TSTP Solution File: ITP341_10 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP341_10 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:14:32 EDT 2024
% Result : Satisfiable 5.44s 1.15s
% Output : FiniteModel 5.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP341_10 : TPTP v8.2.0. Released v8.2.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 18:57:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (23507)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.39 % (23510)WARNING: value z3 for option sas not known
% 0.13/0.39 % (23510)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.39 % (23511)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.39 % (23513)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.39 % (23514)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.39 % (23512)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.39 % (23509)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.39 % (23508)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.48 Detected minimum model sizes of [1,1,1,1,1,1,1,1,1,1,1]
% 0.20/0.48 Detected maximum model sizes of [max,max,max,max,max,max,max,max,max,max,2]
% 0.20/0.48 TRYING [1,1,1,1,1,1,1,1,1,1,1]
% 0.20/0.49 TRYING [1,1,1,1,1,1,1,1,1,1,2]
% 0.20/0.49 TRYING [1,1,1,1,1,1,2,1,1,1,2]
% 0.20/0.50 TRYING [1,1,1,1,2,1,2,1,1,1,2]
% 0.20/0.52 TRYING [1,1,2,1,2,1,2,1,1,1,2]
% 0.20/0.52 TRYING [1]
% 0.20/0.54 TRYING [2]
% 0.20/0.55 TRYING [2,1,2,1,2,1,2,1,1,1,2]
% 1.50/0.59 TRYING [3,1,2,1,2,1,2,1,1,1,2]
% 1.92/0.70 TRYING [2,1,2,1,2,1,2,1,1,2,2]
% 2.64/0.75 TRYING [3,1,2,1,2,1,2,1,1,2,2]
% 3.08/0.80 TRYING [3]
% 3.52/0.86 TRYING [2,1,2,1,2,1,2,1,2,2,2]
% 3.52/0.90 TRYING [2,1,3,1,2,1,2,1,2,2,2]
% 3.52/0.94 TRYING [2,1,2,1,2,1,3,1,2,2,2]
% 4.47/1.00 TRYING [2,1,4,1,2,1,2,1,2,2,2]
% 4.74/1.08 TRYING [2,1,3,1,2,1,2,1,3,2,2]
% 5.44/1.15 Finite Model Found!
% 5.44/1.15 % SZS status Satisfiable for theBenchmark
% 5.44/1.15 % (23511)First to succeed.
% 5.44/1.15 % (23511)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-23507"
% 5.44/1.16 % SZS output start FiniteModel for theBenchmark
% 5.44/1.16 tff(declare_$i,type,$i:$tType).
% 5.44/1.16 tff(declare_$i1,type,fmb_$i_1:$i).
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:$i] : (
% 5.44/1.16 X = fmb_$i_1
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(declare_bool,type,$o:$tType).
% 5.44/1.16 tff(declare_bool1,type,fmb_bool_1:$o).
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:$o] : (
% 5.44/1.16 X = fmb_bool_1
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_n_vec_n_vec_set_set$',type,'A_n_vec_n_vec_set_set$':$tType).
% 5.44/1.16 tff('declare_A_n_vec_n_vec_set_set$1',type,fmb_'A_n_vec_n_vec_set_set$'_1:'A_n_vec_n_vec_set_set$').
% 5.44/1.16 tff('declare_A_n_vec_n_vec_set_set$2',type,fmb_'A_n_vec_n_vec_set_set$'_2:'A_n_vec_n_vec_set_set$').
% 5.44/1.16 tff('declare_A_n_vec_n_vec_set_set$3',type,fmb_'A_n_vec_n_vec_set_set$'_3:'A_n_vec_n_vec_set_set$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_n_vec_n_vec_set_set$'] : (
% 5.44/1.16 X = fmb_'A_n_vec_n_vec_set_set$'_1 | X = fmb_'A_n_vec_n_vec_set_set$'_2 | X = fmb_'A_n_vec_n_vec_set_set$'_3
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 fmb_'A_n_vec_n_vec_set_set$'_1 != fmb_'A_n_vec_n_vec_set_set$'_2 & fmb_'A_n_vec_n_vec_set_set$'_1 != fmb_'A_n_vec_n_vec_set_set$'_3 & fmb_'A_n_vec_n_vec_set_set$'_2 != fmb_'A_n_vec_n_vec_set_set$'_3
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_set_set$',type,'A_set_set$':$tType).
% 5.44/1.16 tff('declare_A_set_set$1',type,fmb_'A_set_set$'_1:'A_set_set$').
% 5.44/1.16 tff('declare_A_set_set$2',type,fmb_'A_set_set$'_2:'A_set_set$').
% 5.44/1.16 tff('declare_A_set_set$3',type,fmb_'A_set_set$'_3:'A_set_set$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_set_set$'] : (
% 5.44/1.16 X = fmb_'A_set_set$'_1 | X = fmb_'A_set_set$'_2 | X = fmb_'A_set_set$'_3
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 fmb_'A_set_set$'_1 != fmb_'A_set_set$'_2 & fmb_'A_set_set$'_1 != fmb_'A_set_set$'_3 & fmb_'A_set_set$'_2 != fmb_'A_set_set$'_3
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_n_vec_set$',type,'A_n_vec_set$':$tType).
% 5.44/1.16 tff('declare_A_n_vec_set$1',type,'zero$f':'A_n_vec_set$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_n_vec_set$'] : (
% 5.44/1.16 X = 'zero$f'
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_n_vec_n_vec_bool_fun$',type,'A_n_vec_n_vec_bool_fun$':$tType).
% 5.44/1.16 tff('declare_A_n_vec_n_vec_bool_fun$1',type,'invertible$':'A_n_vec_n_vec_bool_fun$').
% 5.44/1.16 tff('declare_A_n_vec_n_vec_bool_fun$2',type,'reduced_row_echelon_form$':'A_n_vec_n_vec_bool_fun$').
% 5.44/1.16 tff('declare_A_n_vec_n_vec_bool_fun$3',type,fmb_'A_n_vec_n_vec_bool_fun$'_3:'A_n_vec_n_vec_bool_fun$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_n_vec_n_vec_bool_fun$'] : (
% 5.44/1.16 X = 'invertible$' | X = 'reduced_row_echelon_form$' | X = fmb_'A_n_vec_n_vec_bool_fun$'_3
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 'invertible$' != 'reduced_row_echelon_form$' & 'invertible$' != fmb_'A_n_vec_n_vec_bool_fun$'_3 & 'reduced_row_echelon_form$' != fmb_'A_n_vec_n_vec_bool_fun$'_3
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_n_vec_n_vec$',type,'A_n_vec_n_vec$':$tType).
% 5.44/1.16 tff('declare_A_n_vec_n_vec$1',type,'one$b':'A_n_vec_n_vec$').
% 5.44/1.16 tff('declare_A_n_vec_n_vec$2',type,'zero$a':'A_n_vec_n_vec$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_n_vec_n_vec$'] : (
% 5.44/1.16 X = 'one$b' | X = 'zero$a'
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 'one$b' != 'zero$a'
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_Nat$',type,'Nat$':$tType).
% 5.44/1.16 tff('declare_Nat$1',type,fmb_'Nat$'_1:'Nat$').
% 5.44/1.16 tff('declare_Nat$2',type,fmb_'Nat$'_2:'Nat$').
% 5.44/1.16 tff('declare_Nat$3',type,fmb_'Nat$'_3:'Nat$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'Nat$'] : (
% 5.44/1.16 X = fmb_'Nat$'_1 | X = fmb_'Nat$'_2 | X = fmb_'Nat$'_3
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 fmb_'Nat$'_1 != fmb_'Nat$'_2 & fmb_'Nat$'_1 != fmb_'Nat$'_3 & fmb_'Nat$'_2 != fmb_'Nat$'_3
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_n_vec_n_vec_set$',type,'A_n_vec_n_vec_set$':$tType).
