TSTP Solution File: ITP338_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n026.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 : Tue Aug 22 10:44:30 EDT 2023
% Result : Theorem 18.65s 5.43s
% Output : CNFRefutation 18.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n026.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 : Thu Aug 3 19:20:46 EDT 2023
% 0.13/0.35 % CPUTime :
% 18.65/5.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.65/5.44
% 18.65/5.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.65/5.46 %$ member$b > member$a > member$ > less_eq$d > less_eq$c > less_eq$b > less_eq$ > less$b > less$a > fun_app$s > fun_app$q > fun_app$o > fun_app$m > fun_app$k > fun_app$j > fun_app$i > fun_app$h > fun_app$g > fun_app$f > fun_app$e > upper_triangular$a > upper_triangular$ > divides_aux$ > row_add_iterate_PA$ > gauss_Jordan_in_ij_det_P_iarrays$ > gauss_Jordan_in_ij_det_P$c > gauss_Jordan_in_ij_det_P$b > gauss_Jordan_in_ij_det_P$a > gauss_Jordan_in_ij_det_P$ > gauss_Jordan_in_ij_PA$c > gauss_Jordan_in_ij_PA$b > gauss_Jordan_in_ij_PA$a > gauss_Jordan_in_ij_PA$ > vec_nth$f > vec_nth$e > vec_nth$d > vec_nth$c > vec_nth$b > times$g > times$f > times$e > times$d > times$c > times$a > plus$q > plus$p > plus$o > plus$n > plus$m > plus$l > plus$k > plus$j > plus$i > plus$h > plus$g > plus$f > plus$e > plus$d > plus$c > plus$b > pair$x > pair$w > pair$v > pair$u > pair$t > pair$s > pair$r > pair$q > pair$p > pair$o > pair$n > pair$m > pair$l > pair$k > pair$j > pair$i > pair$h > pair$g > pair$f > pair$e > pair$d > pair$c > pair$b > pair$a > pair$ > map_matrix$ > gauss_Jordan_column_k_det_P_iarrays$ > gauss_Jordan_column_k_det_P$c > gauss_Jordan_column_k_det_P$b > gauss_Jordan_column_k_det_P$a > gauss_Jordan_column_k_det_P$ > gauss_Jordan_column_k_PA$c > gauss_Jordan_column_k_PA$b > gauss_Jordan_column_k_PA$a > gauss_Jordan_column_k_PA$ > fun_app$x > fun_app$w > fun_app$v > fun_app$u > fun_app$t > fun_app$r > fun_app$p > fun_app$n > fun_app$l > fun_app$d > fun_app$c > fun_app$b > fun_app$a > fun_app$ > column_iarray$ > #nlpp > vec_nth$a > vec_nth$ > upper_triangular_upt_k$a > upper_triangular_upt_k$ > to_nat$a > to_nat$ > times$b > times$ > snd$x > snd$w > snd$v > snd$u > snd$t > snd$s > snd$r > snd$q > snd$p > snd$o > snd$n > snd$m > snd$l > snd$k > snd$j > snd$i > snd$h > snd$g > snd$f > snd$e > snd$d > snd$c > snd$b > snd$a > snd$ > plus$a > plus$ > of_nat$ > nrows_iarray$ > nrows$c > nrows$b > nrows$a > nrows$ > ncols$ > nat$ > matrix_to_iarray$ > less_eq$a > less$ > fst$x > fst$w > fst$v > fst$u > fst$t > fst$s > fst$r > fst$q > fst$p > fst$o > fst$n > fst$m > fst$l > fst$k > fst$j > fst$i > fst$h > fst$g > fst$f > fst$e > fst$d > fst$c > fst$b > fst$a > fst$ > from_nat$a > from_nat$ > zero$l > zero$k > zero$j > zero$i > zero$h > zero$g > zero$f > zero$e > zero$d > zero$c > zero$b > zero$a > zero$ > vector_all_zero_from_index$ > uug$ > uuf$ > uue$ > uud$ > uuc$ > uub$ > uua$ > uu$ > tltrue > tlfalse > one$e > one$d > one$c > one$b > one$a > one$ > n$ > k$ > i$ > a$ > #skF_21 > #skF_71 > #skF_35 > #skF_61 > #skF_37 > #skF_44 > #skF_79 > #skF_22 > #skF_47 > #skF_54 > #skF_87 > #skF_46 > #skF_26 > #skF_6 > #skF_66 > #skF_80 > #skF_51 > #skF_27 > #skF_3 > #skF_50 > #skF_15 > #skF_81 > #skF_18 > #skF_57 > #skF_5 > #skF_73 > #skF_56 > #skF_68 > #skF_29 > #skF_63 > #skF_42 > #skF_40 > #skF_59 > #skF_67 > #skF_89 > #skF_39 > #skF_32 > #skF_78 > #skF_49 > #skF_7 > #skF_11 > #skF_8 > #skF_41 > #skF_60 > #skF_82 > #skF_16 > #skF_36 > #skF_2 > #skF_19 > #skF_13 > #skF_45 > #skF_53 > #skF_65 > #skF_4 > #skF_72 > #skF_43 > #skF_85 > #skF_86 > #skF_48 > #skF_10 > #skF_64 > #skF_31 > #skF_58 > #skF_14 > #skF_17 > #skF_55 > #skF_76 > #skF_30 > #skF_52 > #skF_38 > #skF_25 > #skF_1 > #skF_20 > #skF_9 > #skF_88 > #skF_77 > #skF_28 > #skF_23 > #skF_70 > #skF_90 > #skF_75 > #skF_24 > #skF_62 > #skF_84 > #skF_83 > #skF_12 > #skF_74 > #skF_69 > #skF_34 > #skF_33
% 18.65/5.46
% 18.65/5.46 %Foreground sorts:
% 18.65/5.46 tff(A$, type, A$: $tType ).
% 18.65/5.46 tff(B_a_bool_fun_fun$, type, B_a_bool_fun_fun$: $tType ).
% 18.65/5.46 tff(A_a_fun$, type, A_a_fun$: $tType ).
% 18.65/5.46 tff(A_a_prod$, type, A_a_prod$: $tType ).
% 18.65/5.46 tff(A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$, type, A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$: $tType ).
% 18.65/5.46 tff(Int_set$, type, Int_set$: $tType ).
% 18.65/5.46 tff(Nat_a_iarray_iarray_prod_bool_fun$, type, Nat_a_iarray_iarray_prod_bool_fun$: $tType ).
% 18.65/5.46 tff(Nat$, type, Nat$: $tType ).
% 18.65/5.46 tff(Nat_a_c_vec_c_vec_prod$, type, Nat_a_c_vec_c_vec_prod$: $tType ).
% 18.65/5.46 tff(A_a_b_vec_c_vec_prod$, type, A_a_b_vec_c_vec_prod$: $tType ).
% 18.65/5.46 tff(A_b_vec_b_vec_a_b_vec_b_vec_prod$, type, A_b_vec_b_vec_a_b_vec_b_vec_prod$: $tType ).
% 18.65/5.46 tff(A_b_vec$, type, A_b_vec$: $tType ).
% 18.65/5.46 tff(A_iarray_bool_fun$, type, A_iarray_bool_fun$: $tType ).
% 18.65/5.46 tff(A_b_vec_b_vec$, type, A_b_vec_b_vec$: $tType ).
% 18.65/5.46 tff(A_set$, type, A_set$: $tType ).
% 18.65/5.46 tff(A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$, type, A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$: $tType ).
% 18.65/5.46 tff(Int_a_prod$, type, Int_a_prod$: $tType ).
% 18.65/5.46 tff(A_nat_a_b_vec_b_vec_prod_prod$, type, A_nat_a_b_vec_b_vec_prod_prod$: $tType ).
% 18.65/5.46 tff(B$, type, B$: $tType ).
% 18.65/5.46 tff(tlbool, type, tlbool: $tType ).
% 18.65/5.46 tff(Int_int_prod$, type, Int_int_prod$: $tType ).
% 18.65/5.46 tff(C_a_b_vec_bool_fun_fun$, type, C_a_b_vec_bool_fun_fun$: $tType ).
% 18.65/5.46 tff(A_nat_a_c_vec_b_vec_prod_prod$, type, A_nat_a_c_vec_b_vec_prod_prod$: $tType ).
% 18.65/5.46 tff(A_c_vec_b_vec$, type, A_c_vec_b_vec$: $tType ).
% 18.65/5.46 tff(Nat_a_iarray_iarray_bool_fun_fun$, type, Nat_a_iarray_iarray_bool_fun_fun$: $tType ).
% 18.65/5.46 tff(A_bool_fun$, type, A_bool_fun$: $tType ).
% 18.65/5.46 tff(Int_int_fun$, type, Int_int_fun$: $tType ).
% 18.65/5.46 tff(C$, type, C$: $tType ).
% 18.65/5.46 tff(A_a_b_vec_c_vec_bool_fun_fun$, type, A_a_b_vec_c_vec_bool_fun_fun$: $tType ).
% 18.65/5.46 tff(A_a_b_vec_b_vec_prod$, type, A_a_b_vec_b_vec_prod$: $tType ).
