 'fmb_B_c_vec$_1' ) ) ).
tff('declare_times$p',type,
'times$p': ( 'B_set_set$' * 'B_set_set$' ) > 'B_set_set$' ).
tff('function_times$p',axiom,
( ( 'times$p'('fmb_B_set_set$_1','fmb_B_set_set$_1') = 'fmb_B_set_set$_2' )
& ( 'times$p'('fmb_B_set_set$_1','fmb_B_set_set$_2') = 'fmb_B_set_set$_2' )
& ( 'times$p'('fmb_B_set_set$_2','fmb_B_set_set$_1') = 'fmb_B_set_set$_2' )
& ( 'times$p'('fmb_B_set_set$_2','fmb_B_set_set$_2') = 'fmb_B_set_set$_2' ) ) ).
tff('declare_map_matrix$b',type,
'map_matrix$b': ( 'B_c_vec_b_fun$' * 'B_c_vec_a_vec_a_vec$' ) > 'B_a_vec_a_vec$' ).
tff('function_map_matrix$b',axiom,
( ( 'map_matrix$b'('fmb_B_c_vec_b_fun$_1','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'map_matrix$b'('fmb_B_c_vec_b_fun$_1','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'map_matrix$b'('fmb_B_c_vec_b_fun$_2','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'map_matrix$b'('fmb_B_c_vec_b_fun$_2','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_times$g',type,
'times$g': ( 'B_a_vec_c_vec$' * 'B_a_vec_c_vec$' ) > 'B_a_vec_c_vec$' ).
tff('function_times$g',axiom,
( ( 'times$g'('fmb_B_a_vec_c_vec$_1','fmb_B_a_vec_c_vec$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'times$g'('fmb_B_a_vec_c_vec$_1','fmb_B_a_vec_c_vec$_2') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'times$g'('fmb_B_a_vec_c_vec$_2','fmb_B_a_vec_c_vec$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'times$g'('fmb_B_a_vec_c_vec$_2','fmb_B_a_vec_c_vec$_2') = 'fmb_B_a_vec_c_vec$_2' ) ) ).
tff('declare_plus$h',type,
'plus$h': ( 'B_c_vec_c_vec$' * 'B_c_vec_c_vec$' ) > 'B_c_vec_c_vec$' ).
tff('function_plus$h',axiom,
( ( 'plus$h'('fmb_B_c_vec_c_vec$_1','fmb_B_c_vec_c_vec$_1') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'plus$h'('fmb_B_c_vec_c_vec$_1','fmb_B_c_vec_c_vec$_2') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'plus$h'('fmb_B_c_vec_c_vec$_2','fmb_B_c_vec_c_vec$_1') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'plus$h'('fmb_B_c_vec_c_vec$_2','fmb_B_c_vec_c_vec$_2') = 'fmb_B_c_vec_c_vec$_1' ) ) ).
tff('declare_row_add_row$d',type,
'row_add_row$d': ( 'B_a_vec_c_vec$' * 'C$' * 'C$' * 'B$' * 'C$' ) > 'B_a_vec$' ).
tff('function_row_add_row$d',axiom,
( ( 'row_add_row$d'('fmb_B_a_vec_c_vec$_1','fmb_C$_1','fmb_C$_1','fmb_B$_1','fmb_C$_1') = 'fmb_B_a_vec$_1' )
& ( 'row_add_row$d'('fmb_B_a_vec_c_vec$_1','fmb_C$_1','fmb_C$_1','fmb_B$_2','fmb_C$_1') = 'fmb_B_a_vec$_1' )
& ( 'row_add_row$d'('fmb_B_a_vec_c_vec$_2','fmb_C$_1','fmb_C$_1','fmb_B$_1','fmb_C$_1') = 'fmb_B_a_vec$_1' )
& ( 'row_add_row$d'('fmb_B_a_vec_c_vec$_2','fmb_C$_1','fmb_C$_1','fmb_B$_2','fmb_C$_1') = 'fmb_B_a_vec$_1' ) ) ).
tff('declare_vec_nth$f',type,
'vec_nth$f': 'B_a_vec_a_vec$' > 'A_b_a_vec_fun$' ).
tff('function_vec_nth$f',axiom,
( ( 'vec_nth$f'('fmb_B_a_vec_a_vec$_1') = 'fmb_A_b_a_vec_fun$_2' )
& ( 'vec_nth$f'('fmb_B_a_vec_a_vec$_2') = 'fmb_A_b_a_vec_fun$_1' ) ) ).
tff('declare_uua$',type,
'uua$': 'B_c_vec_a_vec_set$' > 'B_c_vec_a_vec_bool_fun$' ).
tff('function_uua$',axiom,
( ( 'uua$'('fmb_B_c_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_bool_fun$_2' )
& ( 'uua$'('fmb_B_c_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_bool_fun$_1' ) ) ).
tff('declare_elt_set_plus$',type,
'elt_set_plus$': ( 'B_a_vec$' * 'B_a_vec_set$' ) > 'B_a_vec_set$' ).
tff('function_elt_set_plus$',axiom,
( ( 'elt_set_plus$'('fmb_B_a_vec$_1','fmb_B_a_vec_set$_1') = 'fmb_B_a_vec_set$_2' )
& ( 'elt_set_plus$'('fmb_B_a_vec$_1','fmb_B_a_vec_set$_2') = 'fmb_B_a_vec_set$_2' )
& ( 'elt_set_plus$'('fmb_B_a_vec$_2','fmb_B_a_vec_set$_1') = 'fmb_B_a_vec_set$_2' )
& ( 'elt_set_plus$'('fmb_B_a_vec$_2','fmb_B_a_vec_set$_2') = 'fmb_B_a_vec_set$_2' ) ) ).
tff('declare_times$f',type,
'times$f': ( 'B_c_vec_a_vec_a_vec$' * 'B_c_vec_a_vec_a_vec$' ) > 'B_c_vec_a_vec_a_vec$' ).
tff('function_times$f',axiom,
( ( 'times$f'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'times$f'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'times$f'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec$_1' )
& ( 'times$f'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec$_1' ) ) ).
tff('declare_vec_nth$',type,
'vec_nth$': 'B_c_vec_a_vec$' > 'A_b_c_vec_fun$' ).