% 5.44/1.16 tff('declare_A_n_vec_n_vec_set$1',type,'zero$e':'A_n_vec_n_vec_set$').
% 5.44/1.16 tff('declare_A_n_vec_n_vec_set$2',type,fmb_'A_n_vec_n_vec_set$'_2:'A_n_vec_n_vec_set$').
% 5.44/1.16 tff('declare_A_n_vec_n_vec_set$3',type,fmb_'A_n_vec_n_vec_set$'_3:'A_n_vec_n_vec_set$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_n_vec_n_vec_set$'] : (
% 5.44/1.16 X = 'zero$e' | X = fmb_'A_n_vec_n_vec_set$'_2 | X = fmb_'A_n_vec_n_vec_set$'_3
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 'zero$e' != fmb_'A_n_vec_n_vec_set$'_2 & 'zero$e' != fmb_'A_n_vec_n_vec_set$'_3 & fmb_'A_n_vec_n_vec_set$'_2 != fmb_'A_n_vec_n_vec_set$'_3
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_N$',type,'N$':$tType).
% 5.44/1.16 tff('declare_N$1',type,fmb_'N$'_1:'N$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'N$'] : (
% 5.44/1.16 X = fmb_'N$'_1
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff('declare_Num$',type,'Num$':$tType).
% 5.44/1.16 tff('declare_Num$1',type,fmb_'Num$'_1:'Num$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'Num$'] : (
% 5.44/1.16 X = fmb_'Num$'_1
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff('declare_Num_set$',type,'Num_set$':$tType).
% 5.44/1.16 tff('declare_Num_set$1',type,fmb_'Num_set$'_1:'Num_set$').
% 5.44/1.16 tff('declare_Num_set$2',type,fmb_'Num_set$'_2:'Num_set$').
% 5.44/1.16 tff('declare_Num_set$3',type,fmb_'Num_set$'_3:'Num_set$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'Num_set$'] : (
% 5.44/1.16 X = fmb_'Num_set$'_1 | X = fmb_'Num_set$'_2 | X = fmb_'Num_set$'_3
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 fmb_'Num_set$'_1 != fmb_'Num_set$'_2 & fmb_'Num_set$'_1 != fmb_'Num_set$'_3 & fmb_'Num_set$'_2 != fmb_'Num_set$'_3
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff(declare_tlbool,type,tlbool:$tType).
% 5.44/1.16 tff(declare_tlbool1,type,tltrue:tlbool).
% 5.44/1.16 tff(declare_tlbool2,type,tlfalse:tlbool).
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:tlbool] : (
% 5.44/1.16 X = tltrue | X = tlfalse
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 tltrue != tlfalse
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_bool_fun$',type,'A_bool_fun$':$tType).
% 5.44/1.16 tff('declare_A_bool_fun$1',type,fmb_'A_bool_fun$'_1:'A_bool_fun$').
% 5.44/1.16 tff('declare_A_bool_fun$2',type,fmb_'A_bool_fun$'_2:'A_bool_fun$').
% 5.44/1.16 tff('declare_A_bool_fun$3',type,fmb_'A_bool_fun$'_3:'A_bool_fun$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_bool_fun$'] : (
% 5.44/1.16 X = fmb_'A_bool_fun$'_1 | X = fmb_'A_bool_fun$'_2 | X = fmb_'A_bool_fun$'_3
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 fmb_'A_bool_fun$'_1 != fmb_'A_bool_fun$'_2 & fmb_'A_bool_fun$'_1 != fmb_'A_bool_fun$'_3 & fmb_'A_bool_fun$'_2 != fmb_'A_bool_fun$'_3
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_set$',type,'A_set$':$tType).
% 5.44/1.16 tff('declare_A_set$1',type,'zero$d':'A_set$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_set$'] : (
% 5.44/1.16 X = 'zero$d'
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_n_vec_set_set$',type,'A_n_vec_set_set$':$tType).
% 5.44/1.16 tff('declare_A_n_vec_set_set$1',type,fmb_'A_n_vec_set_set$'_1:'A_n_vec_set_set$').
% 5.44/1.16 tff('declare_A_n_vec_set_set$2',type,fmb_'A_n_vec_set_set$'_2:'A_n_vec_set_set$').
% 5.44/1.16 tff('declare_A_n_vec_set_set$3',type,fmb_'A_n_vec_set_set$'_3:'A_n_vec_set_set$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_n_vec_set_set$'] : (
% 5.44/1.16 X = fmb_'A_n_vec_set_set$'_1 | X = fmb_'A_n_vec_set_set$'_2 | X = fmb_'A_n_vec_set_set$'_3
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 fmb_'A_n_vec_set_set$'_1 != fmb_'A_n_vec_set_set$'_2 & fmb_'A_n_vec_set_set$'_1 != fmb_'A_n_vec_set_set$'_3 & fmb_'A_n_vec_set_set$'_2 != fmb_'A_n_vec_set_set$'_3
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A$',type,'A$':$tType).
% 5.44/1.16 tff('declare_A$1',type,'one$':'A$').
% 5.44/1.16 tff('declare_A$2',type,'zero$':'A$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A$'] : (
% 5.44/1.16 X = 'one$' | X = 'zero$'
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 'one$' != 'zero$'
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_n_vec$',type,'A_n_vec$':$tType).
% 5.44/1.16 tff('declare_A_n_vec$1',type,'zero$c':'A_n_vec$').
% 5.44/1.16 tff('declare_A_n_vec$2',type,'one$a':'A_n_vec$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_n_vec$'] : (
% 5.44/1.16 X = 'zero$c' | X = 'one$a'
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 'zero$c' != 'one$a'
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_a_fun$',type,'A_a_fun$':$tType).
% 5.44/1.16 tff('declare_A_a_fun$1',type,fmb_'A_a_fun$'_1:'A_a_fun$').
% 5.44/1.16 tff('declare_A_a_fun$2',type,fmb_'A_a_fun$'_2:'A_a_fun$').
% 5.44/1.16 tff('declare_A_a_fun$3',type,fmb_'A_a_fun$'_3:'A_a_fun$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_a_fun$'] : (
% 5.44/1.16 X = fmb_'A_a_fun$'_1 | X = fmb_'A_a_fun$'_2 | X = fmb_'A_a_fun$'_3
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 fmb_'A_a_fun$'_1 != fmb_'A_a_fun$'_2 & fmb_'A_a_fun$'_1 != fmb_'A_a_fun$'_3 & fmb_'A_a_fun$'_2 != fmb_'A_a_fun$'_3
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_n_vec_n_vec_n_vec$',type,'A_n_vec_n_vec_n_vec$':$tType).
% 5.44/1.16 tff('declare_A_n_vec_n_vec_n_vec$1',type,'zero$b':'A_n_vec_n_vec_n_vec$').
% 5.44/1.16 tff('declare_A_n_vec_n_vec_n_vec$2',type,fmb_'A_n_vec_n_vec_n_vec$'_2:'A_n_vec_n_vec_n_vec$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_n_vec_n_vec_n_vec$'] : (
% 5.44/1.16 X = 'zero$b' | X = fmb_'A_n_vec_n_vec_n_vec$'_2
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 'zero$b' != fmb_'A_n_vec_n_vec_n_vec$'_2
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_A_n_vec_bool_fun$',type,'A_n_vec_bool_fun$':$tType).
% 5.44/1.16 tff('declare_A_n_vec_bool_fun$1',type,fmb_'A_n_vec_bool_fun$'_1:'A_n_vec_bool_fun$').