% 18.65/5.46 tff(Nat_a_iarray_bool_fun_fun$, type, Nat_a_iarray_bool_fun_fun$: $tType ).
% 18.65/5.46 tff(Nat_nat_fun$, type, Nat_nat_fun$: $tType ).
% 18.65/5.46 tff(A_a_c_vec_b_vec_prod$, type, A_a_c_vec_b_vec_prod$: $tType ).
% 18.65/5.46 tff(A_int_prod$, type, A_int_prod$: $tType ).
% 18.65/5.46 tff(A_c_vec_c_vec_a_c_vec_c_vec_prod$, type, A_c_vec_c_vec_a_c_vec_c_vec_prod$: $tType ).
% 18.65/5.46 tff(A_nat_a_iarray_iarray_prod_prod_bool_fun$, type, A_nat_a_iarray_iarray_prod_prod_bool_fun$: $tType ).
% 18.65/5.46 tff(A_b_vec_c_vec_bool_fun$, type, A_b_vec_c_vec_bool_fun$: $tType ).
% 18.65/5.46 tff(A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$, type, A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$: $tType ).
% 18.65/5.46 tff(Nat_set$, type, Nat_set$: $tType ).
% 18.65/5.46 tff(A_c_vec_c_vec$, type, A_c_vec_c_vec$: $tType ).
% 18.65/5.46 tff(A_iarray$, type, A_iarray$: $tType ).
% 18.65/5.46 tff(A_nat_a_b_vec_c_vec_prod_prod$, type, A_nat_a_b_vec_c_vec_prod_prod$: $tType ).
% 18.65/5.46 tff(A_b_vec_c_vec$, type, A_b_vec_c_vec$: $tType ).
% 18.65/5.46 tff(A_iarray_iarray_bool_fun$, type, A_iarray_iarray_bool_fun$: $tType ).
% 18.65/5.46 tff(A_b_vec_c_vec_c_vec$, type, A_b_vec_c_vec_c_vec$: $tType ).
% 18.65/5.46 tff(Nat_a_b_vec_c_vec_prod$, type, Nat_a_b_vec_c_vec_prod$: $tType ).
% 18.65/5.46 tff(Nat_bool_fun$, type, Nat_bool_fun$: $tType ).
% 18.65/5.46 tff(A_b_vec_bool_fun$, type, A_b_vec_bool_fun$: $tType ).
% 18.65/5.46 tff(A_nat_a_iarray_iarray_prod_prod$, type, A_nat_a_iarray_iarray_prod_prod$: $tType ).
% 18.65/5.46 tff(Nat_a_iarray_iarray_prod$, type, Nat_a_iarray_iarray_prod$: $tType ).
% 18.65/5.46 tff(C_a_b_vec_fun$, type, C_a_b_vec_fun$: $tType ).
% 18.65/5.46 tff(Nat_a_iarray_prod$, type, Nat_a_iarray_prod$: $tType ).
% 18.65/5.46 tff(A_a_c_vec_c_vec_prod$, type, A_a_c_vec_c_vec_prod$: $tType ).
% 18.65/5.46 tff(Nat_a_b_vec_b_vec_prod$, type, Nat_a_b_vec_b_vec_prod$: $tType ).
% 18.65/5.46 tff(A_iarray_iarray$, type, A_iarray_iarray$: $tType ).
% 18.65/5.46 tff(B_a_fun$, type, B_a_fun$: $tType ).
% 18.65/5.46 tff(Nat_a_iarray_prod_bool_fun$, type, Nat_a_iarray_prod_bool_fun$: $tType ).
% 18.65/5.46 tff(A_c_vec_c_vec_a_b_vec_c_vec_prod$, type, A_c_vec_c_vec_a_b_vec_c_vec_prod$: $tType ).
% 18.65/5.46 tff(Nat_a_b_vec_c_vec_bool_fun_fun$, type, Nat_a_b_vec_c_vec_bool_fun_fun$: $tType ).
% 18.65/5.46 tff(A_a_iarray_iarray_bool_fun_fun$, type, A_a_iarray_iarray_bool_fun_fun$: $tType ).
% 18.65/5.46 tff(A_a_iarray_iarray_prod$, type, A_a_iarray_iarray_prod$: $tType ).
% 18.65/5.46 tff(Nat_a_b_vec_c_vec_prod_bool_fun$, type, Nat_a_b_vec_c_vec_prod_bool_fun$: $tType ).
% 18.65/5.46 tff(Nat_a_c_vec_b_vec_prod$, type, Nat_a_c_vec_b_vec_prod$: $tType ).
% 18.65/5.46 tff(A_nat_a_b_vec_c_vec_prod_prod_bool_fun$, type, A_nat_a_b_vec_c_vec_prod_prod_bool_fun$: $tType ).
% 18.65/5.46 tff(A_nat_a_b_vec_c_vec_prod_bool_fun_fun$, type, A_nat_a_b_vec_c_vec_prod_bool_fun_fun$: $tType ).
% 18.65/5.46 tff(A_nat_a_c_vec_c_vec_prod_prod$, type, A_nat_a_c_vec_c_vec_prod_prod$: $tType ).
% 18.65/5.46 tff(A_c_vec$, type, A_c_vec$: $tType ).
% 18.65/5.46 tff(A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$, type, A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$: $tType ).
% 18.65/5.46 tff(A_nat_a_iarray_iarray_prod_bool_fun_fun$, type, A_nat_a_iarray_iarray_prod_bool_fun_fun$: $tType ).
% 18.65/5.46 tff(A_b_vec_b_vec_a_c_vec_b_vec_prod$, type, A_b_vec_b_vec_a_c_vec_b_vec_prod$: $tType ).
% 18.65/5.46
% 18.65/5.46 %Background operators:
% 18.65/5.46 tff('#skE_2', type, '#skE_2': $int).
% 18.65/5.46 tff('#skE_1', type, '#skE_1': $int).
% 18.65/5.46 tff('#skE_5', type, '#skE_5': $int).
% 18.65/5.46 tff('#skE_4', type, '#skE_4': $int).
% 18.65/5.46 tff('#skE_3', type, '#skE_3': $int).
% 18.65/5.46
% 18.65/5.46 %Foreground operators:
% 18.65/5.46 tff('#skF_21', type, '#skF_21': Nat_a_iarray_iarray_prod$ > A_iarray_iarray$).
% 18.65/5.46 tff(vec_nth$a, type, vec_nth$a: A_b_vec_c_vec$ > C_a_b_vec_fun$).
% 18.65/5.46 tff(fun_app$e, type, fun_app$e: (Nat_a_iarray_prod_bool_fun$ * Nat_a_iarray_prod$) > $o).
% 18.65/5.46 tff(plus$, type, plus$: A$ > A_a_fun$).
% 18.65/5.46 tff(gauss_Jordan_column_k_det_P$b, type, gauss_Jordan_column_k_det_P$b: (A_nat_a_b_vec_b_vec_prod_prod$ * Nat$) > A_nat_a_b_vec_b_vec_prod_prod$).
% 18.65/5.46 tff('#skF_71', type, '#skF_71': A_b_vec_b_vec$ > B$).
% 18.65/5.46 tff('#skF_35', type, '#skF_35': (A_nat_a_iarray_iarray_prod_prod_bool_fun$ * A_nat_a_iarray_iarray_prod_prod$) > A$).
% 18.65/5.46 tff(row_add_iterate_PA$, type, row_add_iterate_PA$: (A_c_vec_c_vec_a_b_vec_c_vec_prod$ * Nat$ * C$ * B$) > A_c_vec_c_vec_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(one$c, type, one$c: B$).
% 18.65/5.46 tff('#skF_61', type, '#skF_61': (A_b_vec$ * A_b_vec$) > B$).
% 18.65/5.46 tff(plus$c, type, plus$c: (B$ * B$) > B$).
% 18.65/5.46 tff(fst$b, type, fst$b: Nat_a_b_vec_c_vec_prod$ > Nat$).
% 18.65/5.46 tff(less_eq$, type, less_eq$: (C$ * C$) > $o).
% 18.65/5.46 tff(fst$r, type, fst$r: A_c_vec_c_vec_a_c_vec_c_vec_prod$ > A_c_vec_c_vec$).
% 18.65/5.46 tff('#skF_37', type, '#skF_37': (A_nat_a_iarray_iarray_prod_prod_bool_fun$ * A_nat_a_iarray_iarray_prod_prod$) > A_iarray_iarray$).
% 18.65/5.46 tff(nrows$c, type, nrows$c: A_b_vec_b_vec$ > Nat$).
% 18.65/5.46 tff(less$b, type, less$b: (B$ * B$) > $o).
% 18.65/5.46 tff(snd$d, type, snd$d: A_nat_a_iarray_iarray_prod_prod$ > Nat_a_iarray_iarray_prod$).
% 18.65/5.46 tff('#skF_44', type, '#skF_44': (A_nat_a_c_vec_c_vec_prod_prod$ * Nat$) > C$).
% 18.65/5.46 tff(fun_app$s, type, fun_app$s: (A_iarray_iarray_bool_fun$ * A_iarray_iarray$) > $o).
% 18.65/5.46 tff('#skF_79', type, '#skF_79': (A_b_vec_b_vec$ * Nat$) > B$).