tff('function_vec_nth$',axiom,
( ( 'vec_nth$'('fmb_B_c_vec_a_vec$_1') = 'fmb_A_b_c_vec_fun$_2' )
& ( 'vec_nth$'('fmb_B_c_vec_a_vec$_2') = 'fmb_A_b_c_vec_fun$_1' ) ) ).
tff('declare_vec_nth$c',type,
'vec_nth$c': 'B_c_vec_a_vec_a_vec$' > 'A_b_c_vec_a_vec_fun$' ).
tff('function_vec_nth$c',axiom,
( ( 'vec_nth$c'('fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_A_b_c_vec_a_vec_fun$_2' )
& ( 'vec_nth$c'('fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_A_b_c_vec_a_vec_fun$_1' ) ) ).
tff('declare_columnvector_row$f',type,
'columnvector_row$f': ( 'B_c_vec_c_vec$' * 'C$' ) > 'B_c_vec_a_vec$' ).
tff('function_columnvector_row$f',axiom,
( ( 'columnvector_row$f'('fmb_B_c_vec_c_vec$_1','fmb_C$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'columnvector_row$f'('fmb_B_c_vec_c_vec$_2','fmb_C$_1') = 'fmb_B_c_vec_a_vec$_2' ) ) ).
tff('declare_map_matrix$f',type,
'map_matrix$f': ( 'B_b_fun$' * 'B_c_vec_c_vec$' ) > 'B_c_vec_c_vec$' ).
tff('function_map_matrix$f',axiom,
( ( 'map_matrix$f'('fmb_B_b_fun$_1','fmb_B_c_vec_c_vec$_1') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'map_matrix$f'('fmb_B_b_fun$_1','fmb_B_c_vec_c_vec$_2') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'map_matrix$f'('fmb_B_b_fun$_2','fmb_B_c_vec_c_vec$_1') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'map_matrix$f'('fmb_B_b_fun$_2','fmb_B_c_vec_c_vec$_2') = 'fmb_B_c_vec_c_vec$_1' ) ) ).
tff('declare_times$o',type,
'times$o': ( 'B_set$' * 'B_set$' ) > 'B_set$' ).
tff('function_times$o',axiom,
( ( 'times$o'('fmb_B_set$_1','fmb_B_set$_1') = 'fmb_B_set$_2' )
& ( 'times$o'('fmb_B_set$_1','fmb_B_set$_2') = 'fmb_B_set$_2' )
& ( 'times$o'('fmb_B_set$_2','fmb_B_set$_1') = 'fmb_B_set$_2' )
& ( 'times$o'('fmb_B_set$_2','fmb_B_set$_2') = 'fmb_B_set$_2' ) ) ).
tff('declare_collect$a',type,
'collect$a': 'B_c_vec_a_vec_bool_fun$' > 'B_c_vec_a_vec_set$' ).
tff('function_collect$a',axiom,
( ( 'collect$a'('fmb_B_c_vec_a_vec_bool_fun$_1') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'collect$a'('fmb_B_c_vec_a_vec_bool_fun$_2') = 'fmb_B_c_vec_a_vec_set$_1' ) ) ).
tff('declare_times$d',type,
'times$d': ( 'B_a_vec$' * 'B_a_vec$' ) > 'B_a_vec$' ).
tff('function_times$d',axiom,
( ( 'times$d'('fmb_B_a_vec$_1','fmb_B_a_vec$_1') = 'fmb_B_a_vec$_1' )
& ( 'times$d'('fmb_B_a_vec$_1','fmb_B_a_vec$_2') = 'fmb_B_a_vec$_1' )
& ( 'times$d'('fmb_B_a_vec$_2','fmb_B_a_vec$_1') = 'fmb_B_a_vec$_1' )
& ( 'times$d'('fmb_B_a_vec$_2','fmb_B_a_vec$_2') = 'fmb_B_a_vec$_1' ) ) ).
tff('declare_columnvector_row$i',type,
'columnvector_row$i': ( 'B_a_vec_a_vec$' * 'A$' ) > 'B_a_vec_c_vec$' ).
tff('function_columnvector_row$i',axiom,
( ( 'columnvector_row$i'('fmb_B_a_vec_a_vec$_1','fmb_A$_1') = 'fmb_B_a_vec_c_vec$_1' )
& ( 'columnvector_row$i'('fmb_B_a_vec_a_vec$_2','fmb_A$_1') = 'fmb_B_a_vec_c_vec$_2' ) ) ).
tff('declare_row_add_row$e',type,
'row_add_row$e': ( 'B_c_vec_a_vec_a_vec$' * 'A$' * 'A$' * 'B_c_vec$' * 'A$' ) > 'B_c_vec_a_vec$' ).
tff('function_row_add_row$e',axiom,
( ( 'row_add_row$e'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1','fmb_B_c_vec$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'row_add_row$e'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1','fmb_B_c_vec$_2','fmb_A$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'row_add_row$e'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1','fmb_B_c_vec$_1','fmb_A$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'row_add_row$e'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1','fmb_B_c_vec$_2','fmb_A$_1') = 'fmb_B_c_vec_a_vec$_1' ) ) ).
tff('declare_times$k',type,
'times$k': ( 'B_c_vec_set$' * 'B_c_vec_set$' ) > 'B_c_vec_set$' ).
tff('function_times$k',axiom,
( ( 'times$k'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set$_1') = 'fmb_B_c_vec_set$_2' )
& ( 'times$k'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set$_2') = 'fmb_B_c_vec_set$_2' )
& ( 'times$k'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set$_1') = 'fmb_B_c_vec_set$_2' )
& ( 'times$k'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set$_2') = 'fmb_B_c_vec_set$_2' ) ) ).
tff('declare_vec_nth$e',type,
'vec_nth$e': 'B_a_vec$' > 'A_b_fun$' ).
tff('function_vec_nth$e',axiom,
( ( 'vec_nth$e'('fmb_B_a_vec$_1') = 'fmb_A_b_fun$_1' )
& ( 'vec_nth$e'('fmb_B_a_vec$_2') = 'fmb_A_b_fun$_2' ) ) ).
tff('declare_elt_set_plus$f',type,
'elt_set_plus$f': ( 'B_c_vec_a_vec$' * 'B_c_vec_a_vec_set$' ) > 'B_c_vec_a_vec_set$' ).