% 5.44/1.16 tff('declare_A_n_vec_bool_fun$2',type,fmb_'A_n_vec_bool_fun$'_2:'A_n_vec_bool_fun$').
% 5.44/1.16 tff('declare_A_n_vec_bool_fun$3',type,fmb_'A_n_vec_bool_fun$'_3:'A_n_vec_bool_fun$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'A_n_vec_bool_fun$'] : (
% 5.44/1.16 X = fmb_'A_n_vec_bool_fun$'_1 | X = fmb_'A_n_vec_bool_fun$'_2 | X = fmb_'A_n_vec_bool_fun$'_3
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 fmb_'A_n_vec_bool_fun$'_1 != fmb_'A_n_vec_bool_fun$'_2 & fmb_'A_n_vec_bool_fun$'_1 != fmb_'A_n_vec_bool_fun$'_3 & fmb_'A_n_vec_bool_fun$'_2 != fmb_'A_n_vec_bool_fun$'_3
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_N_a_n_vec_n_vec_fun$',type,'N_a_n_vec_n_vec_fun$':$tType).
% 5.44/1.16 tff('declare_N_a_n_vec_n_vec_fun$1',type,fmb_'N_a_n_vec_n_vec_fun$'_1:'N_a_n_vec_n_vec_fun$').
% 5.44/1.16 tff('declare_N_a_n_vec_n_vec_fun$2',type,fmb_'N_a_n_vec_n_vec_fun$'_2:'N_a_n_vec_n_vec_fun$').
% 5.44/1.16 tff('declare_N_a_n_vec_n_vec_fun$3',type,fmb_'N_a_n_vec_n_vec_fun$'_3:'N_a_n_vec_n_vec_fun$').
% 5.44/1.16 tff(finite_domain,axiom,
% 5.44/1.16 ! [X:'N_a_n_vec_n_vec_fun$'] : (
% 5.44/1.16 X = fmb_'N_a_n_vec_n_vec_fun$'_1 | X = fmb_'N_a_n_vec_n_vec_fun$'_2 | X = fmb_'N_a_n_vec_n_vec_fun$'_3
% 5.44/1.16 ) ).
% 5.44/1.16
% 5.44/1.16 tff(distinct_domain,axiom,
% 5.44/1.16 fmb_'N_a_n_vec_n_vec_fun$'_1 != fmb_'N_a_n_vec_n_vec_fun$'_2 & fmb_'N_a_n_vec_n_vec_fun$'_1 != fmb_'N_a_n_vec_n_vec_fun$'_3 & fmb_'N_a_n_vec_n_vec_fun$'_2 != fmb_'N_a_n_vec_n_vec_fun$'_3
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_a$',type,'a$':'A_n_vec_n_vec$').
% 5.44/1.16 tff('a$_definition',axiom,'a$' = 'one$b').
% 5.44/1.16 tff('declare_orthogonal_matrix$',type,'orthogonal_matrix$':'A_n_vec_n_vec_bool_fun$').
% 5.44/1.16 tff('orthogonal_matrix$_definition',axiom,'orthogonal_matrix$' = 'invertible$').
% 5.44/1.16 tff('declare_one$c',type,'one$c':'A_set$').
% 5.44/1.16 tff('one$c_definition',axiom,'one$c' = 'zero$d').
% 5.44/1.16 tff('declare_p$',type,'p$':'A_n_vec_n_vec$').
% 5.44/1.16 tff('p$_definition',axiom,'p$' = 'one$b').
% 5.44/1.16 tff('declare_numeral$a',type,'numeral$a': 'Num$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_numeral$a',axiom,
% 5.44/1.16 'numeral$a'(fmb_'Num$'_1) = 'one$b'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_uu$',type,'uu$': 'A_set$' > 'A_bool_fun$').
% 5.44/1.16 tff('function_uu$',axiom,
% 5.44/1.16 'uu$'('zero$d') = fmb_'A_bool_fun$'_2
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_mat$',type,'mat$': 'A$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_mat$',axiom,
% 5.44/1.16 'mat$'('one$') = 'one$b'
% 5.44/1.16 & 'mat$'('zero$') = 'zero$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_uub$',type,'uub$': 'A_n_vec_set$' > 'A_n_vec_bool_fun$').
% 5.44/1.16 tff('function_uub$',axiom,
% 5.44/1.16 'uub$'('zero$f') = fmb_'A_n_vec_bool_fun$'_2
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_times$d',type,'times$d': 'A_n_vec_set$' * 'A_n_vec_set$' > 'A_n_vec_set$').
% 5.44/1.16 tff('function_times$d',axiom,
% 5.44/1.16 'times$d'('zero$f','zero$f') = 'zero$f'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_vector_matrix_mult$a',type,'vector_matrix_mult$a': 'A_n_vec$' * 'A_n_vec_n_vec$' > 'A_n_vec$').
% 5.44/1.16 tff('function_vector_matrix_mult$a',axiom,
% 5.44/1.16 'vector_matrix_mult$a'('zero$c','one$b') = 'zero$c'
% 5.44/1.16 & 'vector_matrix_mult$a'('zero$c','zero$a') = 'zero$c'
% 5.44/1.16 & 'vector_matrix_mult$a'('one$a','one$b') = 'one$a'
% 5.44/1.16 & 'vector_matrix_mult$a'('one$a','zero$a') = 'zero$c'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_axis$',type,'axis$': 'N$' * 'A_n_vec$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_axis$',axiom,
% 5.44/1.16 'axis$'(fmb_'N$'_1,'zero$c') = 'zero$a'
% 5.44/1.16 & 'axis$'(fmb_'N$'_1,'one$a') = 'one$b'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_columnvector$',type,'columnvector$': 'A_n_vec$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_columnvector$',axiom,
% 5.44/1.16 'columnvector$'('zero$c') = 'zero$a'
% 5.44/1.16 & 'columnvector$'('one$a') = 'zero$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_plus$g',type,'plus$g': 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_plus$g',axiom,
% 5.44/1.16 'plus$g'('one$b','one$b') = 'zero$a'
% 5.44/1.16 & 'plus$g'('one$b','zero$a') = 'one$b'
% 5.44/1.16 & 'plus$g'('zero$a','one$b') = 'one$b'
% 5.44/1.16 & 'plus$g'('zero$a','zero$a') = 'zero$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_times$g',type,'times$g': 'Num$' * 'Num$' > 'Num$').
% 5.44/1.16 tff('function_times$g',axiom,
% 5.44/1.16 'times$g'(fmb_'Num$'_1,fmb_'Num$'_1) = fmb_'Num$'_1
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_collect$a',type,'collect$a': 'A_n_vec_n_vec_bool_fun$' > 'A_n_vec_n_vec_set$').
% 5.44/1.16 tff('function_collect$a',axiom,
% 5.44/1.16 'collect$a'('invertible$') = fmb_'A_n_vec_n_vec_set$'_2
% 5.44/1.16 & 'collect$a'('reduced_row_echelon_form$') = fmb_'A_n_vec_n_vec_set$'_3
% 5.44/1.16 & 'collect$a'(fmb_'A_n_vec_n_vec_bool_fun$'_3) = 'zero$e'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_axis$a',type,'axis$a': 'N$' * 'A$' > 'A_n_vec$').
% 5.44/1.16 tff('function_axis$a',axiom,
% 5.44/1.16 'axis$a'(fmb_'N$'_1,'one$') = 'one$a'
% 5.44/1.16 & 'axis$a'(fmb_'N$'_1,'zero$') = 'zero$c'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_plus$c',type,'plus$c': 'A_n_vec_n_vec_set_set$' * 'A_n_vec_n_vec_set_set$' > 'A_n_vec_n_vec_set_set$').
