TSTP Solution File: ITP339_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP001_1 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n029.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 : Wed May 29 17:14:07 EDT 2024
% Result : Theorem 0.60s 1.00s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.21 % Problem : ITP001_1 : TPTP v8.2.0. Released v8.1.0.
% 0.21/0.22 % Command : do_cvc5 %s %d
% 0.23/0.43 % Computer : n029.cluster.edu
% 0.23/0.43 % Model : x86_64 x86_64
% 0.23/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.43 % Memory : 8042.1875MB
% 0.23/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.23/0.43 % CPULimit : 300
% 0.23/0.43 % WCLimit : 300
% 0.23/0.43 % DateTime : Sun May 26 02:22:24 EDT 2024
% 0.23/0.43 % CPUTime :
% 0.52/0.74 %----Proving TF0_ARI
% 0.60/1.00 --- Run --finite-model-find --decision=internal at 15...
% 0.60/1.00 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.Rvl98d6hE4/cvc5---1.0.5_1917.smt2
% 0.60/1.00 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.Rvl98d6hE4/cvc5---1.0.5_1917.smt2
% 0.60/1.00 (assume a0 (not (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))))
% 0.60/1.00 (assume a1 (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1) 1)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))))
% 0.60/1.00 (assume a2 (= |tptp.'a$a'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))
% 0.60/1.00 (assume a3 (= |tptp.'a$a'| (|tptp.'pair$'| (|tptp.'fst$'| |tptp.'a$a'|) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| |tptp.'a$a'|)) (|tptp.'snd$a'| (|tptp.'snd$'| |tptp.'a$a'|))))))
% 0.60/1.00 (assume a4 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'pair$b'| (|tptp.'fst$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v0)) A__questionmark_v0)))
% 0.60/1.00 (assume a5 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (= (|tptp.'pair$c'| (|tptp.'fst$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v0)) A__questionmark_v0)))
% 0.60/1.00 (assume a6 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'pair$a'| (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v0)) A__questionmark_v0)))
% 0.60/1.00 (assume a7 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (= (|tptp.'pair$d'| (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v0)) A__questionmark_v0)))
% 0.60/1.00 (assume a8 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (= (|tptp.'pair$'| (|tptp.'fst$'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v0)) A__questionmark_v0)))
% 0.60/1.00 (assume a9 (forall ((A__questionmark_v0 |tptp.'Nat_nat_prod$'|)) (= (|tptp.'pair$e'| (|tptp.'fst$e'| A__questionmark_v0) (|tptp.'snd$e'| A__questionmark_v0)) A__questionmark_v0)))
% 0.60/1.00 (assume a10 (forall ((A__questionmark_v0 |tptp.'Nat_int_prod$'|)) (= (|tptp.'pair$f'| (|tptp.'fst$f'| A__questionmark_v0) (|tptp.'snd$f'| A__questionmark_v0)) A__questionmark_v0)))
% 0.60/1.00 (assume a11 (forall ((A__questionmark_v0 |tptp.'Int_nat_prod$'|)) (= (|tptp.'pair$g'| (|tptp.'fst$g'| A__questionmark_v0) (|tptp.'snd$g'| A__questionmark_v0)) A__questionmark_v0)))
% 0.60/1.00 (assume a12 (forall ((A__questionmark_v0 |tptp.'Int_int_prod$'|)) (= (|tptp.'pair$h'| (|tptp.'fst$h'| A__questionmark_v0) (|tptp.'snd$h'| A__questionmark_v0)) A__questionmark_v0)))
% 0.60/1.00 (assume a13 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_prod$'|)) (= (|tptp.'pair$i'| (|tptp.'fst$i'| A__questionmark_v0) (|tptp.'snd$i'| A__questionmark_v0)) A__questionmark_v0)))
% 0.60/1.00 (assume a14 (= (|tptp.'mat$'| |tptp.'zero$'|) |tptp.'zero$a'|))
% 0.60/1.00 (assume a15 (= (|tptp.'fst$g'| |tptp.'zero$b'|) 0))
% 0.60/1.00 (assume a16 (= (|tptp.'fst$j'| |tptp.'zero$c'|) |tptp.'zero$d'|))
% 0.60/1.00 (assume a17 (= (|tptp.'fst$e'| |tptp.'zero$e'|) |tptp.'zero$d'|))
% 0.60/1.00 (assume a18 (= (|tptp.'fst$f'| |tptp.'zero$f'|) |tptp.'zero$d'|))
% 0.60/1.00 (assume a19 (= (|tptp.'fst$h'| |tptp.'zero$g'|) 0))
% 0.60/1.00 (assume a20 (= (|tptp.'fst$'| |tptp.'zero$h'|) |tptp.'zero$a'|))
% 0.60/1.00 (assume a21 (= (|tptp.'fst$a'| |tptp.'zero$i'|) |tptp.'zero$d'|))
% 0.60/1.00 (assume a22 (= (|tptp.'snd$j'| |tptp.'zero$c'|) |tptp.'zero$a'|))
% 0.60/1.00 (assume a23 (= (|tptp.'snd$f'| |tptp.'zero$f'|) 0))
% 0.60/1.00 (assume a24 (= (|tptp.'snd$e'| |tptp.'zero$e'|) |tptp.'zero$d'|))
% 0.60/1.00 (assume a25 (= (|tptp.'snd$g'| |tptp.'zero$b'|) |tptp.'zero$d'|))
% 0.60/1.00 (assume a26 (= (|tptp.'snd$h'| |tptp.'zero$g'|) 0))
% 0.60/1.00 (assume a27 (= (|tptp.'snd$'| |tptp.'zero$h'|) |tptp.'zero$i'|))
% 0.60/1.00 (assume a28 (= (|tptp.'snd$a'| |tptp.'zero$i'|) |tptp.'zero$j'|))