tff('function_elt_set_plus$f',axiom,
( ( 'elt_set_plus$f'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'elt_set_plus$f'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'elt_set_plus$f'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_set$_2' )
& ( 'elt_set_plus$f'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_set$_2' ) ) ).
tff('declare_fun_app$k',type,
'fun_app$k': ( 'B_b_fun$' * 'B$' ) > 'B$' ).
tff('function_fun_app$k',axiom,
( ( 'fun_app$k'('fmb_B_b_fun$_1','fmb_B$_1') = 'fmb_B$_1' )
& ( 'fun_app$k'('fmb_B_b_fun$_1','fmb_B$_2') = 'fmb_B$_1' )
& ( 'fun_app$k'('fmb_B_b_fun$_2','fmb_B$_1') = 'fmb_B$_1' )
& ( 'fun_app$k'('fmb_B_b_fun$_2','fmb_B$_2') = 'fmb_B$_1' ) ) ).
tff('declare_elt_set_plus$e',type,
'elt_set_plus$e': ( 'B$' * 'B_set$' ) > 'B_set$' ).
tff('function_elt_set_plus$e',axiom,
( ( 'elt_set_plus$e'('fmb_B$_1','fmb_B_set$_1') = 'fmb_B_set$_2' )
& ( 'elt_set_plus$e'('fmb_B$_1','fmb_B_set$_2') = 'fmb_B_set$_2' )
& ( 'elt_set_plus$e'('fmb_B$_2','fmb_B_set$_1') = 'fmb_B_set$_2' )
& ( 'elt_set_plus$e'('fmb_B$_2','fmb_B_set$_2') = 'fmb_B_set$_2' ) ) ).
tff('declare_row_add$',type,
'row_add$': ( 'B_c_vec_a_vec$' * 'A$' * 'A$' * 'B$' ) > 'B_c_vec_a_vec$' ).
tff('function_row_add$',axiom,
( ( 'row_add$'('fmb_B_c_vec_a_vec$_1','fmb_A$_1','fmb_A$_1','fmb_B$_1') = 'fmb_B_c_vec_a_vec$_2' )
& ( 'row_add$'('fmb_B_c_vec_a_vec$_1','fmb_A$_1','fmb_A$_1','fmb_B$_2') = 'fmb_B_c_vec_a_vec$_2' )
& ( 'row_add$'('fmb_B_c_vec_a_vec$_2','fmb_A$_1','fmb_A$_1','fmb_B$_1') = 'fmb_B_c_vec_a_vec$_2' )
& ( 'row_add$'('fmb_B_c_vec_a_vec$_2','fmb_A$_1','fmb_A$_1','fmb_B$_2') = 'fmb_B_c_vec_a_vec$_2' ) ) ).
tff('declare_transpose$a',type,
'transpose$a': 'B_c_vec_a_vec_a_vec_a_vec$' > 'B_c_vec_a_vec_a_vec_a_vec$' ).
tff('function_transpose$a',axiom,
( ( 'transpose$a'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_1' )
& ( 'transpose$a'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2') = 'fmb_B_c_vec_a_vec_a_vec_a_vec$_2' ) ) ).
tff('declare_interchange_rows_row$b',type,
'interchange_rows_row$b': ( 'B_a_vec_a_vec$' * 'A$' * 'A$' ) > 'A_b_a_vec_fun$' ).
tff('function_interchange_rows_row$b',axiom,
( ( 'interchange_rows_row$b'('fmb_B_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_a_vec_fun$_2' )
& ( 'interchange_rows_row$b'('fmb_B_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_a_vec_fun$_1' ) ) ).
tff('declare_transpose_row$i',type,
'transpose_row$i': ( 'B_a_vec_a_vec_c_vec$' * 'A$' ) > 'B_a_vec_c_vec$' ).
tff('function_transpose_row$i',axiom,
( ( 'transpose_row$i'('fmb_B_a_vec_a_vec_c_vec$_1','fmb_A$_1') = 'fmb_B_a_vec_c_vec$_2' )
& ( 'transpose_row$i'('fmb_B_a_vec_a_vec_c_vec$_2','fmb_A$_1') = 'fmb_B_a_vec_c_vec$_2' ) ) ).
tff('declare_row_add_row$a',type,
'row_add_row$a': ( 'B_c_vec_c_vec$' * 'C$' * 'C$' * 'B$' * 'C$' ) > 'B_c_vec$' ).
tff('function_row_add_row$a',axiom,
( ( 'row_add_row$a'('fmb_B_c_vec_c_vec$_1','fmb_C$_1','fmb_C$_1','fmb_B$_1','fmb_C$_1') = 'fmb_B_c_vec$_2' )
& ( 'row_add_row$a'('fmb_B_c_vec_c_vec$_1','fmb_C$_1','fmb_C$_1','fmb_B$_2','fmb_C$_1') = 'fmb_B_c_vec$_2' )
& ( 'row_add_row$a'('fmb_B_c_vec_c_vec$_2','fmb_C$_1','fmb_C$_1','fmb_B$_1','fmb_C$_1') = 'fmb_B_c_vec$_2' )
& ( 'row_add_row$a'('fmb_B_c_vec_c_vec$_2','fmb_C$_1','fmb_C$_1','fmb_B$_2','fmb_C$_1') = 'fmb_B_c_vec$_2' ) ) ).
tff('declare_fun_app$p',type,
'fun_app$p': ( 'B_c_vec_b_c_vec_a_vec_fun$' * 'B_c_vec$' ) > 'B_c_vec_a_vec$' ).
tff('function_fun_app$p',axiom,
( ( 'fun_app$p'('fmb_B_c_vec_b_c_vec_a_vec_fun$_1','fmb_B_c_vec$_1') = 'fmb_B_c_vec_a_vec$_2' )
& ( 'fun_app$p'('fmb_B_c_vec_b_c_vec_a_vec_fun$_1','fmb_B_c_vec$_2') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'fun_app$p'('fmb_B_c_vec_b_c_vec_a_vec_fun$_2','fmb_B_c_vec$_1') = 'fmb_B_c_vec_a_vec$_2' )
& ( 'fun_app$p'('fmb_B_c_vec_b_c_vec_a_vec_fun$_2','fmb_B_c_vec$_2') = 'fmb_B_c_vec_a_vec$_1' ) ) ).