% 18.65/5.46 tff(fun_app$k, type, fun_app$k: (A_bool_fun$ * A$) > $o).
% 18.65/5.46 tff('#skF_22', type, '#skF_22': A_nat_a_b_vec_c_vec_prod_prod$ > A$).
% 18.65/5.46 tff('#skF_47', type, '#skF_47': (A_nat_a_b_vec_c_vec_prod_prod$ * Nat$) > C$).
% 18.65/5.46 tff('#skF_54', type, '#skF_54': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 18.65/5.46 tff(snd$a, type, snd$a: A_nat_a_b_vec_c_vec_prod_prod$ > Nat_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(snd$n, type, snd$n: Nat_a_b_vec_b_vec_prod$ > A_b_vec_b_vec$).
% 18.65/5.46 tff('#skF_87', type, '#skF_87': (Nat$ * Nat_set$ * Nat_set$) > Nat$).
% 18.65/5.46 tff(plus$p, type, plus$p: (Int_set$ * Int_set$) > Int_set$).
% 18.65/5.46 tff(pair$g, type, pair$g: (A$ * Nat_a_c_vec_c_vec_prod$) > A_nat_a_c_vec_c_vec_prod_prod$).
% 18.65/5.46 tff(fst$s, type, fst$s: A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$ > A_b_vec_b_vec$).
% 18.65/5.46 tff(fun_app$b, type, fun_app$b: (A_a_fun$ * A$) > A$).
% 18.65/5.46 tff(fun_app$t, type, fun_app$t: (Nat_a_iarray_iarray_bool_fun_fun$ * Nat$) > A_iarray_iarray_bool_fun$).
% 18.65/5.46 tff('#skF_46', type, '#skF_46': (A_nat_a_b_vec_b_vec_prod_prod$ * Nat$) > B$).
% 18.65/5.46 tff(zero$b, type, zero$b: A_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(fun_app$r, type, fun_app$r: (Nat_a_iarray_bool_fun_fun$ * Nat$) > A_iarray_bool_fun$).
% 18.65/5.46 tff(fst$k, type, fst$k: A_nat_a_c_vec_b_vec_prod_prod$ > A$).
% 18.65/5.46 tff(gauss_Jordan_in_ij_PA$, type, gauss_Jordan_in_ij_PA$: (A_c_vec_c_vec_a_c_vec_c_vec_prod$ * C$ * C$) > A_c_vec_c_vec_a_c_vec_c_vec_prod$).
% 18.65/5.46 tff(fun_app$, type, fun_app$: (Int_int_fun$ * $int) > $int).
% 18.65/5.46 tff(less$a, type, less$a: (C$ * C$) > $o).
% 18.65/5.46 tff('#skF_26', type, '#skF_26': Nat_a_iarray_prod$ > Nat$).
% 18.65/5.46 tff('#skF_6', type, '#skF_6': (Nat_a_iarray_prod_bool_fun$ * Nat_a_iarray_prod$) > Nat$).
% 18.65/5.46 tff('#skF_66', type, '#skF_66': B_a_bool_fun_fun$ > A_b_vec$).
% 18.65/5.46 tff(times$g, type, times$g: (Nat_set$ * Nat_set$) > Nat_set$).
% 18.65/5.46 tff(fst$u, type, fst$u: A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$ > A_b_vec_b_vec$).
% 18.65/5.46 tff('#skF_80', type, '#skF_80': (A_b_vec_b_vec$ * Nat$) > B$).
% 18.65/5.46 tff(pair$h, type, pair$h: (Nat$ * A_c_vec_c_vec$) > Nat_a_c_vec_c_vec_prod$).
% 18.65/5.46 tff(plus$g, type, plus$g: (A_iarray_iarray$ * A_iarray_iarray$) > A_iarray_iarray$).
% 18.65/5.46 tff(snd$h, type, snd$h: Nat_a_c_vec_c_vec_prod$ > A_c_vec_c_vec$).
% 18.65/5.46 tff('#skF_51', type, '#skF_51': (Nat_bool_fun$ * Nat$ * Nat$) > Nat$).
% 18.65/5.46 tff('#skF_27', type, '#skF_27': Nat_a_iarray_prod$ > A_iarray$).
% 18.65/5.46 tff('#skF_3', type, '#skF_3': (A_nat_a_b_vec_c_vec_prod_prod_bool_fun$ * A_nat_a_b_vec_c_vec_prod_prod$) > Nat_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff('#skF_50', type, '#skF_50': (Nat_bool_fun$ * Nat$) > Nat$).
% 18.65/5.46 tff(nrows_iarray$, type, nrows_iarray$: A_iarray_iarray$ > Nat$).
% 18.65/5.46 tff('#skF_15', type, '#skF_15': Nat_a_b_vec_c_vec_prod$ > A_b_vec_c_vec$).
% 18.65/5.46 tff('#skF_81', type, '#skF_81': (A_b_vec_c_vec_c_vec$ * Nat$) > C$).
% 18.65/5.46 tff('#skF_18', type, '#skF_18': A_nat_a_iarray_iarray_prod_prod$ > A$).
% 18.65/5.46 tff(snd$s, type, snd$s: A_c_vec_c_vec_a_c_vec_c_vec_prod$ > A_c_vec_c_vec$).
% 18.65/5.46 tff(snd$p, type, snd$p: Int_int_prod$ > $int).
% 18.65/5.46 tff(vec_nth$c, type, vec_nth$c: (A_c_vec_c_vec$ * C$) > A_c_vec$).
% 18.65/5.46 tff(snd$m, type, snd$m: A_nat_a_b_vec_b_vec_prod_prod$ > Nat_a_b_vec_b_vec_prod$).
% 18.65/5.46 tff(gauss_Jordan_in_ij_PA$c, type, gauss_Jordan_in_ij_PA$c: (A_c_vec_c_vec_a_b_vec_c_vec_prod$ * C$ * B$) > A_c_vec_c_vec_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(fun_app$q, type, fun_app$q: (A_iarray_bool_fun$ * A_iarray$) > $o).
% 18.65/5.46 tff(fst$w, type, fst$w: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$ > A_c_vec_c_vec$).
% 18.65/5.46 tff(snd$l, type, snd$l: A_a_c_vec_b_vec_prod$ > A_c_vec_b_vec$).
% 18.65/5.46 tff(plus$k, type, plus$k: (A_nat_a_iarray_iarray_prod_prod$ * A_nat_a_iarray_iarray_prod_prod$) > A_nat_a_iarray_iarray_prod_prod$).
% 18.65/5.46 tff('#skF_57', type, '#skF_57': (Nat$ * Nat$) > Nat$).
% 18.65/5.46 tff(snd$c, type, snd$c: Nat_a_iarray_iarray_prod$ > A_iarray_iarray$).
% 18.65/5.46 tff('#skF_5', type, '#skF_5': (Nat_a_b_vec_c_vec_prod_bool_fun$ * Nat_a_b_vec_c_vec_prod$) > A_b_vec_c_vec$).
% 18.65/5.46 tff('#skF_73', type, '#skF_73': A_b_vec_c_vec_c_vec$ > C$).
% 18.65/5.46 tff('#skF_56', type, '#skF_56': (Nat$ * Nat$) > Nat$).
% 18.65/5.46 tff(plus$h, type, plus$h: (A_b_vec_c_vec$ * A_b_vec_c_vec$) > A_b_vec_c_vec$).
% 18.65/5.46 tff(pair$a, type, pair$a: (Nat$ * A_b_vec_c_vec$) > Nat_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(gauss_Jordan_in_ij_PA$b, type, gauss_Jordan_in_ij_PA$b: (A_b_vec_b_vec_a_b_vec_b_vec_prod$ * B$ * B$) > A_b_vec_b_vec_a_b_vec_b_vec_prod$).
% 18.65/5.46 tff(snd$k, type, snd$k: Nat_a_c_vec_b_vec_prod$ > A_c_vec_b_vec$).
% 18.65/5.46 tff(one$b, type, one$b: C$).
% 18.65/5.46 tff(fst$p, type, fst$p: Int_int_prod$ > $int).
% 18.65/5.46 tff(fst$c, type, fst$c: Nat_a_iarray_prod$ > Nat$).
% 18.65/5.46 tff(times$a, type, times$a: ($int * $int) > $int).
% 18.65/5.46 tff(snd$e, type, snd$e: A_a_iarray_iarray_prod$ > A_iarray_iarray$).
% 18.65/5.46 tff('#skF_68', type, '#skF_68': (C_a_b_vec_bool_fun_fun$ * C$) > A_b_vec$).
% 18.65/5.46 tff(fst$l, type, fst$l: A_a_c_vec_b_vec_prod$ > A$).
% 18.65/5.46 tff(nrows$, type, nrows$: A_b_vec_c_vec$ > Nat$).
% 18.65/5.46 tff(snd$u, type, snd$u: A_b_vec_b_vec_a_c_vec_b_vec_prod$ > A_c_vec_b_vec$).
% 18.65/5.46 tff('#skF_29', type, '#skF_29': A_nat_a_iarray_iarray_prod_prod$ > Nat_a_iarray_iarray_prod$).