% 5.44/1.16 tff('function_plus$c',axiom,
% 5.44/1.16 'plus$c'(fmb_'A_n_vec_n_vec_set_set$'_1,fmb_'A_n_vec_n_vec_set_set$'_1) = fmb_'A_n_vec_n_vec_set_set$'_2
% 5.44/1.16 & 'plus$c'(fmb_'A_n_vec_n_vec_set_set$'_1,fmb_'A_n_vec_n_vec_set_set$'_2) = fmb_'A_n_vec_n_vec_set_set$'_3
% 5.44/1.16 & 'plus$c'(fmb_'A_n_vec_n_vec_set_set$'_1,fmb_'A_n_vec_n_vec_set_set$'_3) = fmb_'A_n_vec_n_vec_set_set$'_2
% 5.44/1.16 & 'plus$c'(fmb_'A_n_vec_n_vec_set_set$'_2,fmb_'A_n_vec_n_vec_set_set$'_1) = fmb_'A_n_vec_n_vec_set_set$'_3
% 5.44/1.16 & 'plus$c'(fmb_'A_n_vec_n_vec_set_set$'_2,fmb_'A_n_vec_n_vec_set_set$'_2) = fmb_'A_n_vec_n_vec_set_set$'_2
% 5.44/1.16 & 'plus$c'(fmb_'A_n_vec_n_vec_set_set$'_2,fmb_'A_n_vec_n_vec_set_set$'_3) = fmb_'A_n_vec_n_vec_set_set$'_3
% 5.44/1.16 & 'plus$c'(fmb_'A_n_vec_n_vec_set_set$'_3,fmb_'A_n_vec_n_vec_set_set$'_1) = fmb_'A_n_vec_n_vec_set_set$'_2
% 5.44/1.16 & 'plus$c'(fmb_'A_n_vec_n_vec_set_set$'_3,fmb_'A_n_vec_n_vec_set_set$'_2) = fmb_'A_n_vec_n_vec_set_set$'_3
% 5.44/1.16 & 'plus$c'(fmb_'A_n_vec_n_vec_set_set$'_3,fmb_'A_n_vec_n_vec_set_set$'_3) = fmb_'A_n_vec_n_vec_set_set$'_2
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_plus$i',type,'plus$i': 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' > 'A_n_vec_n_vec_n_vec$').
% 5.44/1.16 tff('function_plus$i',axiom,
% 5.44/1.16 'plus$i'('zero$b','zero$b') = 'zero$b'
% 5.44/1.16 & 'plus$i'('zero$b',fmb_'A_n_vec_n_vec_n_vec$'_2) = fmb_'A_n_vec_n_vec_n_vec$'_2
% 5.44/1.16 & 'plus$i'(fmb_'A_n_vec_n_vec_n_vec$'_2,'zero$b') = fmb_'A_n_vec_n_vec_n_vec$'_2
% 5.44/1.16 & 'plus$i'(fmb_'A_n_vec_n_vec_n_vec$'_2,fmb_'A_n_vec_n_vec_n_vec$'_2) = 'zero$b'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_vec$a',type,'vec$a': 'A_n_vec$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_vec$a',axiom,
% 5.44/1.16 'vec$a'('zero$c') = 'zero$a'
% 5.44/1.16 & 'vec$a'('one$a') = 'one$b'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_times$a',type,'times$a': 'A_n_vec$' * 'A_n_vec$' > 'A_n_vec$').
% 5.44/1.16 tff('function_times$a',axiom,
% 5.44/1.16 'times$a'('zero$c','zero$c') = 'zero$c'
% 5.44/1.16 & 'times$a'('zero$c','one$a') = 'zero$c'
% 5.44/1.16 & 'times$a'('one$a','zero$c') = 'zero$c'
% 5.44/1.16 & 'times$a'('one$a','one$a') = 'one$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_times$',type,'times$': 'A$' * 'A$' > 'A$').
% 5.44/1.16 tff('function_times$',axiom,
% 5.44/1.16 'times$'('one$','one$') = 'one$'
% 5.44/1.16 & 'times$'('one$','zero$') = 'zero$'
% 5.44/1.16 & 'times$'('zero$','one$') = 'zero$'
% 5.44/1.16 & 'times$'('zero$','zero$') = 'zero$'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_collect$',type,'collect$': 'A_bool_fun$' > 'A_set$').
% 5.44/1.16 tff('function_collect$',axiom,
% 5.44/1.16 'collect$'(fmb_'A_bool_fun$'_1) = 'zero$d'
% 5.44/1.16 & 'collect$'(fmb_'A_bool_fun$'_2) = 'zero$d'
% 5.44/1.16 & 'collect$'(fmb_'A_bool_fun$'_3) = 'zero$d'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_matrix_inv$',type,'matrix_inv$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_matrix_inv$',axiom,
% 5.44/1.16 'matrix_inv$'('one$b') = 'one$b'
% 5.44/1.16 & 'matrix_inv$'('zero$a') = 'one$b'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_equivalent_matrices$',type,'equivalent_matrices$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_bool_fun$').
% 5.44/1.16 tff('function_equivalent_matrices$',axiom,
% 5.44/1.16 'equivalent_matrices$'('one$b') = 'invertible$'
% 5.44/1.16 & 'equivalent_matrices$'('zero$a') = fmb_'A_n_vec_n_vec_bool_fun$'_3
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_plus$a',type,'plus$a': 'A_set_set$' * 'A_set_set$' > 'A_set_set$').
% 5.44/1.16 tff('function_plus$a',axiom,
% 5.44/1.16 'plus$a'(fmb_'A_set_set$'_1,fmb_'A_set_set$'_1) = fmb_'A_set_set$'_1
% 5.44/1.16 & 'plus$a'(fmb_'A_set_set$'_1,fmb_'A_set_set$'_2) = fmb_'A_set_set$'_1
% 5.44/1.16 & 'plus$a'(fmb_'A_set_set$'_1,fmb_'A_set_set$'_3) = fmb_'A_set_set$'_1
% 5.44/1.16 & 'plus$a'(fmb_'A_set_set$'_2,fmb_'A_set_set$'_1) = fmb_'A_set_set$'_1
% 5.44/1.16 & 'plus$a'(fmb_'A_set_set$'_2,fmb_'A_set_set$'_2) = fmb_'A_set_set$'_2
% 5.44/1.16 & 'plus$a'(fmb_'A_set_set$'_2,fmb_'A_set_set$'_3) = fmb_'A_set_set$'_2
% 5.44/1.16 & 'plus$a'(fmb_'A_set_set$'_3,fmb_'A_set_set$'_1) = fmb_'A_set_set$'_1
% 5.44/1.16 & 'plus$a'(fmb_'A_set_set$'_3,fmb_'A_set_set$'_2) = fmb_'A_set_set$'_2
% 5.44/1.16 & 'plus$a'(fmb_'A_set_set$'_3,fmb_'A_set_set$'_3) = fmb_'A_set_set$'_3
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_plus$',type,'plus$': 'A_set$' * 'A_set$' > 'A_set$').
% 5.44/1.16 tff('function_plus$',axiom,
% 5.44/1.16 'plus$'('zero$d','zero$d') = 'zero$d'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_plus$h',type,'plus$h': 'A$' * 'A$' > 'A$').