tff('declare_elt_set_plus$a',type,
'elt_set_plus$a': ( 'B_c_vec_a_vec_a_vec$' * 'B_c_vec_a_vec_a_vec_set$' ) > 'B_c_vec_a_vec_a_vec_set$' ).
tff('function_elt_set_plus$a',axiom,
( ( 'elt_set_plus$a'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'elt_set_plus$a'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'elt_set_plus$a'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_set$_1') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' )
& ( 'elt_set_plus$a'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_set$_2') = 'fmb_B_c_vec_a_vec_a_vec_set$_2' ) ) ).
tff('declare_transpose_row$a',type,
'transpose_row$a': 'B_c_vec_a_vec_a_vec$' > 'A_b_c_vec_a_vec_fun$' ).
tff('function_transpose_row$a',axiom,
( ( 'transpose_row$a'('fmb_B_c_vec_a_vec_a_vec$_1') = 'fmb_A_b_c_vec_a_vec_fun$_2' )
& ( 'transpose_row$a'('fmb_B_c_vec_a_vec_a_vec$_2') = 'fmb_A_b_c_vec_a_vec_fun$_1' ) ) ).
tff('declare_vec$',type,
'vec$': 'B$' > 'B_a_vec$' ).
tff('function_vec$',axiom,
( ( 'vec$'('fmb_B$_1') = 'fmb_B_a_vec$_1' )
& ( 'vec$'('fmb_B$_2') = 'fmb_B_a_vec$_2' ) ) ).
tff('declare_vec_nth$h',type,
'vec_nth$h': ( 'B_c_vec_a_vec_c_vec$' * 'C$' ) > 'B_c_vec_a_vec$' ).
tff('function_vec_nth$h',axiom,
( ( 'vec_nth$h'('fmb_B_c_vec_a_vec_c_vec$_1','fmb_C$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'vec_nth$h'('fmb_B_c_vec_a_vec_c_vec$_2','fmb_C$_1') = 'fmb_B_c_vec_a_vec$_2' ) ) ).
tff('declare_elt_set_times$d',type,
'elt_set_times$d': ( 'B_set$' * 'B_set_set$' ) > 'B_set_set$' ).
tff('function_elt_set_times$d',axiom,
( ( 'elt_set_times$d'('fmb_B_set$_1','fmb_B_set_set$_1') = 'fmb_B_set_set$_2' )
& ( 'elt_set_times$d'('fmb_B_set$_1','fmb_B_set_set$_2') = 'fmb_B_set_set$_2' )
& ( 'elt_set_times$d'('fmb_B_set$_2','fmb_B_set_set$_1') = 'fmb_B_set_set$_2' )
& ( 'elt_set_times$d'('fmb_B_set$_2','fmb_B_set_set$_2') = 'fmb_B_set_set$_2' ) ) ).
tff('declare_fun_app$c',type,
'fun_app$c': ( 'C_b_fun$' * 'C$' ) > 'B$' ).
tff('function_fun_app$c',axiom,
( ( 'fun_app$c'('fmb_C_b_fun$_1','fmb_C$_1') = 'fmb_B$_1' )
& ( 'fun_app$c'('fmb_C_b_fun$_2','fmb_C$_1') = 'fmb_B$_2' ) ) ).
tff('declare_interchange_columns$b',type,
'interchange_columns$b': ( 'B_c_vec_c_vec$' * 'C$' * 'C$' ) > 'B_c_vec_c_vec$' ).
tff('function_interchange_columns$b',axiom,
( ( 'interchange_columns$b'('fmb_B_c_vec_c_vec$_1','fmb_C$_1','fmb_C$_1') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'interchange_columns$b'('fmb_B_c_vec_c_vec$_2','fmb_C$_1','fmb_C$_1') = 'fmb_B_c_vec_c_vec$_2' ) ) ).
tff('declare_plus$i',type,
'plus$i': ( 'B_a_vec_set$' * 'B_a_vec_set$' ) > 'B_a_vec_set$' ).
tff('function_plus$i',axiom,
( ( 'plus$i'('fmb_B_a_vec_set$_1','fmb_B_a_vec_set$_1') = 'fmb_B_a_vec_set$_2' )
& ( 'plus$i'('fmb_B_a_vec_set$_1','fmb_B_a_vec_set$_2') = 'fmb_B_a_vec_set$_2' )
& ( 'plus$i'('fmb_B_a_vec_set$_2','fmb_B_a_vec_set$_1') = 'fmb_B_a_vec_set$_2' )
& ( 'plus$i'('fmb_B_a_vec_set$_2','fmb_B_a_vec_set$_2') = 'fmb_B_a_vec_set$_2' ) ) ).
tff('declare_fun_app$l',type,
'fun_app$l': ( 'B_b_c_vec_fun$' * 'B$' ) > 'B_c_vec$' ).
tff('function_fun_app$l',axiom,
( ( 'fun_app$l'('fmb_B_b_c_vec_fun$_1','fmb_B$_1') = 'fmb_B_c_vec$_2' )
& ( 'fun_app$l'('fmb_B_b_c_vec_fun$_1','fmb_B$_2') = 'fmb_B_c_vec$_1' )
& ( 'fun_app$l'('fmb_B_b_c_vec_fun$_2','fmb_B$_1') = 'fmb_B_c_vec$_2' )
& ( 'fun_app$l'('fmb_B_b_c_vec_fun$_2','fmb_B$_2') = 'fmb_B_c_vec$_1' ) ) ).
tff('declare_plus$d',type,
'plus$d': ( 'B_a_vec$' * 'B_a_vec$' ) > 'B_a_vec$' ).
tff('function_plus$d',axiom,
( ( 'plus$d'('fmb_B_a_vec$_1','fmb_B_a_vec$_1') = 'fmb_B_a_vec$_1' )
& ( 'plus$d'('fmb_B_a_vec$_1','fmb_B_a_vec$_2') = 'fmb_B_a_vec$_1' )
& ( 'plus$d'('fmb_B_a_vec$_2','fmb_B_a_vec$_1') = 'fmb_B_a_vec$_1' )
& ( 'plus$d'('fmb_B_a_vec$_2','fmb_B_a_vec$_2') = 'fmb_B_a_vec$_1' ) ) ).
tff('declare_columnvector_row$g',type,
'columnvector_row$g': ( 'B_a_vec_a_vec$' * 'A$' ) > 'B_a_vec_a_vec$' ).