% 18.65/5.46 tff('#skF_63', type, '#skF_63': (B_a_bool_fun_fun$ * A_b_vec$) > B$).
% 18.65/5.46 tff('#skF_42', type, '#skF_42': A_nat_a_iarray_iarray_prod_prod$ > Nat$).
% 18.65/5.46 tff('#skF_40', type, '#skF_40': A_nat_a_b_vec_c_vec_prod_prod$ > A_b_vec_c_vec$).
% 18.65/5.46 tff(less_eq$d, type, less_eq$d: (Int_set$ * Int_set$) > $o).
% 18.65/5.46 tff(gauss_Jordan_column_k_PA$a, type, gauss_Jordan_column_k_PA$a: (A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$ * Nat$) > A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$).
% 18.65/5.46 tff(uub$, type, uub$: Int_int_fun$).
% 18.65/5.46 tff(pair$w, type, pair$w: (A_b_vec_b_vec$ * A_b_vec_b_vec$) > A_b_vec_b_vec_a_b_vec_b_vec_prod$).
% 18.65/5.46 tff(uu$, type, uu$: A_a_fun$).
% 18.65/5.46 tff(gauss_Jordan_in_ij_det_P$, type, gauss_Jordan_in_ij_det_P$: (A_b_vec_c_vec$ * C$ * B$) > A_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(pair$e, type, pair$e: (A$ * A_b_vec_c_vec$) > A_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(tlfalse, type, tlfalse: tlbool).
% 18.65/5.46 tff('#skF_59', type, '#skF_59': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 18.65/5.46 tff(gauss_Jordan_in_ij_det_P$c, type, gauss_Jordan_in_ij_det_P$c: (A_b_vec_b_vec$ * B$ * B$) > A_a_b_vec_b_vec_prod$).
% 18.65/5.46 tff(zero$e, type, zero$e: Nat_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(plus$e, type, plus$e: (A_a_iarray_iarray_prod$ * A_a_iarray_iarray_prod$) > A_a_iarray_iarray_prod$).
% 18.65/5.46 tff(pair$p, type, pair$p: ($int * A$) > Int_a_prod$).
% 18.65/5.46 tff(divides_aux$, type, divides_aux$: Int_int_prod$ > $o).
% 18.65/5.46 tff('#skF_67', type, '#skF_67': (C_a_b_vec_bool_fun_fun$ * A_b_vec_c_vec$) > C$).
% 18.65/5.46 tff('#skF_89', type, '#skF_89': ($int * Int_set$ * Int_set$) > $int).
% 18.65/5.46 tff(gauss_Jordan_in_ij_PA$a, type, gauss_Jordan_in_ij_PA$a: (A_b_vec_b_vec_a_c_vec_b_vec_prod$ * B$ * C$) > A_b_vec_b_vec_a_c_vec_b_vec_prod$).
% 18.65/5.46 tff(fst$a, type, fst$a: A_a_iarray_iarray_prod$ > A$).
% 18.65/5.46 tff(fun_app$n, type, fun_app$n: (C_a_b_vec_bool_fun_fun$ * C$) > A_b_vec_bool_fun$).
% 18.65/5.46 tff(pair$b, type, pair$b: (Nat$ * A_iarray$) > Nat_a_iarray_prod$).
% 18.65/5.46 tff('#skF_39', type, '#skF_39': A_nat_a_b_vec_c_vec_prod_prod$ > Nat$).
% 18.65/5.46 tff(fst$t, type, fst$t: A_b_vec_b_vec_a_c_vec_b_vec_prod$ > A_b_vec_b_vec$).
% 18.65/5.46 tff(fun_app$f, type, fun_app$f: (A_nat_a_b_vec_c_vec_prod_prod_bool_fun$ * A_nat_a_b_vec_c_vec_prod_prod$) > $o).
% 18.65/5.46 tff('#skF_32', type, '#skF_32': (A_nat_a_b_vec_c_vec_prod_prod_bool_fun$ * A_nat_a_b_vec_c_vec_prod_prod$) > A$).
% 18.65/5.46 tff(zero$f, type, zero$f: C$).
% 18.65/5.46 tff('#skF_78', type, '#skF_78': (A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$ * Nat$) > C$).
% 18.65/5.46 tff(plus$m, type, plus$m: (A_iarray$ * A_iarray$) > A_iarray$).
% 18.65/5.46 tff('#skF_49', type, '#skF_49': (Nat_bool_fun$ * Nat$) > Nat$).
% 18.65/5.46 tff(plus$l, type, plus$l: (Nat_a_iarray_prod$ * Nat_a_iarray_prod$) > Nat_a_iarray_prod$).
% 18.65/5.46 tff(upper_triangular_upt_k$a, type, upper_triangular_upt_k$a: A_b_vec_c_vec_c_vec$ > Nat_bool_fun$).
% 18.65/5.46 tff('#skF_7', type, '#skF_7': (Nat_a_iarray_prod_bool_fun$ * Nat_a_iarray_prod$) > A_iarray$).
% 18.65/5.46 tff(fun_app$p, type, fun_app$p: (Nat_a_b_vec_c_vec_bool_fun_fun$ * Nat$) > A_b_vec_c_vec_bool_fun$).
% 18.65/5.46 tff(member$b, type, member$b: (Nat$ * Nat_set$) > $o).
% 18.65/5.46 tff(matrix_to_iarray$, type, matrix_to_iarray$: A_b_vec_c_vec$ > A_iarray_iarray$).
% 18.65/5.46 tff(snd$v, type, snd$v: A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$ > Nat_a_b_vec_b_vec_prod$).
% 18.65/5.46 tff(member$, type, member$: ($int * Int_set$) > $o).
% 18.65/5.46 tff(fst$g, type, fst$g: Nat_a_c_vec_c_vec_prod$ > Nat$).
% 18.65/5.46 tff(nrows$a, type, nrows$a: A_c_vec_c_vec$ > Nat$).
% 18.65/5.46 tff('#skF_11', type, '#skF_11': (Nat_a_iarray_iarray_prod_bool_fun$ * Nat_a_iarray_iarray_prod$) > A_iarray_iarray$).
% 18.65/5.46 tff(vec_nth$, type, vec_nth$: A_b_vec$ > B_a_fun$).
% 18.65/5.46 tff(pair$u, type, pair$u: (A_b_vec_b_vec$ * A_c_vec_b_vec$) > A_b_vec_b_vec_a_c_vec_b_vec_prod$).
% 18.65/5.46 tff(pair$d, type, pair$d: (Nat$ * A_iarray_iarray$) > Nat_a_iarray_iarray_prod$).
% 18.65/5.46 tff('#skF_8', type, '#skF_8': (A_nat_a_iarray_iarray_prod_prod_bool_fun$ * A_nat_a_iarray_iarray_prod_prod$) > A$).
% 18.65/5.46 tff(fst$f, type, fst$f: A_nat_a_iarray_iarray_prod_prod$ > A$).
% 18.65/5.46 tff(fst$h, type, fst$h: A_nat_a_c_vec_c_vec_prod_prod$ > A$).
% 18.65/5.46 tff('#skF_41', type, '#skF_41': A_nat_a_iarray_iarray_prod_prod$ > A$).
% 18.65/5.46 tff('#skF_60', type, '#skF_60': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 18.65/5.46 tff('#skF_82', type, '#skF_82': (A_b_vec_c_vec_c_vec$ * Nat$) > C$).
% 18.65/5.46 tff(zero$d, type, zero$d: A_nat_a_b_vec_c_vec_prod_prod$).
% 18.65/5.46 tff('#skF_16', type, '#skF_16': Nat_a_iarray_prod$ > Nat$).
% 18.65/5.46 tff(less_eq$b, type, less_eq$b: (B$ * B$) > $o).
% 18.65/5.46 tff(vec_nth$e, type, vec_nth$e: (A_b_vec_b_vec$ * B$) > A_b_vec$).
% 18.65/5.46 tff(vector_all_zero_from_index$, type, vector_all_zero_from_index$: Nat_a_iarray_prod_bool_fun$).
% 18.65/5.46 tff(zero$g, type, zero$g: A_a_prod$).
% 18.65/5.46 tff(snd$j, type, snd$j: A_nat_a_c_vec_b_vec_prod_prod$ > Nat_a_c_vec_b_vec_prod$).
% 18.65/5.46 tff(snd$r, type, snd$r: A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$ > Nat_a_c_vec_c_vec_prod$).
% 18.65/5.46 tff(plus$i, type, plus$i: (A_nat_a_b_vec_c_vec_prod_prod$ * A_nat_a_b_vec_c_vec_prod_prod$) > A_nat_a_b_vec_c_vec_prod_prod$).
% 18.65/5.46 tff(fun_app$h, type, fun_app$h: (A_nat_a_iarray_iarray_prod_prod_bool_fun$ * A_nat_a_iarray_iarray_prod_prod$) > $o).
% 18.65/5.46 tff(fst$n, type, fst$n: A_nat_a_b_vec_b_vec_prod_prod$ > A$).
% 18.65/5.46 tff(pair$o, type, pair$o: (A$ * $int) > A_int_prod$).