% 5.44/1.16 tff('function_plus$h',axiom,
% 5.44/1.16 'plus$h'('one$','one$') = 'zero$'
% 5.44/1.16 & 'plus$h'('one$','zero$') = 'one$'
% 5.44/1.16 & 'plus$h'('zero$','one$') = 'one$'
% 5.44/1.16 & 'plus$h'('zero$','zero$') = 'zero$'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_row_add$',type,'row_add$': 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_row_add$',axiom,
% 5.44/1.16 'row_add$'('one$b',fmb_'N$'_1,fmb_'N$'_1,'one$') = 'one$b'
% 5.44/1.16 % 'row_add$'('one$b',fmb_'N$'_1,fmb_'N$'_1,'zero$') undefined in model
% 5.44/1.16 & 'row_add$'('zero$a',fmb_'N$'_1,fmb_'N$'_1,'one$') = 'zero$a'
% 5.44/1.16 % 'row_add$'('zero$a',fmb_'N$'_1,fmb_'N$'_1,'zero$') undefined in model
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_numeral$',type,'numeral$': 'Num$' > 'A_n_vec$').
% 5.44/1.16 tff('function_numeral$',axiom,
% 5.44/1.16 'numeral$'(fmb_'Num$'_1) = 'one$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_mat$a',type,'mat$a': 'A_n_vec$' > 'A_n_vec_n_vec_n_vec$').
% 5.44/1.16 tff('function_mat$a',axiom,
% 5.44/1.16 'mat$a'('zero$c') = fmb_'A_n_vec_n_vec_n_vec$'_2
% 5.44/1.16 & 'mat$a'('one$a') = fmb_'A_n_vec_n_vec_n_vec$'_2
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_collect$b',type,'collect$b': 'A_n_vec_bool_fun$' > 'A_n_vec_set$').
% 5.44/1.16 tff('function_collect$b',axiom,
% 5.44/1.16 'collect$b'(fmb_'A_n_vec_bool_fun$'_1) = 'zero$f'
% 5.44/1.16 & 'collect$b'(fmb_'A_n_vec_bool_fun$'_2) = 'zero$f'
% 5.44/1.16 & 'collect$b'(fmb_'A_n_vec_bool_fun$'_3) = 'zero$f'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_mult_column$',type,'mult_column$': 'A_n_vec_n_vec$' * 'N$' * 'A$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_mult_column$',axiom,
% 5.44/1.16 'mult_column$'('one$b',fmb_'N$'_1,'one$') = 'one$b'
% 5.44/1.16 & 'mult_column$'('one$b',fmb_'N$'_1,'zero$') = 'zero$a'
% 5.44/1.16 & 'mult_column$'('zero$a',fmb_'N$'_1,'one$') = 'zero$a'
% 5.44/1.16 & 'mult_column$'('zero$a',fmb_'N$'_1,'zero$') = 'zero$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_column_add$',type,'column_add$': 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_column_add$',axiom,
% 5.44/1.16 'column_add$'('one$b',fmb_'N$'_1,fmb_'N$'_1,'one$') = 'one$b'
% 5.44/1.16 % 'column_add$'('one$b',fmb_'N$'_1,fmb_'N$'_1,'zero$') undefined in model
% 5.44/1.16 & 'column_add$'('zero$a',fmb_'N$'_1,fmb_'N$'_1,'one$') = 'zero$a'
% 5.44/1.16 % 'column_add$'('zero$a',fmb_'N$'_1,fmb_'N$'_1,'zero$') undefined in model
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_plus$b',type,'plus$b': 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$' > 'A_n_vec_n_vec_set$').
% 5.44/1.16 tff('function_plus$b',axiom,
% 5.44/1.16 'plus$b'('zero$e','zero$e') = 'zero$e'
% 5.44/1.16 & 'plus$b'('zero$e',fmb_'A_n_vec_n_vec_set$'_2) = fmb_'A_n_vec_n_vec_set$'_2
% 5.44/1.16 & 'plus$b'('zero$e',fmb_'A_n_vec_n_vec_set$'_3) = fmb_'A_n_vec_n_vec_set$'_3
% 5.44/1.16 & 'plus$b'(fmb_'A_n_vec_n_vec_set$'_2,'zero$e') = fmb_'A_n_vec_n_vec_set$'_2
% 5.44/1.16 & 'plus$b'(fmb_'A_n_vec_n_vec_set$'_2,fmb_'A_n_vec_n_vec_set$'_2) = 'zero$e'
% 5.44/1.16 & 'plus$b'(fmb_'A_n_vec_n_vec_set$'_2,fmb_'A_n_vec_n_vec_set$'_3) = fmb_'A_n_vec_n_vec_set$'_3
% 5.44/1.16 & 'plus$b'(fmb_'A_n_vec_n_vec_set$'_3,'zero$e') = fmb_'A_n_vec_n_vec_set$'_3
% 5.44/1.16 & 'plus$b'(fmb_'A_n_vec_n_vec_set$'_3,fmb_'A_n_vec_n_vec_set$'_2) = fmb_'A_n_vec_n_vec_set$'_3
% 5.44/1.16 & 'plus$b'(fmb_'A_n_vec_n_vec_set$'_3,fmb_'A_n_vec_n_vec_set$'_3) = fmb_'A_n_vec_n_vec_set$'_3
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_divide$',type,'divide$': 'A$' > 'A_a_fun$').
% 5.44/1.16 tff('function_divide$',axiom,
% 5.44/1.16 'divide$'('one$') = fmb_'A_a_fun$'_2
% 5.44/1.16 & 'divide$'('zero$') = fmb_'A_a_fun$'_1
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_matrix_matrix_mult$',type,'matrix_matrix_mult$': 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_matrix_matrix_mult$',axiom,
% 5.44/1.16 'matrix_matrix_mult$'('one$b','one$b') = 'one$b'
% 5.44/1.16 & 'matrix_matrix_mult$'('one$b','zero$a') = 'zero$a'
% 5.44/1.16 & 'matrix_matrix_mult$'('zero$a','one$b') = 'zero$a'
% 5.44/1.16 & 'matrix_matrix_mult$'('zero$a','zero$a') = 'zero$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_transpose$',type,'transpose$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_transpose$',axiom,
% 5.44/1.16 'transpose$'('one$b') = 'one$b'
% 5.44/1.16 & 'transpose$'('zero$a') = 'zero$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_fun_app$d',type,'fun_app$d': 'A_a_fun$' * 'A$' > 'A$').
% 5.44/1.16 tff('function_fun_app$d',axiom,
% 5.44/1.16 'fun_app$d'(fmb_'A_a_fun$'_1,'one$') = 'zero$'
% 5.44/1.16 & 'fun_app$d'(fmb_'A_a_fun$'_1,'zero$') = 'zero$'
% 5.44/1.16 & 'fun_app$d'(fmb_'A_a_fun$'_2,'one$') = 'one$'
% 5.44/1.16 & 'fun_app$d'(fmb_'A_a_fun$'_2,'zero$') = 'zero$'
% 5.44/1.16 & 'fun_app$d'(fmb_'A_a_fun$'_3,'one$') = 'one$'
% 5.44/1.16 & 'fun_app$d'(fmb_'A_a_fun$'_3,'zero$') = 'one$'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_uua$',type,'uua$': 'A_n_vec_n_vec_set$' > 'A_n_vec_n_vec_bool_fun$').
% 5.44/1.16 tff('function_uua$',axiom,
% 5.44/1.16 'uua$'('zero$e') = fmb_'A_n_vec_n_vec_bool_fun$'_3
% 5.44/1.16 & 'uua$'(fmb_'A_n_vec_n_vec_set$'_2) = 'invertible$'
% 5.44/1.16 & 'uua$'(fmb_'A_n_vec_n_vec_set$'_3) = 'reduced_row_echelon_form$'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_matrix_vector_mult$a',type,'matrix_vector_mult$a': 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_matrix_vector_mult$a',axiom,
% 5.44/1.16 'matrix_vector_mult$a'('zero$b','one$b') = 'zero$a'
% 5.44/1.16 & 'matrix_vector_mult$a'('zero$b','zero$a') = 'zero$a'
% 5.44/1.16 & 'matrix_vector_mult$a'(fmb_'A_n_vec_n_vec_n_vec$'_2,'one$b') = 'one$b'
% 5.44/1.16 & 'matrix_vector_mult$a'(fmb_'A_n_vec_n_vec_n_vec$'_2,'zero$a') = 'zero$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_column$',type,'column$': 'N$' * 'A_n_vec_n_vec$' > 'A_n_vec$').