tff('function_columnvector_row$g',axiom,
( ( 'columnvector_row$g'('fmb_B_a_vec_a_vec$_1','fmb_A$_1') = 'fmb_B_a_vec_a_vec$_1' )
& ( 'columnvector_row$g'('fmb_B_a_vec_a_vec$_2','fmb_A$_1') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_fun_app$v',type,
'fun_app$v': ( 'C_b_c_vec_bool_fun_fun$' * 'C$' ) > 'B_c_vec_bool_fun$' ).
tff('function_fun_app$v',axiom,
( ( 'fun_app$v'('fmb_C_b_c_vec_bool_fun_fun$_1','fmb_C$_1') = 'fmb_B_c_vec_bool_fun$_2' )
& ( 'fun_app$v'('fmb_C_b_c_vec_bool_fun_fun$_2','fmb_C$_1') = 'fmb_B_c_vec_bool_fun$_2' ) ) ).
tff('declare_transpose_row$g',type,
'transpose_row$g': ( 'B_a_vec_a_vec_a_vec$' * 'A$' ) > 'B_a_vec_a_vec$' ).
tff('function_transpose_row$g',axiom,
( ( 'transpose_row$g'('fmb_B_a_vec_a_vec_a_vec$_1','fmb_A$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'transpose_row$g'('fmb_B_a_vec_a_vec_a_vec$_2','fmb_A$_1') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_vec_nth$i',type,
'vec_nth$i': ( 'B_c_vec_c_vec_a_vec$' * 'A$' ) > 'B_c_vec_c_vec$' ).
tff('function_vec_nth$i',axiom,
( ( 'vec_nth$i'('fmb_B_c_vec_c_vec_a_vec$_1','fmb_A$_1') = 'fmb_B_c_vec_c_vec$_2' )
& ( 'vec_nth$i'('fmb_B_c_vec_c_vec_a_vec$_2','fmb_A$_1') = 'fmb_B_c_vec_c_vec$_2' ) ) ).
tff('declare_vector_scalar_mult$',type,
'vector_scalar_mult$': ( 'B_a_vec$' * 'B_a_vec_a_vec$' ) > 'B_a_vec_a_vec$' ).
tff('function_vector_scalar_mult$',axiom,
( ( 'vector_scalar_mult$'('fmb_B_a_vec$_1','fmb_B_a_vec_a_vec$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'vector_scalar_mult$'('fmb_B_a_vec$_1','fmb_B_a_vec_a_vec$_2') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'vector_scalar_mult$'('fmb_B_a_vec$_2','fmb_B_a_vec_a_vec$_1') = 'fmb_B_a_vec_a_vec$_2' )
& ( 'vector_scalar_mult$'('fmb_B_a_vec$_2','fmb_B_a_vec_a_vec$_2') = 'fmb_B_a_vec_a_vec$_2' ) ) ).
tff('declare_interchange_columns$e',type,
'interchange_columns$e': ( 'B_c_vec_a_vec$' * 'C$' * 'C$' ) > 'B_c_vec_a_vec$' ).
tff('function_interchange_columns$e',axiom,
( ( 'interchange_columns$e'('fmb_B_c_vec_a_vec$_1','fmb_C$_1','fmb_C$_1') = 'fmb_B_c_vec_a_vec$_1' )
& ( 'interchange_columns$e'('fmb_B_c_vec_a_vec$_2','fmb_C$_1','fmb_C$_1') = 'fmb_B_c_vec_a_vec$_2' ) ) ).
tff('declare_columnvector_row$c',type,
'columnvector_row$c': ( 'B_c_vec$' * 'C$' ) > 'B_a_vec$' ).
tff('function_columnvector_row$c',axiom,
( ( 'columnvector_row$c'('fmb_B_c_vec$_1','fmb_C$_1') = 'fmb_B_a_vec$_2' )
& ( 'columnvector_row$c'('fmb_B_c_vec$_2','fmb_C$_1') = 'fmb_B_a_vec$_1' ) ) ).
tff('declare_uu$',type,
'uu$': 'B_c_vec_set$' > 'B_c_vec_bool_fun$' ).
tff('function_uu$',axiom,
( ( 'uu$'('fmb_B_c_vec_set$_1') = 'fmb_B_c_vec_bool_fun$_2' )
& ( 'uu$'('fmb_B_c_vec_set$_2') = 'fmb_B_c_vec_bool_fun$_1' ) ) ).
tff('declare_times$n',type,
'times$n': ( 'B_c_vec_a_vec_set_set$' * 'B_c_vec_a_vec_set_set$' ) > 'B_c_vec_a_vec_set_set$' ).
tff('function_times$n',axiom,
( ( 'times$n'('fmb_B_c_vec_a_vec_set_set$_1','fmb_B_c_vec_a_vec_set_set$_1') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'times$n'('fmb_B_c_vec_a_vec_set_set$_1','fmb_B_c_vec_a_vec_set_set$_2') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'times$n'('fmb_B_c_vec_a_vec_set_set$_2','fmb_B_c_vec_a_vec_set_set$_1') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'times$n'('fmb_B_c_vec_a_vec_set_set$_2','fmb_B_c_vec_a_vec_set_set$_2') = 'fmb_B_c_vec_a_vec_set_set$_2' ) ) ).
tff('declare_interchange_rows_row$a',type,
'interchange_rows_row$a': ( 'B_c_vec_a_vec_a_vec_a_vec$' * 'A$' * 'A$' ) > 'A_b_c_vec_a_vec_a_vec_fun$' ).
tff('function_interchange_rows_row$a',axiom,
( ( 'interchange_rows_row$a'('fmb_B_c_vec_a_vec_a_vec_a_vec$_1','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_1' )
& ( 'interchange_rows_row$a'('fmb_B_c_vec_a_vec_a_vec_a_vec$_2','fmb_A$_1','fmb_A$_1') = 'fmb_A_b_c_vec_a_vec_a_vec_fun$_2' ) ) ).
tff('declare_interchange_columns_row$',type,
'interchange_columns_row$': ( 'B_c_vec_c_vec$' * 'C$' * 'C$' ) > 'C_b_c_vec_fun$' ).
tff('function_interchange_columns_row$',axiom,
( ( 'interchange_columns_row$'('fmb_B_c_vec_c_vec$_1','fmb_C$_1','fmb_C$_1') = 'fmb_C_b_c_vec_fun$_2' )
& ( 'interchange_columns_row$'('fmb_B_c_vec_c_vec$_2','fmb_C$_1','fmb_C$_1') = 'fmb_C_b_c_vec_fun$_1' ) ) ).