% 18.65/5.46 tff(gauss_Jordan_in_ij_det_P$a, type, gauss_Jordan_in_ij_det_P$a: (A_c_vec_c_vec$ * C$ * C$) > A_a_c_vec_c_vec_prod$).
% 18.65/5.46 tff(plus$q, type, plus$q: (A_set$ * A_set$) > A_set$).
% 18.65/5.46 tff('#skF_36', type, '#skF_36': (A_nat_a_iarray_iarray_prod_prod_bool_fun$ * A_nat_a_iarray_iarray_prod_prod$) > Nat$).
% 18.65/5.46 tff('#skF_2', type, '#skF_2': (A_nat_a_b_vec_c_vec_prod_prod_bool_fun$ * A_nat_a_b_vec_c_vec_prod_prod$) > A$).
% 18.65/5.46 tff(fst$o, type, fst$o: A_a_b_vec_b_vec_prod$ > A$).
% 18.65/5.46 tff('#skF_19', type, '#skF_19': A_nat_a_iarray_iarray_prod_prod$ > Nat_a_iarray_iarray_prod$).
% 18.65/5.46 tff('#skF_13', type, '#skF_13': A_nat_a_b_vec_c_vec_prod_prod$ > Nat_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(gauss_Jordan_column_k_PA$b, type, gauss_Jordan_column_k_PA$b: (A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$ * Nat$) > A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$).
% 18.65/5.46 tff('#skF_45', type, '#skF_45': (A_nat_a_c_vec_b_vec_prod_prod$ * Nat$) > B$).
% 18.65/5.46 tff(fst$i, type, fst$i: A_a_c_vec_c_vec_prod$ > A$).
% 18.65/5.46 tff(map_matrix$, type, map_matrix$: (A_a_fun$ * A_b_vec_c_vec$) > A_b_vec_c_vec$).
% 18.65/5.46 tff('#skF_53', type, '#skF_53': (Nat_nat_fun$ * Nat$ * Nat$) > Nat$).
% 18.65/5.46 tff(to_nat$, type, to_nat$: C$ > Nat$).
% 18.65/5.46 tff(fun_app$g, type, fun_app$g: (Nat_a_b_vec_c_vec_prod_bool_fun$ * Nat_a_b_vec_c_vec_prod$) > $o).
% 18.65/5.46 tff(plus$b, type, plus$b: (C$ * C$) > C$).
% 18.65/5.46 tff(snd$o, type, snd$o: A_a_b_vec_b_vec_prod$ > A_b_vec_b_vec$).
% 18.65/5.46 tff(pair$c, type, pair$c: (A$ * Nat_a_iarray_iarray_prod$) > A_nat_a_iarray_iarray_prod_prod$).
% 18.65/5.46 tff('#skF_65', type, '#skF_65': B_a_bool_fun_fun$ > B$).
% 18.65/5.46 tff(gauss_Jordan_column_k_det_P_iarrays$, type, gauss_Jordan_column_k_det_P_iarrays$: (A_nat_a_iarray_iarray_prod_prod$ * Nat$) > A_nat_a_iarray_iarray_prod_prod$).
% 18.65/5.46 tff(zero$, type, zero$: Nat$).
% 18.65/5.46 tff('#skF_4', type, '#skF_4': (Nat_a_b_vec_c_vec_prod_bool_fun$ * Nat_a_b_vec_c_vec_prod$) > Nat$).
% 18.65/5.46 tff(upper_triangular_upt_k$, type, upper_triangular_upt_k$: A_b_vec_b_vec$ > Nat_bool_fun$).
% 18.65/5.46 tff(k$, type, k$: Nat$).
% 18.65/5.46 tff('#skF_72', type, '#skF_72': A_b_vec_b_vec$ > B$).
% 18.65/5.46 tff(times$d, type, times$d: (A_b_vec_c_vec$ * A_b_vec_c_vec$) > A_b_vec_c_vec$).
% 18.65/5.46 tff(times$f, type, times$f: (Int_set$ * Int_set$) > Int_set$).
% 18.65/5.46 tff(snd$, type, snd$: Nat_a_b_vec_c_vec_prod$ > A_b_vec_c_vec$).
% 18.65/5.46 tff(fun_app$o, type, fun_app$o: (A_b_vec_c_vec_bool_fun$ * A_b_vec_c_vec$) > $o).
% 18.65/5.46 tff(uug$, type, uug$: Nat_nat_fun$).
% 18.65/5.46 tff('#skF_43', type, '#skF_43': A_nat_a_iarray_iarray_prod_prod$ > A_iarray_iarray$).
% 18.65/5.46 tff(gauss_Jordan_column_k_det_P$a, type, gauss_Jordan_column_k_det_P$a: (A_nat_a_c_vec_b_vec_prod_prod$ * Nat$) > A_nat_a_c_vec_b_vec_prod_prod$).
% 18.65/5.46 tff(zero$k, type, zero$k: B$).
% 18.65/5.46 tff(n$, type, n$: A$).
% 18.65/5.46 tff(plus$d, type, plus$d: (A_a_b_vec_c_vec_prod$ * A_a_b_vec_c_vec_prod$) > A_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(gauss_Jordan_column_k_det_P$c, type, gauss_Jordan_column_k_det_P$c: (A_nat_a_b_vec_c_vec_prod_prod$ * Nat$) > A_nat_a_b_vec_c_vec_prod_prod$).
% 18.65/5.46 tff(one$, type, one$: A$).
% 18.65/5.46 tff(fun_app$v, type, fun_app$v: (A_nat_a_b_vec_c_vec_prod_bool_fun_fun$ * A$) > Nat_a_b_vec_c_vec_prod_bool_fun$).
% 18.65/5.46 tff(snd$w, type, snd$w: A_b_vec_b_vec_a_b_vec_b_vec_prod$ > A_b_vec_b_vec$).
% 18.65/5.46 tff(plus$n, type, plus$n: (Int_int_prod$ * Int_int_prod$) > Int_int_prod$).
% 18.65/5.46 tff(uud$, type, uud$: A_a_fun$).
% 18.65/5.46 tff('#skF_85', type, '#skF_85': ($int * Int_set$ * Int_set$) > $int).
% 18.65/5.46 tff(gauss_Jordan_column_k_det_P$, type, gauss_Jordan_column_k_det_P$: (A_nat_a_c_vec_c_vec_prod_prod$ * Nat$) > A_nat_a_c_vec_c_vec_prod_prod$).
% 18.65/5.46 tff(pair$f, type, pair$f: (A$ * A_iarray_iarray$) > A_a_iarray_iarray_prod$).
% 18.65/5.46 tff(upper_triangular$, type, upper_triangular$: A_b_vec_b_vec$ > $o).
% 18.65/5.46 tff(uua$, type, uua$: Int_int_fun$).
% 18.65/5.46 tff(zero$j, type, zero$j: Int_int_prod$).
% 18.65/5.46 tff(gauss_Jordan_in_ij_det_P_iarrays$, type, gauss_Jordan_in_ij_det_P_iarrays$: (A_iarray_iarray$ * Nat$ * Nat$) > A_a_iarray_iarray_prod$).
% 18.65/5.46 tff('#skF_86', type, '#skF_86': ($int * Int_set$ * Int_set$) > $int).
% 18.65/5.46 tff('#skF_48', type, '#skF_48': (Nat_bool_fun$ * Nat$) > Nat$).
% 18.65/5.46 tff(plus$j, type, plus$j: (Nat_a_b_vec_c_vec_prod$ * Nat_a_b_vec_c_vec_prod$) > Nat_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(zero$l, type, zero$l: A_b_vec$).
% 18.65/5.46 tff(times$b, type, times$b: Nat$ > Nat_nat_fun$).
% 18.65/5.46 tff('#skF_10', type, '#skF_10': (Nat_a_iarray_iarray_prod_bool_fun$ * Nat_a_iarray_iarray_prod$) > Nat$).
% 18.65/5.46 tff(plus$f, type, plus$f: (Nat_a_iarray_iarray_prod$ * Nat_a_iarray_iarray_prod$) > Nat_a_iarray_iarray_prod$).
% 18.65/5.46 tff('#skF_64', type, '#skF_64': (B_a_bool_fun_fun$ * B$) > A$).
% 18.65/5.46 tff(pair$x, type, pair$x: (A_c_vec_c_vec$ * A_b_vec_c_vec$) > A_c_vec_c_vec_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(ncols$, type, ncols$: A_b_vec_c_vec$ > Nat$).
% 18.65/5.46 tff(snd$b, type, snd$b: A_a_b_vec_c_vec_prod$ > A_b_vec_c_vec$).
% 18.65/5.46 tff(fst$x, type, fst$x: A_c_vec_c_vec_a_b_vec_c_vec_prod$ > A_c_vec_c_vec$).
% 18.65/5.46 tff('#skF_31', type, '#skF_31': Nat_a_iarray_iarray_prod$ > A_iarray_iarray$).
% 18.65/5.46 tff(one$d, type, one$d: A_b_vec$).
% 18.65/5.46 tff(pair$v, type, pair$v: (A_b_vec_b_vec$ * Nat_a_b_vec_b_vec_prod$) > A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$).
% 18.65/5.46 tff(one$e, type, one$e: A_b_vec_c_vec$).