% 5.44/1.16 tff('function_column$',axiom,
% 5.44/1.16 'column$'(fmb_'N$'_1,'one$b') = 'zero$c'
% 5.44/1.16 & 'column$'(fmb_'N$'_1,'zero$a') = 'zero$c'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_vec$',type,'vec$': 'A$' > 'A_n_vec$').
% 5.44/1.16 tff('function_vec$',axiom,
% 5.44/1.16 'vec$'('one$') = 'one$a'
% 5.44/1.16 & 'vec$'('zero$') = 'zero$c'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_times$b',type,'times$b': 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_times$b',axiom,
% 5.44/1.16 'times$b'('one$b','one$b') = 'one$b'
% 5.44/1.16 & 'times$b'('one$b','zero$a') = 'zero$a'
% 5.44/1.16 & 'times$b'('zero$a','one$b') = 'zero$a'
% 5.44/1.16 & 'times$b'('zero$a','zero$a') = 'zero$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_plus$d',type,'plus$d': 'A_n_vec$' * 'A_n_vec$' > 'A_n_vec$').
% 5.44/1.16 tff('function_plus$d',axiom,
% 5.44/1.16 'plus$d'('zero$c','zero$c') = 'zero$c'
% 5.44/1.16 & 'plus$d'('zero$c','one$a') = 'one$a'
% 5.44/1.16 & 'plus$d'('one$a','zero$c') = 'one$a'
% 5.44/1.16 & 'plus$d'('one$a','one$a') = 'zero$c'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_fun_app$c',type,'fun_app$c': 'N_a_n_vec_n_vec_fun$' * 'N$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_fun_app$c',axiom,
% 5.44/1.16 'fun_app$c'(fmb_'N_a_n_vec_n_vec_fun$'_1,fmb_'N$'_1) = 'one$b'
% 5.44/1.16 & 'fun_app$c'(fmb_'N_a_n_vec_n_vec_fun$'_2,fmb_'N$'_1) = 'zero$a'
% 5.44/1.16 & 'fun_app$c'(fmb_'N_a_n_vec_n_vec_fun$'_3,fmb_'N$'_1) = 'zero$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_numeral$b',type,'numeral$b': 'Num$' > 'A$').
% 5.44/1.16 tff('function_numeral$b',axiom,
% 5.44/1.16 'numeral$b'(fmb_'Num$'_1) = 'zero$'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_plus$e',type,'plus$e': 'A_n_vec_set$' * 'A_n_vec_set$' > 'A_n_vec_set$').
% 5.44/1.16 tff('function_plus$e',axiom,
% 5.44/1.16 'plus$e'('zero$f','zero$f') = 'zero$f'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_times$h',type,'times$h': 'Num_set$' * 'Num_set$' > 'Num_set$').
% 5.44/1.16 tff('function_times$h',axiom,
% 5.44/1.16 'times$h'(fmb_'Num_set$'_1,fmb_'Num_set$'_1) = fmb_'Num_set$'_1
% 5.44/1.16 & 'times$h'(fmb_'Num_set$'_1,fmb_'Num_set$'_2) = fmb_'Num_set$'_1
% 5.44/1.16 & 'times$h'(fmb_'Num_set$'_1,fmb_'Num_set$'_3) = fmb_'Num_set$'_1
% 5.44/1.16 & 'times$h'(fmb_'Num_set$'_2,fmb_'Num_set$'_1) = fmb_'Num_set$'_2
% 5.44/1.16 & 'times$h'(fmb_'Num_set$'_2,fmb_'Num_set$'_2) = fmb_'Num_set$'_2
% 5.44/1.16 & 'times$h'(fmb_'Num_set$'_2,fmb_'Num_set$'_3) = fmb_'Num_set$'_2
% 5.44/1.16 & 'times$h'(fmb_'Num_set$'_3,fmb_'Num_set$'_1) = fmb_'Num_set$'_3
% 5.44/1.16 & 'times$h'(fmb_'Num_set$'_3,fmb_'Num_set$'_2) = fmb_'Num_set$'_3
% 5.44/1.16 & 'times$h'(fmb_'Num_set$'_3,fmb_'Num_set$'_3) = fmb_'Num_set$'_3
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_similar_matrices$',type,'similar_matrices$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_bool_fun$').
% 5.44/1.16 tff('function_similar_matrices$',axiom,
% 5.44/1.16 'similar_matrices$'('one$b') = 'invertible$'
% 5.44/1.16 & 'similar_matrices$'('zero$a') = fmb_'A_n_vec_n_vec_bool_fun$'_3
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_transpose$a',type,'transpose$a': 'A_n_vec_n_vec_n_vec$' > 'A_n_vec_n_vec_n_vec$').
% 5.44/1.16 tff('function_transpose$a',axiom,
% 5.44/1.16 'transpose$a'('zero$b') = 'zero$b'
% 5.44/1.16 & 'transpose$a'(fmb_'A_n_vec_n_vec_n_vec$'_2) = fmb_'A_n_vec_n_vec_n_vec$'_2
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_times$c',type,'times$c': 'A_set$' * 'A_set$' > 'A_set$').
% 5.44/1.16 tff('function_times$c',axiom,
% 5.44/1.16 'times$c'('zero$d','zero$d') = 'zero$d'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_mult_row$',type,'mult_row$': 'A_n_vec_n_vec$' * 'N$' * 'A$' > 'A_n_vec_n_vec$').
% 5.44/1.16 tff('function_mult_row$',axiom,
% 5.44/1.16 'mult_row$'('one$b',fmb_'N$'_1,'one$') = 'one$b'
% 5.44/1.16 & 'mult_row$'('one$b',fmb_'N$'_1,'zero$') = 'zero$a'
% 5.44/1.16 & 'mult_row$'('zero$a',fmb_'N$'_1,'one$') = 'zero$a'
% 5.44/1.16 & 'mult_row$'('zero$a',fmb_'N$'_1,'zero$') = 'zero$a'
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_matrix_matrix_mult$a',type,'matrix_matrix_mult$a': 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' > 'A_n_vec_n_vec_n_vec$').
% 5.44/1.16 tff('function_matrix_matrix_mult$a',axiom,
% 5.44/1.16 'matrix_matrix_mult$a'('zero$b','zero$b') = 'zero$b'
% 5.44/1.16 & 'matrix_matrix_mult$a'('zero$b',fmb_'A_n_vec_n_vec_n_vec$'_2) = 'zero$b'
% 5.44/1.16 & 'matrix_matrix_mult$a'(fmb_'A_n_vec_n_vec_n_vec$'_2,'zero$b') = 'zero$b'
% 5.44/1.16 & 'matrix_matrix_mult$a'(fmb_'A_n_vec_n_vec_n_vec$'_2,fmb_'A_n_vec_n_vec_n_vec$'_2) = fmb_'A_n_vec_n_vec_n_vec$'_2
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_interchange_rows$',type,'interchange_rows$': 'A_n_vec_n_vec$' * 'N$' > 'N_a_n_vec_n_vec_fun$').