tff('declare_columnvector_row$d',type,
'columnvector_row$d': ( 'B_a_vec$' * 'A$' ) > 'B_a_vec$' ).
tff('function_columnvector_row$d',axiom,
( ( 'columnvector_row$d'('fmb_B_a_vec$_1','fmb_A$_1') = 'fmb_B_a_vec$_1' )
& ( 'columnvector_row$d'('fmb_B_a_vec$_2','fmb_A$_1') = 'fmb_B_a_vec$_2' ) ) ).
tff('declare_elt_set_plus$b',type,
'elt_set_plus$b': ( 'B_c_vec_set$' * 'B_c_vec_set_set$' ) > 'B_c_vec_set_set$' ).
tff('function_elt_set_plus$b',axiom,
( ( 'elt_set_plus$b'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set_set$_1') = 'fmb_B_c_vec_set_set$_2' )
& ( 'elt_set_plus$b'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set_set$_2') = 'fmb_B_c_vec_set_set$_2' )
& ( 'elt_set_plus$b'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set_set$_1') = 'fmb_B_c_vec_set_set$_2' )
& ( 'elt_set_plus$b'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set_set$_2') = 'fmb_B_c_vec_set_set$_2' ) ) ).
tff('declare_fun_app$j',type,
'fun_app$j': ( 'A_b_c_vec_fun$' * 'A$' ) > 'B_c_vec$' ).
tff('function_fun_app$j',axiom,
( ( 'fun_app$j'('fmb_A_b_c_vec_fun$_1','fmb_A$_1') = 'fmb_B_c_vec$_1' )
& ( 'fun_app$j'('fmb_A_b_c_vec_fun$_2','fmb_A$_1') = 'fmb_B_c_vec$_2' ) ) ).
tff('declare_vector_scalar_mult$f',type,
'vector_scalar_mult$f': ( 'B$' * 'B_a_vec$' ) > 'B_a_vec$' ).
tff('function_vector_scalar_mult$f',axiom,
( ( 'vector_scalar_mult$f'('fmb_B$_1','fmb_B_a_vec$_1') = 'fmb_B_a_vec$_1' )
& ( 'vector_scalar_mult$f'('fmb_B$_1','fmb_B_a_vec$_2') = 'fmb_B_a_vec$_1' )
& ( 'vector_scalar_mult$f'('fmb_B$_2','fmb_B_a_vec$_1') = 'fmb_B_a_vec$_1' )
& ( 'vector_scalar_mult$f'('fmb_B$_2','fmb_B_a_vec$_2') = 'fmb_B_a_vec$_1' ) ) ).
tff('declare_plus$n',type,
'plus$n': ( 'B_c_vec_a_vec_set_set$' * 'B_c_vec_a_vec_set_set$' ) > 'B_c_vec_a_vec_set_set$' ).
tff('function_plus$n',axiom,
( ( 'plus$n'('fmb_B_c_vec_a_vec_set_set$_1','fmb_B_c_vec_a_vec_set_set$_1') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'plus$n'('fmb_B_c_vec_a_vec_set_set$_1','fmb_B_c_vec_a_vec_set_set$_2') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'plus$n'('fmb_B_c_vec_a_vec_set_set$_2','fmb_B_c_vec_a_vec_set_set$_1') = 'fmb_B_c_vec_a_vec_set_set$_2' )
& ( 'plus$n'('fmb_B_c_vec_a_vec_set_set$_2','fmb_B_c_vec_a_vec_set_set$_2') = 'fmb_B_c_vec_a_vec_set_set$_2' ) ) ).
tff('declare_times$h',type,
'times$h': ( 'B_c_vec_c_vec$' * 'B_c_vec_c_vec$' ) > 'B_c_vec_c_vec$' ).
tff('function_times$h',axiom,
( ( 'times$h'('fmb_B_c_vec_c_vec$_1','fmb_B_c_vec_c_vec$_1') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'times$h'('fmb_B_c_vec_c_vec$_1','fmb_B_c_vec_c_vec$_2') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'times$h'('fmb_B_c_vec_c_vec$_2','fmb_B_c_vec_c_vec$_1') = 'fmb_B_c_vec_c_vec$_1' )
& ( 'times$h'('fmb_B_c_vec_c_vec$_2','fmb_B_c_vec_c_vec$_2') = 'fmb_B_c_vec_c_vec$_1' ) ) ).
tff('declare_fun_app$h',type,
'fun_app$h': ( 'A_b_a_vec_fun$' * 'A$' ) > 'B_a_vec$' ).
tff('function_fun_app$h',axiom,
( ( 'fun_app$h'('fmb_A_b_a_vec_fun$_1','fmb_A$_1') = 'fmb_B_a_vec$_1' )
& ( 'fun_app$h'('fmb_A_b_a_vec_fun$_2','fmb_A$_1') = 'fmb_B_a_vec$_2' ) ) ).
tff('declare_member$f',type,
'member$f': ( 'B_c_vec_a_vec_set$' * 'B_c_vec_a_vec_set_set$' ) > $o ).
tff('predicate_member$f',axiom,
( ~ 'member$f'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set_set$_1')
& ~ 'member$f'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set_set$_2')
& ~ 'member$f'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set_set$_1')
& ~ 'member$f'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set_set$_2') ) ).
tff('declare_member$b',type,
'member$b': ( 'B$' * 'B_set$' ) > $o ).
tff('predicate_member$b',axiom,
( ~ 'member$b'('fmb_B$_1','fmb_B_set$_1')
& ~ 'member$b'('fmb_B$_1','fmb_B_set$_2')
& ~ 'member$b'('fmb_B$_2','fmb_B_set$_1')
& ~ 'member$b'('fmb_B$_2','fmb_B_set$_2') ) ).
tff('declare_member$',type,
'member$': ( 'B_c_vec_a_vec$' * 'B_c_vec_a_vec_set$' ) > $o ).
tff('predicate_member$',axiom,
( ~ 'member$'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec_set$_1')
& ~ 'member$'('fmb_B_c_vec_a_vec$_1','fmb_B_c_vec_a_vec_set$_2')
& ~ 'member$'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec_set$_1')
& ~ 'member$'('fmb_B_c_vec_a_vec$_2','fmb_B_c_vec_a_vec_set$_2') ) ).