% 18.65/5.46 tff(fst$j, type, fst$j: Nat_a_c_vec_b_vec_prod$ > Nat$).
% 18.65/5.46 tff(from_nat$a, type, from_nat$a: Nat$ > B$).
% 18.65/5.46 tff('#skF_58', type, '#skF_58': (Nat$ * Nat$) > Nat$).
% 18.65/5.46 tff(fun_app$l, type, fun_app$l: (B_a_bool_fun_fun$ * B$) > A_bool_fun$).
% 18.65/5.46 tff('#skF_14', type, '#skF_14': Nat_a_b_vec_c_vec_prod$ > Nat$).
% 18.65/5.46 tff('#skF_17', type, '#skF_17': Nat_a_iarray_prod$ > A_iarray$).
% 18.65/5.46 tff(pair$m, type, pair$m: ($int * $int) > Int_int_prod$).
% 18.65/5.46 tff('#skF_55', type, '#skF_55': (Nat_bool_fun$ * Nat$) > Nat$).
% 18.65/5.46 tff(member$a, type, member$a: (A$ * A_set$) > $o).
% 18.65/5.46 tff('#skF_76', type, '#skF_76': (A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$ * Nat$) > B$).
% 18.65/5.46 tff(vec_nth$d, type, vec_nth$d: (A_c_vec_b_vec$ * B$) > A_c_vec$).
% 18.65/5.46 tff(fst$v, type, fst$v: A_b_vec_b_vec_a_b_vec_b_vec_prod$ > A_b_vec_b_vec$).
% 18.65/5.46 tff('#skF_30', type, '#skF_30': Nat_a_iarray_iarray_prod$ > Nat$).
% 18.65/5.46 tff('#skF_52', type, '#skF_52': (Nat_bool_fun$ * Nat$ * Nat$) > Nat$).
% 18.65/5.46 tff(pair$, type, pair$: (A$ * Nat_a_b_vec_c_vec_prod$) > A_nat_a_b_vec_c_vec_prod_prod$).
% 18.65/5.46 tff(less_eq$c, type, less_eq$c: (A_set$ * A_set$) > $o).
% 18.65/5.46 tff(pair$q, type, pair$q: (A_c_vec_c_vec$ * Nat_a_b_vec_c_vec_prod$) > A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$).
% 18.65/5.46 tff(a$, type, a$: A_b_vec_c_vec$).
% 18.65/5.46 tff(fun_app$c, type, fun_app$c: (B_a_fun$ * B$) > A$).
% 18.65/5.46 tff(to_nat$a, type, to_nat$a: B$ > Nat$).
% 18.65/5.46 tff('#skF_38', type, '#skF_38': A_nat_a_b_vec_c_vec_prod_prod$ > A$).
% 18.65/5.46 tff('#skF_25', type, '#skF_25': Nat_a_b_vec_c_vec_prod$ > A_b_vec_c_vec$).
% 18.65/5.46 tff(fun_app$m, type, fun_app$m: (A_b_vec_bool_fun$ * A_b_vec$) > $o).
% 18.65/5.46 tff(pair$r, type, pair$r: (A_c_vec_c_vec$ * Nat_a_c_vec_c_vec_prod$) > A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$).
% 18.65/5.46 tff('#skF_1', type, '#skF_1': C$).
% 18.65/5.46 tff(fst$e, type, fst$e: A_nat_a_b_vec_c_vec_prod_prod$ > A$).
% 18.65/5.46 tff(uuc$, type, uuc$: Nat_nat_fun$).
% 18.65/5.46 tff(i$, type, i$: Nat$).
% 18.65/5.46 tff('#skF_20', type, '#skF_20': Nat_a_iarray_iarray_prod$ > Nat$).
% 18.65/5.46 tff(snd$t, type, snd$t: A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$ > Nat_a_c_vec_b_vec_prod$).
% 18.65/5.46 tff(of_nat$, type, of_nat$: Nat$ > $int).
% 18.65/5.46 tff(nat$, type, nat$: $int > Nat$).
% 18.65/5.46 tff(uue$, type, uue$: Int_int_fun$).
% 18.65/5.46 tff('#skF_9', type, '#skF_9': (A_nat_a_iarray_iarray_prod_prod_bool_fun$ * A_nat_a_iarray_iarray_prod_prod$) > Nat_a_iarray_iarray_prod$).
% 18.65/5.46 tff(fun_app$u, type, fun_app$u: (A_a_b_vec_c_vec_bool_fun_fun$ * A$) > A_b_vec_c_vec_bool_fun$).
% 18.65/5.46 tff(one$a, type, one$a: Nat$).
% 18.65/5.46 tff('#skF_88', type, '#skF_88': (Nat$ * Nat_set$ * Nat_set$) > Nat$).
% 18.65/5.46 tff('#skF_77', type, '#skF_77': (A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$ * Nat$) > B$).
% 18.65/5.46 tff(times$e, type, times$e: (A_set$ * A_set$) > A_set$).
% 18.65/5.46 tff(snd$g, type, snd$g: A_nat_a_c_vec_c_vec_prod_prod$ > Nat_a_c_vec_c_vec_prod$).
% 18.65/5.46 tff(plus$a, type, plus$a: Nat$ > Nat_nat_fun$).
% 18.65/5.46 tff('#skF_28', type, '#skF_28': A_nat_a_iarray_iarray_prod_prod$ > A$).
% 18.65/5.46 tff(zero$i, type, zero$i: Int_a_prod$).
% 18.65/5.46 tff(column_iarray$, type, column_iarray$: (Nat$ * A_iarray_iarray$) > A_iarray$).
% 18.65/5.46 tff('#skF_23', type, '#skF_23': A_nat_a_b_vec_c_vec_prod_prod$ > Nat_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(fst$q, type, fst$q: A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$ > A_c_vec_c_vec$).
% 18.65/5.46 tff(times$c, type, times$c: (A_b_vec$ * A_b_vec$) > A_b_vec$).
% 18.65/5.46 tff(fst$, type, fst$: A_a_b_vec_c_vec_prod$ > A$).
% 18.65/5.46 tff('#skF_70', type, '#skF_70': C_a_b_vec_bool_fun_fun$ > A_b_vec_c_vec$).
% 18.65/5.46 tff('#skF_90', type, '#skF_90': ($int * Int_set$ * Int_set$) > $int).
% 18.65/5.46 tff(plus$o, type, plus$o: (A_b_vec$ * A_b_vec$) > A_b_vec$).
% 18.65/5.46 tff(tltrue, type, tltrue: tlbool).
% 18.65/5.46 tff(pair$k, type, pair$k: (A$ * Nat_a_b_vec_b_vec_prod$) > A_nat_a_b_vec_b_vec_prod_prod$).
% 18.65/5.46 tff(nrows$b, type, nrows$b: A_c_vec_b_vec$ > Nat$).
% 18.65/5.46 tff(pair$s, type, pair$s: (A_c_vec_c_vec$ * A_c_vec_c_vec$) > A_c_vec_c_vec_a_c_vec_c_vec_prod$).
% 18.65/5.46 tff(snd$q, type, snd$q: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$ > Nat_a_b_vec_c_vec_prod$).
% 18.65/5.46 tff(pair$i, type, pair$i: (A$ * Nat_a_c_vec_b_vec_prod$) > A_nat_a_c_vec_b_vec_prod_prod$).
% 18.65/5.46 tff('#skF_75', type, '#skF_75': (A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$ * Nat$) > C$).
% 18.65/5.46 tff('#skF_24', type, '#skF_24': Nat_a_b_vec_c_vec_prod$ > Nat$).
% 18.65/5.46 tff(fst$m, type, fst$m: Nat_a_b_vec_b_vec_prod$ > Nat$).
% 18.65/5.46 tff(zero$h, type, zero$h: A_int_prod$).
% 18.65/5.46 tff(zero$c, type, zero$c: A_b_vec_c_vec$).
% 18.65/5.46 tff(less_eq$a, type, less_eq$a: Nat$ > Nat_bool_fun$).
% 18.65/5.46 tff('#skF_62', type, '#skF_62': (A_b_vec_c_vec$ * A_b_vec_c_vec$) > C$).
% 18.65/5.46 tff(less$, type, less$: Nat$ > Nat_bool_fun$).
% 18.65/5.46 tff(pair$l, type, pair$l: (Nat$ * A_b_vec_b_vec$) > Nat_a_b_vec_b_vec_prod$).
% 18.65/5.46 tff(vec_nth$f, type, vec_nth$f: (A_b_vec_c_vec_c_vec$ * C$) > A_b_vec_c_vec$).
% 18.65/5.46 tff(pair$t, type, pair$t: (A_b_vec_b_vec$ * Nat_a_c_vec_b_vec_prod$) > A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$).
% 18.65/5.46 tff(pair$j, type, pair$j: (Nat$ * A_c_vec_b_vec$) > Nat_a_c_vec_b_vec_prod$).
% 18.65/5.46 tff(gauss_Jordan_column_k_PA$, type, gauss_Jordan_column_k_PA$: (A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$ * Nat$) > A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$).
% 18.65/5.46 tff(zero$a, type, zero$a: A$).