% 5.44/1.16 tff('function_interchange_rows$',axiom,
% 5.44/1.16 'interchange_rows$'('one$b',fmb_'N$'_1) = fmb_'N_a_n_vec_n_vec_fun$'_1
% 5.44/1.16 & 'interchange_rows$'('zero$a',fmb_'N$'_1) = fmb_'N_a_n_vec_n_vec_fun$'_3
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_times$e',type,'times$e': 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$' > 'A_n_vec_n_vec_set$').
% 5.44/1.16 tff('function_times$e',axiom,
% 5.44/1.16 'times$e'('zero$e','zero$e') = 'zero$e'
% 5.44/1.16 & 'times$e'('zero$e',fmb_'A_n_vec_n_vec_set$'_2) = 'zero$e'
% 5.44/1.16 & 'times$e'('zero$e',fmb_'A_n_vec_n_vec_set$'_3) = 'zero$e'
% 5.44/1.16 & 'times$e'(fmb_'A_n_vec_n_vec_set$'_2,'zero$e') = 'zero$e'
% 5.44/1.16 & 'times$e'(fmb_'A_n_vec_n_vec_set$'_2,fmb_'A_n_vec_n_vec_set$'_2) = fmb_'A_n_vec_n_vec_set$'_2
% 5.44/1.16 & 'times$e'(fmb_'A_n_vec_n_vec_set$'_2,fmb_'A_n_vec_n_vec_set$'_3) = fmb_'A_n_vec_n_vec_set$'_3
% 5.44/1.16 & 'times$e'(fmb_'A_n_vec_n_vec_set$'_3,'zero$e') = 'zero$e'
% 5.44/1.16 & 'times$e'(fmb_'A_n_vec_n_vec_set$'_3,fmb_'A_n_vec_n_vec_set$'_2) = fmb_'A_n_vec_n_vec_set$'_3
% 5.44/1.16 & 'times$e'(fmb_'A_n_vec_n_vec_set$'_3,fmb_'A_n_vec_n_vec_set$'_3) = fmb_'A_n_vec_n_vec_set$'_3
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_times$f',type,'times$f': 'A_set_set$' * 'A_set_set$' > 'A_set_set$').
% 5.44/1.16 tff('function_times$f',axiom,
% 5.44/1.16 'times$f'(fmb_'A_set_set$'_1,fmb_'A_set_set$'_1) = fmb_'A_set_set$'_1
% 5.44/1.16 & 'times$f'(fmb_'A_set_set$'_1,fmb_'A_set_set$'_2) = fmb_'A_set_set$'_1
% 5.44/1.16 & 'times$f'(fmb_'A_set_set$'_1,fmb_'A_set_set$'_3) = fmb_'A_set_set$'_3
% 5.44/1.16 & 'times$f'(fmb_'A_set_set$'_2,fmb_'A_set_set$'_1) = fmb_'A_set_set$'_2
% 5.44/1.16 & 'times$f'(fmb_'A_set_set$'_2,fmb_'A_set_set$'_2) = fmb_'A_set_set$'_2
% 5.44/1.16 & 'times$f'(fmb_'A_set_set$'_2,fmb_'A_set_set$'_3) = fmb_'A_set_set$'_3
% 5.44/1.16 & 'times$f'(fmb_'A_set_set$'_3,fmb_'A_set_set$'_1) = fmb_'A_set_set$'_3
% 5.44/1.16 & 'times$f'(fmb_'A_set_set$'_3,fmb_'A_set_set$'_2) = fmb_'A_set_set$'_3
% 5.44/1.16 & 'times$f'(fmb_'A_set_set$'_3,fmb_'A_set_set$'_3) = fmb_'A_set_set$'_3
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_plus$f',type,'plus$f': 'A_n_vec_set_set$' * 'A_n_vec_set_set$' > 'A_n_vec_set_set$').
% 5.44/1.16 tff('function_plus$f',axiom,
% 5.44/1.16 'plus$f'(fmb_'A_n_vec_set_set$'_1,fmb_'A_n_vec_set_set$'_1) = fmb_'A_n_vec_set_set$'_1
% 5.44/1.16 & 'plus$f'(fmb_'A_n_vec_set_set$'_1,fmb_'A_n_vec_set_set$'_2) = fmb_'A_n_vec_set_set$'_1
% 5.44/1.16 & 'plus$f'(fmb_'A_n_vec_set_set$'_1,fmb_'A_n_vec_set_set$'_3) = fmb_'A_n_vec_set_set$'_2
% 5.44/1.16 & 'plus$f'(fmb_'A_n_vec_set_set$'_2,fmb_'A_n_vec_set_set$'_1) = fmb_'A_n_vec_set_set$'_1
% 5.44/1.16 & 'plus$f'(fmb_'A_n_vec_set_set$'_2,fmb_'A_n_vec_set_set$'_2) = fmb_'A_n_vec_set_set$'_2
% 5.44/1.16 & 'plus$f'(fmb_'A_n_vec_set_set$'_2,fmb_'A_n_vec_set_set$'_3) = fmb_'A_n_vec_set_set$'_2
% 5.44/1.16 & 'plus$f'(fmb_'A_n_vec_set_set$'_3,fmb_'A_n_vec_set_set$'_1) = fmb_'A_n_vec_set_set$'_3
% 5.44/1.16 & 'plus$f'(fmb_'A_n_vec_set_set$'_3,fmb_'A_n_vec_set_set$'_2) = fmb_'A_n_vec_set_set$'_2
% 5.44/1.16 & 'plus$f'(fmb_'A_n_vec_set_set$'_3,fmb_'A_n_vec_set_set$'_3) = fmb_'A_n_vec_set_set$'_3
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_member$f',type,'member$f': 'A_n_vec_set$' * 'A_n_vec_set_set$' > $o ).
% 5.44/1.16 tff('predicate_member$f',axiom,
% 5.44/1.16 ~'member$f'('zero$f',fmb_'A_n_vec_set_set$'_1)
% 5.44/1.16 & ~'member$f'('zero$f',fmb_'A_n_vec_set_set$'_2)
% 5.44/1.16 & ~'member$f'('zero$f',fmb_'A_n_vec_set_set$'_3)
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_member$',type,'member$': 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_set$' > $o ).
% 5.44/1.16 tff('predicate_member$',axiom,
% 5.44/1.16 ~'member$'('one$b','zero$e')
% 5.44/1.16 & 'member$'('one$b',fmb_'A_n_vec_n_vec_set$'_2)
% 5.44/1.16 & 'member$'('one$b',fmb_'A_n_vec_n_vec_set$'_3)
% 5.44/1.16 & 'member$'('zero$a','zero$e')
% 5.44/1.16 & ~'member$'('zero$a',fmb_'A_n_vec_n_vec_set$'_2)
% 5.44/1.16 & 'member$'('zero$a',fmb_'A_n_vec_n_vec_set$'_3)
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_member$e',type,'member$e': 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set_set$' > $o ).
% 5.44/1.16 tff('predicate_member$e',axiom,
% 5.44/1.16 ~'member$e'('zero$e',fmb_'A_n_vec_n_vec_set_set$'_1)
% 5.44/1.16 & 'member$e'('zero$e',fmb_'A_n_vec_n_vec_set_set$'_2)
% 5.44/1.16 & ~'member$e'('zero$e',fmb_'A_n_vec_n_vec_set_set$'_3)
% 5.44/1.16 & 'member$e'(fmb_'A_n_vec_n_vec_set$'_2,fmb_'A_n_vec_n_vec_set_set$'_1)
% 5.44/1.16 & ~'member$e'(fmb_'A_n_vec_n_vec_set$'_2,fmb_'A_n_vec_n_vec_set_set$'_2)
% 5.44/1.16 & 'member$e'(fmb_'A_n_vec_n_vec_set$'_2,fmb_'A_n_vec_n_vec_set_set$'_3)
% 5.44/1.16 & ~'member$e'(fmb_'A_n_vec_n_vec_set$'_3,fmb_'A_n_vec_n_vec_set_set$'_1)
% 5.44/1.16 & ~'member$e'(fmb_'A_n_vec_n_vec_set$'_3,fmb_'A_n_vec_n_vec_set_set$'_2)
% 5.44/1.16 & ~'member$e'(fmb_'A_n_vec_n_vec_set$'_3,fmb_'A_n_vec_n_vec_set_set$'_3)
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_member$d',type,'member$d': 'Num$' * 'Num_set$' > $o ).