tff('declare_fun_app$a',type,
'fun_app$a': ( 'B_c_vec_bool_fun$' * 'B_c_vec$' ) > $o ).
tff('predicate_fun_app$a',axiom,
( ~ 'fun_app$a'('fmb_B_c_vec_bool_fun$_1','fmb_B_c_vec$_1')
& ~ 'fun_app$a'('fmb_B_c_vec_bool_fun$_1','fmb_B_c_vec$_2')
& ~ 'fun_app$a'('fmb_B_c_vec_bool_fun$_2','fmb_B_c_vec$_1')
& ~ 'fun_app$a'('fmb_B_c_vec_bool_fun$_2','fmb_B_c_vec$_2') ) ).
tff('declare_fun_app$',type,
'fun_app$': ( 'B_c_vec_a_vec_bool_fun$' * 'B_c_vec_a_vec$' ) > $o ).
tff('predicate_fun_app$',axiom,
( ~ 'fun_app$'('fmb_B_c_vec_a_vec_bool_fun$_1','fmb_B_c_vec_a_vec$_1')
& ~ 'fun_app$'('fmb_B_c_vec_a_vec_bool_fun$_1','fmb_B_c_vec_a_vec$_2')
& ~ 'fun_app$'('fmb_B_c_vec_a_vec_bool_fun$_2','fmb_B_c_vec_a_vec$_1')
& ~ 'fun_app$'('fmb_B_c_vec_a_vec_bool_fun$_2','fmb_B_c_vec_a_vec$_2') ) ).
tff('declare_fun_app$q',type,
'fun_app$q': ( 'B_a_vec_bool_fun$' * 'B_a_vec$' ) > $o ).
tff('predicate_fun_app$q',axiom,
( ~ 'fun_app$q'('fmb_B_a_vec_bool_fun$_1','fmb_B_a_vec$_1')
& ~ 'fun_app$q'('fmb_B_a_vec_bool_fun$_1','fmb_B_a_vec$_2')
& ~ 'fun_app$q'('fmb_B_a_vec_bool_fun$_2','fmb_B_a_vec$_1')
& ~ 'fun_app$q'('fmb_B_a_vec_bool_fun$_2','fmb_B_a_vec$_2') ) ).
tff('declare_member$e',type,
'member$e': ( 'B_c_vec_set$' * 'B_c_vec_set_set$' ) > $o ).
tff('predicate_member$e',axiom,
( ~ 'member$e'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set_set$_1')
& ~ 'member$e'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set_set$_2')
& ~ 'member$e'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set_set$_1')
& ~ 'member$e'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set_set$_2') ) ).
tff('declare_member$c',type,
'member$c': ( 'B_a_vec$' * 'B_a_vec_set$' ) > $o ).
tff('predicate_member$c',axiom,
( ~ 'member$c'('fmb_B_a_vec$_1','fmb_B_a_vec_set$_1')
& ~ 'member$c'('fmb_B_a_vec$_1','fmb_B_a_vec_set$_2')
& ~ 'member$c'('fmb_B_a_vec$_2','fmb_B_a_vec_set$_1')
& ~ 'member$c'('fmb_B_a_vec$_2','fmb_B_a_vec_set$_2') ) ).
tff('declare_member$d',type,
'member$d': ( 'B_c_vec_a_vec_a_vec$' * 'B_c_vec_a_vec_a_vec_set$' ) > $o ).
tff('predicate_member$d',axiom,
( ~ 'member$d'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_set$_1')
& ~ 'member$d'('fmb_B_c_vec_a_vec_a_vec$_1','fmb_B_c_vec_a_vec_a_vec_set$_2')
& ~ 'member$d'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_set$_1')
& ~ 'member$d'('fmb_B_c_vec_a_vec_a_vec$_2','fmb_B_c_vec_a_vec_a_vec_set$_2') ) ).
tff('declare_less_eq$b',type,
'less_eq$b': ( 'B_set$' * 'B_set$' ) > $o ).
tff('predicate_less_eq$b',axiom,
( 'less_eq$b'('fmb_B_set$_1','fmb_B_set$_1')
& 'less_eq$b'('fmb_B_set$_1','fmb_B_set$_2')
& 'less_eq$b'('fmb_B_set$_2','fmb_B_set$_1')
& 'less_eq$b'('fmb_B_set$_2','fmb_B_set$_2') ) ).
tff('declare_member$g',type,
'member$g': ( 'B_set$' * 'B_set_set$' ) > $o ).
tff('predicate_member$g',axiom,
( ~ 'member$g'('fmb_B_set$_1','fmb_B_set_set$_1')
& ~ 'member$g'('fmb_B_set$_1','fmb_B_set_set$_2')
& ~ 'member$g'('fmb_B_set$_2','fmb_B_set_set$_1')
& ~ 'member$g'('fmb_B_set$_2','fmb_B_set_set$_2') ) ).
tff('declare_fun_app$s',type,
'fun_app$s': ( 'B_c_vec_a_vec_a_vec_bool_fun$' * 'B_c_vec_a_vec_a_vec$' ) > $o ).
tff('predicate_fun_app$s',axiom,
( ~ 'fun_app$s'('fmb_B_c_vec_a_vec_a_vec_bool_fun$_1','fmb_B_c_vec_a_vec_a_vec$_1')
& ~ 'fun_app$s'('fmb_B_c_vec_a_vec_a_vec_bool_fun$_1','fmb_B_c_vec_a_vec_a_vec$_2')
& ~ 'fun_app$s'('fmb_B_c_vec_a_vec_a_vec_bool_fun$_2','fmb_B_c_vec_a_vec_a_vec$_1')
& ~ 'fun_app$s'('fmb_B_c_vec_a_vec_a_vec_bool_fun$_2','fmb_B_c_vec_a_vec_a_vec$_2') ) ).
tff('declare_less_eq$',type,
'less_eq$': ( 'B_c_vec_set$' * 'B_c_vec_set$' ) > $o ).
tff('predicate_less_eq$',axiom,
( 'less_eq$'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set$_1')
& 'less_eq$'('fmb_B_c_vec_set$_1','fmb_B_c_vec_set$_2')
& 'less_eq$'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set$_1')
& 'less_eq$'('fmb_B_c_vec_set$_2','fmb_B_c_vec_set$_2') ) ).