% 18.65/5.46 tff(upper_triangular$a, type, upper_triangular$a: A_b_vec_c_vec_c_vec$ > $o).
% 18.65/5.46 tff('#skF_84', type, '#skF_84': (A$ * A_set$ * A_set$) > A$).
% 18.65/5.46 tff(uuf$, type, uuf$: Int_int_fun$).
% 18.65/5.46 tff(snd$f, type, snd$f: Nat_a_iarray_prod$ > A_iarray$).
% 18.65/5.46 tff(from_nat$, type, from_nat$: Nat$ > C$).
% 18.65/5.46 tff(times$, type, times$: A$ > A_a_fun$).
% 18.65/5.46 tff(vec_nth$b, type, vec_nth$b: (A_c_vec$ * C$) > A$).
% 18.65/5.46 tff(fun_app$j, type, fun_app$j: (Nat_bool_fun$ * Nat$) > $o).
% 18.65/5.46 tff('#skF_83', type, '#skF_83': (A$ * A_set$ * A_set$) > A$).
% 18.65/5.46 tff('#skF_12', type, '#skF_12': A_nat_a_b_vec_c_vec_prod_prod$ > A$).
% 18.65/5.46 tff(snd$x, type, snd$x: A_c_vec_c_vec_a_b_vec_c_vec_prod$ > A_b_vec_c_vec$).
% 18.65/5.46 tff(fst$d, type, fst$d: Nat_a_iarray_iarray_prod$ > Nat$).
% 18.65/5.46 tff('#skF_74', type, '#skF_74': A_b_vec_c_vec_c_vec$ > C$).
% 18.65/5.46 tff('#skF_69', type, '#skF_69': C_a_b_vec_bool_fun_fun$ > C$).
% 18.65/5.46 tff('#skF_34', type, '#skF_34': (A_nat_a_b_vec_c_vec_prod_prod_bool_fun$ * A_nat_a_b_vec_c_vec_prod_prod$) > A_b_vec_c_vec$).
% 18.65/5.46 tff(gauss_Jordan_column_k_PA$c, type, gauss_Jordan_column_k_PA$c: (A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$ * Nat$) > A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$).
% 18.65/5.46 tff('#skF_33', type, '#skF_33': (A_nat_a_b_vec_c_vec_prod_prod_bool_fun$ * A_nat_a_b_vec_c_vec_prod_prod$) > Nat$).
% 18.65/5.46 tff(fun_app$x, type, fun_app$x: (A_a_iarray_iarray_bool_fun_fun$ * A$) > A_iarray_iarray_bool_fun$).
% 18.65/5.46 tff(fun_app$w, type, fun_app$w: (A_nat_a_iarray_iarray_prod_bool_fun_fun$ * A$) > Nat_a_iarray_iarray_prod_bool_fun$).
% 18.65/5.46 tff(gauss_Jordan_in_ij_det_P$b, type, gauss_Jordan_in_ij_det_P$b: (A_c_vec_b_vec$ * B$ * C$) > A_a_c_vec_b_vec_prod$).
% 18.65/5.46 tff(fun_app$d, type, fun_app$d: (C_a_b_vec_fun$ * C$) > A_b_vec$).
% 18.65/5.46 tff(snd$i, type, snd$i: A_a_c_vec_c_vec_prod$ > A_c_vec_c_vec$).
% 18.65/5.46 tff(fun_app$i, type, fun_app$i: (Nat_a_iarray_iarray_prod_bool_fun$ * Nat_a_iarray_iarray_prod$) > $o).
% 18.65/5.46 tff(fun_app$a, type, fun_app$a: (Nat_nat_fun$ * Nat$) > Nat$).
% 18.65/5.46 tff(pair$n, type, pair$n: (A$ * A$) > A_a_prod$).
% 18.65/5.46
% 18.65/5.47 tff(f_3419, axiom, (![A__questionmark_v0:A_b_vec_c_vec$]: (of_nat$(nrows$(A__questionmark_v0)) = of_nat$(nrows_iarray$(matrix_to_iarray$(A__questionmark_v0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', axiom571)).
% 18.65/5.47 tff(f_1644, axiom, (![A__questionmark_v0:Nat$, A__questionmark_v1:A_iarray_iarray$, A__questionmark_v2:A_iarray_iarray$]: ((snd$c(pair$d(A__questionmark_v0, A__questionmark_v1)) = A__questionmark_v2) => (A__questionmark_v1 = A__questionmark_v2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', axiom280)).
% 18.65/5.47 tff(f_1634, axiom, (![A__questionmark_v0:Nat$, A__questionmark_v1:A_b_vec_c_vec$, A__questionmark_v2:A_b_vec_c_vec$]: ((snd$(pair$a(A__questionmark_v0, A__questionmark_v1)) = A__questionmark_v2) => (A__questionmark_v1 = A__questionmark_v2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', axiom278)).
% 18.65/5.47 tff(f_1654, axiom, (![A__questionmark_v0:A$, A__questionmark_v1:Nat_a_b_vec_c_vec_prod$, A__questionmark_v2:Nat_a_b_vec_c_vec_prod$]: ((snd$a(pair$(A__questionmark_v0, A__questionmark_v1)) = A__questionmark_v2) => (A__questionmark_v1 = A__questionmark_v2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', axiom282)).
% 18.65/5.47 tff(f_1659, axiom, (![A__questionmark_v0:A$, A__questionmark_v1:Nat_a_iarray_iarray_prod$, A__questionmark_v2:Nat_a_iarray_iarray_prod$]: ((snd$d(pair$c(A__questionmark_v0, A__questionmark_v1)) = A__questionmark_v2) => (A__questionmark_v1 = A__questionmark_v2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', axiom283)).
% 18.65/5.47 tff(f_98, negated_conjecture, ~((((![A__questionmark_v0:C$]: (less_eq$(from_nat$(i$), A__questionmark_v0) => (fun_app$c(vec_nth$(fun_app$d(vec_nth$a(a$), A__questionmark_v0)), from_nat$a(k$)) = zero$a))) | (of_nat$(i$) = of_nat$(nrows$(a$)))) => (((fun_app$e(vector_all_zero_from_index$, pair$b(i$, column_iarray$(k$, matrix_to_iarray$(a$)))) | (of_nat$(i$) = of_nat$(nrows_iarray$(matrix_to_iarray$(a$))))) => (matrix_to_iarray$(snd$(snd$a(pair$(n$, pair$a(i$, a$))))) = snd$c(snd$d(pair$c(n$, pair$d(i$, matrix_to_iarray$(a$))))))) & (~(fun_app$e(vector_all_zero_from_index$, pair$b(i$, column_iarray$(k$, matrix_to_iarray$(a$)))) | (of_nat$(i$) = of_nat$(nrows_iarray$(matrix_to_iarray$(a$))))) => (matrix_to_iarray$(snd$(snd$a(pair$(n$, pair$a(i$, a$))))) = snd$c(snd$d(pair$c(fun_app$b(times$(fst$a(gauss_Jordan_in_ij_det_P_iarrays$(matrix_to_iarray$(a$), i$, k$))), n$), pair$d(nat$($sum(of_nat$(i$), 1)), snd$e(gauss_Jordan_in_ij_det_P_iarrays$(matrix_to_iarray$(a$), i$, k$)))))))))) & (~((![A__questionmark_v0:C$]: (less_eq$(from_nat$(i$), A__questionmark_v0) => (fun_app$c(vec_nth$(fun_app$d(vec_nth$a(a$), A__questionmark_v0)), from_nat$a(k$)) = zero$a))) | (of_nat$(i$) = of_nat$(nrows$(a$)))) => (((fun_app$e(vector_all_zero_from_index$, pair$b(i$, column_iarray$(k$, matrix_to_iarray$(a$)))) | (of_nat$(i$) = of_nat$(nrows_iarray$(matrix_to_iarray$(a$))))) => (matrix_to_iarray$(snd$(snd$a(pair$(fun_app$b(times$(fst$(gauss_Jordan_in_ij_det_P$(a$, from_nat$(i$), from_nat$a(k$)))), n$), pair$a(nat$($sum(of_nat$(i$), 1)), snd$b(gauss_Jordan_in_ij_det_P$(a$, from_nat$(i$), from_nat$a(k$)))))))) = snd$c(snd$d(pair$c(n$, pair$d(i$, matrix_to_iarray$(a$))))))) & (~(fun_app$e(vector_all_zero_from_index$, pair$b(i$, column_iarray$(k$, matrix_to_iarray$(a$)))) | (of_nat$(i$) = of_nat$(nrows_iarray$(matrix_to_iarray$(a$))))) => (matrix_to_iarray$(snd$(snd$a(pair$(fun_app$b(times$(fst$(gauss_Jordan_in_ij_det_P$(a$, from_nat$(i$), from_nat$a(k$)))), n$), pair$a(nat$($sum(of_nat$(i$), 1)), snd$b(gauss_Jordan_in_ij_det_P$(a$, from_nat$(i$), from_nat$a(k$)))))))) = snd$c(snd$d(pair$c(fun_app$b(times$(fst$a(gauss_Jordan_in_ij_det_P_iarrays$(matrix_to_iarray$(a$), i$, k$))), n$), pair$d(nat$($sum(of_nat$(i$), 1)), snd$e(gauss_Jordan_in_ij_det_P_iarrays$(matrix_to_iarray$(a$), i$, k$))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conjecture8)).