% 5.44/1.16 tff('predicate_member$d',axiom,
% 5.44/1.16 ~'member$d'(fmb_'Num$'_1,fmb_'Num_set$'_1)
% 5.44/1.16 & ~'member$d'(fmb_'Num$'_1,fmb_'Num_set$'_2)
% 5.44/1.16 & ~'member$d'(fmb_'Num$'_1,fmb_'Num_set$'_3)
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_member$b',type,'member$b': 'A$' * 'A_set$' > $o ).
% 5.44/1.16 tff('predicate_member$b',axiom,
% 5.44/1.16 ~'member$b'('one$','zero$d')
% 5.44/1.16 & 'member$b'('zero$','zero$d')
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_fun_app$b',type,'fun_app$b': 'A_bool_fun$' * 'A$' > $o ).
% 5.44/1.16 tff('predicate_fun_app$b',axiom,
% 5.44/1.16 ~'fun_app$b'(fmb_'A_bool_fun$'_1,'one$')
% 5.44/1.16 & 'fun_app$b'(fmb_'A_bool_fun$'_1,'zero$')
% 5.44/1.16 & ~'fun_app$b'(fmb_'A_bool_fun$'_2,'one$')
% 5.44/1.16 & 'fun_app$b'(fmb_'A_bool_fun$'_2,'zero$')
% 5.44/1.16 & ~'fun_app$b'(fmb_'A_bool_fun$'_3,'one$')
% 5.44/1.16 & 'fun_app$b'(fmb_'A_bool_fun$'_3,'zero$')
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_less_eq$',type,'less_eq$': 'A_n_vec_set$' * 'A_n_vec_set$' > $o ).
% 5.44/1.16 tff('predicate_less_eq$',axiom,
% 5.44/1.16 'less_eq$'('zero$f','zero$f')
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_fun_app$a',type,'fun_app$a': 'A_n_vec_bool_fun$' * 'A_n_vec$' > $o ).
% 5.44/1.16 tff('predicate_fun_app$a',axiom,
% 5.44/1.16 'fun_app$a'(fmb_'A_n_vec_bool_fun$'_1,'zero$c')
% 5.44/1.16 & ~'fun_app$a'(fmb_'A_n_vec_bool_fun$'_1,'one$a')
% 5.44/1.16 & 'fun_app$a'(fmb_'A_n_vec_bool_fun$'_2,'zero$c')
% 5.44/1.16 & ~'fun_app$a'(fmb_'A_n_vec_bool_fun$'_2,'one$a')
% 5.44/1.16 & 'fun_app$a'(fmb_'A_n_vec_bool_fun$'_3,'zero$c')
% 5.44/1.16 & ~'fun_app$a'(fmb_'A_n_vec_bool_fun$'_3,'one$a')
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_invertible$a',type,'invertible$a': 'A_n_vec_n_vec_n_vec$' > $o ).
% 5.44/1.16 tff('predicate_invertible$a',axiom,
% 5.44/1.16 % 'invertible$a'('zero$b') undefined in model
% 5.44/1.16 % 'invertible$a'(fmb_'A_n_vec_n_vec_n_vec$'_2) undefined in model
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_less_eq$a',type,'less_eq$a': 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$' > $o ).
% 5.44/1.16 tff('predicate_less_eq$a',axiom,
% 5.44/1.16 'less_eq$a'('zero$e','zero$e')
% 5.44/1.16 & ~'less_eq$a'('zero$e',fmb_'A_n_vec_n_vec_set$'_2)
% 5.44/1.16 & 'less_eq$a'('zero$e',fmb_'A_n_vec_n_vec_set$'_3)
% 5.44/1.16 & ~'less_eq$a'(fmb_'A_n_vec_n_vec_set$'_2,'zero$e')
% 5.44/1.16 & 'less_eq$a'(fmb_'A_n_vec_n_vec_set$'_2,fmb_'A_n_vec_n_vec_set$'_2)
% 5.44/1.16 & 'less_eq$a'(fmb_'A_n_vec_n_vec_set$'_2,fmb_'A_n_vec_n_vec_set$'_3)
% 5.44/1.16 & ~'less_eq$a'(fmb_'A_n_vec_n_vec_set$'_3,'zero$e')
% 5.44/1.16 & ~'less_eq$a'(fmb_'A_n_vec_n_vec_set$'_3,fmb_'A_n_vec_n_vec_set$'_2)
% 5.44/1.16 & 'less_eq$a'(fmb_'A_n_vec_n_vec_set$'_3,fmb_'A_n_vec_n_vec_set$'_3)
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_less_eq$b',type,'less_eq$b': 'A_set$' * 'A_set$' > $o ).
% 5.44/1.16 tff('predicate_less_eq$b',axiom,
% 5.44/1.16 'less_eq$b'('zero$d','zero$d')
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_member$c',type,'member$c': 'A_set$' * 'A_set_set$' > $o ).
% 5.44/1.16 tff('predicate_member$c',axiom,
% 5.44/1.16 ~'member$c'('zero$d',fmb_'A_set_set$'_1)
% 5.44/1.16 & ~'member$c'('zero$d',fmb_'A_set_set$'_2)
% 5.44/1.16 & ~'member$c'('zero$d',fmb_'A_set_set$'_3)
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_member$a',type,'member$a': 'A_n_vec$' * 'A_n_vec_set$' > $o ).
% 5.44/1.16 tff('predicate_member$a',axiom,
% 5.44/1.16 'member$a'('zero$c','zero$f')
% 5.44/1.16 & ~'member$a'('one$a','zero$f')
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 tff('declare_fun_app$',type,'fun_app$': 'A_n_vec_n_vec_bool_fun$' * 'A_n_vec_n_vec$' > $o ).
% 5.44/1.16 tff('predicate_fun_app$',axiom,
% 5.44/1.16 'fun_app$'('invertible$','one$b')
% 5.44/1.16 & ~'fun_app$'('invertible$','zero$a')
% 5.44/1.16 & 'fun_app$'('reduced_row_echelon_form$','one$b')
% 5.44/1.16 & 'fun_app$'('reduced_row_echelon_form$','zero$a')
% 5.44/1.16 & ~'fun_app$'(fmb_'A_n_vec_n_vec_bool_fun$'_3,'one$b')
% 5.44/1.16 & 'fun_app$'(fmb_'A_n_vec_n_vec_bool_fun$'_3,'zero$a')
% 5.44/1.16
% 5.44/1.16 ).
% 5.44/1.16
% 5.44/1.16 % SZS output end FiniteModel for theBenchmark
% 5.44/1.16 % (23511)------------------------------
% 5.44/1.16 % (23511)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 5.44/1.16 % (23511)Termination reason: Satisfiable
% 5.44/1.16
% 5.44/1.16 % (23511)Memory used [KB]: 5479
% 5.44/1.16 % (23511)Time elapsed: 0.763 s
% 5.44/1.16 % (23511)Instructions burned: 2169 (million)
% 5.44/1.16 % (23507)Success in time 0.79 s
%------------------------------------------------------------------------------