tff('declare_less_eq$a',type,
'less_eq$a': ( 'B_c_vec_a_vec_set$' * 'B_c_vec_a_vec_set$' ) > $o ).
tff('predicate_less_eq$a',axiom,
( 'less_eq$a'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set$_1')
& 'less_eq$a'('fmb_B_c_vec_a_vec_set$_1','fmb_B_c_vec_a_vec_set$_2')
& 'less_eq$a'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set$_1')
& 'less_eq$a'('fmb_B_c_vec_a_vec_set$_2','fmb_B_c_vec_a_vec_set$_2') ) ).
tff('declare_fun_app$b',type,
'fun_app$b': ( 'B_bool_fun$' * 'B$' ) > $o ).
tff('predicate_fun_app$b',axiom,
( ~ 'fun_app$b'('fmb_B_bool_fun$_1','fmb_B$_1')
& ~ 'fun_app$b'('fmb_B_bool_fun$_1','fmb_B$_2')
& ~ 'fun_app$b'('fmb_B_bool_fun$_2','fmb_B$_1')
& ~ 'fun_app$b'('fmb_B_bool_fun$_2','fmb_B$_2') ) ).
tff('declare_member$a',type,
'member$a': ( 'B_c_vec$' * 'B_c_vec_set$' ) > $o ).
tff('predicate_member$a',axiom,
( ~ 'member$a'('fmb_B_c_vec$_1','fmb_B_c_vec_set$_1')
& ~ 'member$a'('fmb_B_c_vec$_1','fmb_B_c_vec_set$_2')
& ~ 'member$a'('fmb_B_c_vec$_2','fmb_B_c_vec_set$_1')
& ~ 'member$a'('fmb_B_c_vec$_2','fmb_B_c_vec_set$_2') ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP323_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n026.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 12:57:12 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.43 Running first-order model finding
% 0.10/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.84/0.61 % (2817858)Will run a generic schedule for satisfiability detection.
% 0.84/0.61 % (2817873)dis+10_1_sil=32000:sp=arity:random_seed=2588232709:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.84/0.61 % (2817871)% WARNING: option uhcvi not known.
% 0.84/0.61 % (2817870)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=76831533_2999 on theBenchmark for (2999ds/0Mi)
% 0.84/0.61 % (2817871)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2605362325:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.84/0.61 % (2817872)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=93276899:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.84/0.61 % (2817874)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1144161376:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.84/0.61 % (2817875)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2148081073:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.84/0.61 % (2817876)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3498887064:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.84/0.61 % (2817873)Instruction limit reached!
% 0.84/0.61 % (2817873)------------------------------
% 0.84/0.61 % (2817873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.61 % (2817873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.61 % (2817873)CaDiCaL version: 2.1.3
% 0.84/0.61 % (2817873)Termination reason: Instruction limit
% 0.84/0.61 % (2817873)Termination phase: Saturation
% 0.84/0.61 % (2817873)Time elapsed: 0.035 s
% 0.84/0.61 % (2817873)Peak memory usage: 13 MB
% 0.84/0.61 % (2817873)Instructions burned: 103 (million)
% 0.84/0.61 % (2817884)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2951077413:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.84/0.61 % (2817874)Instruction limit reached!
% 0.84/0.61 % (2817874)------------------------------
% 0.84/0.61 % (2817874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.61 % (2817874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.61 % (2817874)CaDiCaL version: 2.1.3
% 0.84/0.61 % (2817874)Termination reason: Instruction limit
% 0.84/0.61 % (2817874)Termination phase: Saturation
% 0.84/0.61 % (2817874)Time elapsed: 0.065 s
% 0.84/0.61 % (2817874)Peak memory usage: 13 MB
% 0.84/0.61 % (2817874)Instructions burned: 116 (million)
% 0.84/0.61 % (2817875)Instruction limit reached!
% 0.84/0.61 % (2817875)------------------------------
% 0.84/0.61 % (2817875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.61 % (2817875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.61 % (2817875)CaDiCaL version: 2.1.3
% 0.84/0.61 % (2817875)Termination reason: Instruction limit
% 0.84/0.61 % (2817875)Termination phase: Saturation
% 0.84/0.61 % (2817875)Time elapsed: 0.077 s
% 0.84/0.61 % (2817875)Peak memory usage: 14 MB
% 0.84/0.61 % (2817875)Instructions burned: 131 (million)
% 0.84/0.61 % TRYING [1]
% 0.84/0.61 % (2817886)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=520139292:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.84/0.61 % TRYING [2]
% 0.84/0.61 % (2817887)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=2879557790:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.84/0.61 % (2817876)Instruction limit reached!
% 0.84/0.61 % (2817876)------------------------------
% 0.84/0.61 % (2817876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.61 % (2817876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.61 % (2817876)CaDiCaL version: 2.1.3
% 0.84/0.61 % (2817876)Termination reason: Instruction limit
% 0.84/0.61 % (2817876)Termination phase: Saturation
% 0.84/0.61 % (2817876)Time elapsed: 0.099 s
% 0.84/0.61 % (2817876)Peak memory usage: 15 MB
% 0.84/0.61 % (2817876)Instructions burned: 159 (million)
% 0.84/0.61 % (2817895)ott-21_1_sil=16000:fs=off:random_seed=1695923623:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.84/0.61 % Finite Model Found!
% 0.84/0.61 % SZS status CounterSatisfiable for theBenchmark
% 0.84/0.61 % (2817884) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2817858-2817884"...
% 0.84/0.61 % (2817884)...printing done.
% 0.84/0.61 % SZS output start FiniteModel for theBenchmark
% See solution above
% 0.84/0.62 % (2817884)------------------------------
% 0.84/0.62 % (2817884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.84/0.62 % (2817884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.62 % (2817884)CaDiCaL version: 2.1.3
% 0.84/0.62 % (2817884)Termination reason: Satisfiable
% 0.84/0.62 % (2817884)Time elapsed: 0.089 s
% 0.84/0.62 % (2817884)Peak memory usage: 22 MB
% 0.84/0.62 % (2817884)Instructions burned: 361 (million)
% 0.84/0.62 % (2817858)Success in time 0.173 s
% 0.84/0.62 % Vampire exiting
%------------------------------------------------------------------------------