% 18.65/5.47 tff(f_3871, axiom, (![A__questionmark_v0:Nat$]: (nat$(of_nat$(A__questionmark_v0)) = A__questionmark_v0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', axiom631)).
% 18.65/5.47 tff(f_100, axiom, $lesseq(of_nat$(i$), of_nat$(nrows$(a$))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', axiom9)).
% 18.65/5.47 tff(f_103, axiom, ~$less(of_nat$(i$), of_nat$(nrows$(a$))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', axiom10)).
% 18.65/5.47 tff(c_2101, plain, (![A__questionmark_v0_1167:A_b_vec_c_vec$]: (of_nat$(nrows_iarray$(matrix_to_iarray$(A__questionmark_v0_1167)))=of_nat$(nrows$(A__questionmark_v0_1167)))), inference(cnfTransformation, [status(thm)], [f_3419])).
% 18.65/5.47 tff(c_829, plain, (![A__questionmark_v0_484:Nat$, A__questionmark_v1_485:A_iarray_iarray$]: (snd$c(pair$d(A__questionmark_v0_484, A__questionmark_v1_485))=A__questionmark_v1_485)), inference(cnfTransformation, [status(thm)], [f_1644])).
% 18.65/5.47 tff(c_825, plain, (![A__questionmark_v0_478:Nat$, A__questionmark_v1_479:A_b_vec_c_vec$]: (snd$(pair$a(A__questionmark_v0_478, A__questionmark_v1_479))=A__questionmark_v1_479)), inference(cnfTransformation, [status(thm)], [f_1634])).
% 18.65/5.47 tff(c_833, plain, (![A__questionmark_v0_490:A$, A__questionmark_v1_491:Nat_a_b_vec_c_vec_prod$]: (snd$a(pair$(A__questionmark_v0_490, A__questionmark_v1_491))=A__questionmark_v1_491)), inference(cnfTransformation, [status(thm)], [f_1654])).
% 18.65/5.47 tff(c_835, plain, (![A__questionmark_v0_493:A$, A__questionmark_v1_494:Nat_a_iarray_iarray_prod$]: (snd$d(pair$c(A__questionmark_v0_493, A__questionmark_v1_494))=A__questionmark_v1_494)), inference(cnfTransformation, [status(thm)], [f_1659])).
% 18.65/5.47 tff(c_2561, plain, (snd$c(snd$d(pair$c(n$, pair$d(i$, matrix_to_iarray$(a$)))))!=matrix_to_iarray$(snd$(snd$a(pair$(n$, pair$a(i$, a$))))) | of_nat$(nrows_iarray$(matrix_to_iarray$(a$)))!=of_nat$(i$) | of_nat$(nrows$(a$))!=of_nat$(i$)), inference(cnfTransformation, [status(thm)], [f_98])).
% 18.65/5.47 tff(c_2843, plain, (of_nat$(nrows$(a$))!=of_nat$(i$)), inference(demodulation, [status(thm), theory('equality')], [c_2101, c_829, c_825, c_833, c_835, c_2561])).
% 18.65/5.47 tff(c_2921, plain, (of_nat$(nrows$(a$))='#skE_1'), inference(define, [status(thm), theory('equality')], [c_2843])).
% 18.65/5.47 tff(c_3137, plain, (![A__questionmark_v0_1848:Nat$]: (nat$(of_nat$(A__questionmark_v0_1848))=A__questionmark_v0_1848)), inference(cnfTransformation, [status(thm)], [f_3871])).
% 18.65/5.47 tff(c_4669, plain, (nrows$(a$)=nat$('#skE_1')), inference(superposition, [status(thm), theory('equality')], [c_2921, c_3137])).
% 18.65/5.47 tff(c_4750, plain, (of_nat$(nat$('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_4669, c_2921])).
% 18.65/5.47 tff(c_2922, plain, (of_nat$(i$)='#skE_2'), inference(define, [status(thm), theory('equality')], [c_2843])).
% 18.65/5.47 tff(c_146, plain, ($lesseq(of_nat$(i$), of_nat$(nrows$(a$)))), inference(cnfTransformation, [status(thm)], [f_100])).
% 18.65/5.47 tff(c_2545, plain, (~$less(of_nat$(nrows$(a$)), of_nat$(i$))), inference(backgroundSimplification, [status(thm), theory('LRFIA')], [c_146])).
% 18.65/5.47 tff(c_5080, plain, (~$less('#skE_1', '#skE_2')), inference(demodulation, [status(thm), theory('equality')], [c_4750, c_4669, c_2922, c_2545])).
% 18.65/5.47 tff(c_2544, plain, (~$less(of_nat$(i$), of_nat$(nrows$(a$)))), inference(cnfTransformation, [status(thm)], [f_103])).
% 18.65/5.47 tff(c_4737, plain, (~$less('#skE_2', of_nat$(nat$('#skE_1')))), inference(demodulation, [status(thm), theory('equality')], [c_4669, c_2922, c_2544])).
% 18.65/5.47 tff(c_4999, plain, (of_nat$(nat$('#skE_1'))='#skE_5'), inference(define, [status(thm), theory('equality')], [c_4737])).
% 18.65/5.47 tff(c_4677, plain, (of_nat$(nat$('#skE_1'))='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_4669, c_2921])).
% 18.65/5.47 tff(c_5027, plain, ('#skE_5'='#skE_1'), inference(superposition, [status(thm), theory('equality')], [c_4999, c_4677])).
% 18.65/5.47 tff(c_5029, plain, ('#skE_5'='#skE_1'), inference(backgroundSimplification, [status(thm), theory('LIA')], [c_5027])).
% 18.65/5.47 tff(c_4739, plain, (of_nat$(nat$('#skE_1'))='#skE_5'), inference(define, [status(thm), theory('equality')], [c_4737])).
% 18.65/5.47 tff(c_4738, plain, (~$less('#skE_2', of_nat$(nat$('#skE_1')))), inference(demodulation, [status(thm), theory('equality')], [c_4669, c_2922, c_2544])).
% 18.65/5.47 tff(c_4746, plain, (~$less('#skE_2', '#skE_5')), inference(demodulation, [status(thm), theory('equality')], [c_4739, c_4738])).
% 18.65/5.47 tff(c_5055, plain, (~$less('#skE_2', '#skE_1')), inference(demodulation, [status(thm), theory('equality')], [c_5029, c_4746])).
% 18.65/5.47 tff(c_2918, plain, (of_nat$(i$)='#skE_2'), inference(define, [status(thm), theory('equality')], [c_2843])).
% 18.65/5.47 tff(c_2917, plain, (of_nat$(nrows$(a$))='#skE_1'), inference(define, [status(thm), theory('equality')], [c_2843])).
% 18.65/5.47 tff(c_2923, plain, ('#skE_2'!='#skE_1'), inference(demodulation, [status(thm), theory('equality')], [c_2918, c_2917, c_2843])).
% 18.65/5.47 tff(c_5081, plain, $false, inference(close, [status(thm), theory('LIA')], [c_5080, c_5055, c_2923])).
% 18.65/5.47 % SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.65/5.47
% 18.65/5.47 Inference rules
% 18.65/5.47 ----------------------
% 18.65/5.47 #Ref : 3
% 18.65/5.47 #Sup : 528
% 18.65/5.47 #Fact : 1
% 18.65/5.47 #Define : 5
% 18.65/5.47 #Split : 11
% 18.65/5.47 #Chain : 0
% 18.65/5.47 #Close : 1
% 18.65/5.47
% 18.65/5.47 Ordering : LPO
% 18.65/5.47
% 18.65/5.47 Simplification rules
% 18.65/5.47 ----------------------
% 18.65/5.47 #Subsume : 234
% 18.65/5.47 #Demod : 577
% 18.65/5.47 #Tautology : 765
% 18.65/5.47 #SimpNegUnit : 13
% 18.65/5.47 #BackRed : 31
% 18.65/5.47
% 18.65/5.47 #Partial instantiations: 165
% 18.65/5.47 #Strategies tried : 1
% 18.65/5.47
% 18.65/5.47 Timing (in seconds)
% 18.65/5.47 ----------------------
% 18.65/5.48 Preprocessing : 2.50
% 18.65/5.48 Parsing : 1.07
% 18.65/5.48 CNF conversion : 0.17
% 18.65/5.48 Main loop : 1.98
% 18.65/5.48 Inferencing : 0.29
% 18.65/5.48 Reduction : 0.80
% 18.65/5.48 Demodulation : 0.59
% 18.65/5.48 BG Simplification : 0.31
% 18.65/5.48 Subsumption : 0.60
% 18.65/5.48 Abstraction : 0.08
% 18.65/5.48 MUC search : 0.01
% 18.65/5.48 Cooper : 0.10
% 18.65/5.48 Total : 4.54
% 18.65/5.48 Index Insertion : 0.00
% 18.65/5.48 Index Deletion : 0.00
% 18.65/5.48 Index Matching : 0.00
% 18.65/5.48 BG Taut test : 0.00
%------------------------------------------------------------------------------