% 0.60/1.00 (assume a29 (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$k'| (|tptp.'gauss_Jordan_upt_k_PA$'| |tptp.'a$'| (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1) 1))))))))
% 0.60/1.00 (assume a30 (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$k'| (|tptp.'gauss_Jordan_upt_k_PA$'| |tptp.'a$'| (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))))
% 0.60/1.00 (assume a31 (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))
% 0.60/1.00 (assume a32 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$b'| (|tptp.'fst$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v0))) false) false)))
% 0.60/1.00 (assume a33 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$c'| (|tptp.'fst$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v0))) false) false)))
% 0.60/1.00 (assume a34 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$a'| (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v0))) false) false)))
% 0.60/1.00 (assume a35 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$d'| (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v0))) false) false)))
% 0.60/1.00 (assume a36 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$'| (|tptp.'fst$'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v0))) false) false)))
% 0.60/1.00 (assume a37 (forall ((A__questionmark_v0 |tptp.'Nat_nat_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$e'| (|tptp.'fst$e'| A__questionmark_v0) (|tptp.'snd$e'| A__questionmark_v0))) false) false)))
% 0.60/1.00 (assume a38 (forall ((A__questionmark_v0 |tptp.'Nat_int_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$f'| (|tptp.'fst$f'| A__questionmark_v0) (|tptp.'snd$f'| A__questionmark_v0))) false) false)))
% 0.60/1.00 (assume a39 (forall ((A__questionmark_v0 |tptp.'Int_nat_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$g'| (|tptp.'fst$g'| A__questionmark_v0) (|tptp.'snd$g'| A__questionmark_v0))) false) false)))
% 0.60/1.00 (assume a40 (forall ((A__questionmark_v0 |tptp.'Int_int_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$h'| (|tptp.'fst$h'| A__questionmark_v0) (|tptp.'snd$h'| A__questionmark_v0))) false) false)))
% 0.60/1.00 (assume a41 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$i'| (|tptp.'fst$i'| A__questionmark_v0) (|tptp.'snd$i'| A__questionmark_v0))) false) false)))
% 0.60/1.00 (assume a42 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray$'|)) (= (= (|tptp.'pair$i'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$i'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a43 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (= (= (|tptp.'pair$e'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$e'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a44 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 Int)) (= (= (|tptp.'pair$f'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$f'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a45 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 Int) (A__questionmark_v3 |tptp.'Nat$'|)) (= (= (|tptp.'pair$g'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$g'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a46 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (= (= (|tptp.'pair$h'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$h'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a47 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v3 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (= (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a48 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_b_vec_c_vec$'|)) (= (= (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$a'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a49 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (= (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a50 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|)) (= (= (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a51 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray$'|)) (= (= (|tptp.'pair$i'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$i'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a52 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (= (= (|tptp.'pair$e'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$e'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a53 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 Int)) (= (= (|tptp.'pair$f'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$f'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a54 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 Int) (A__questionmark_v3 |tptp.'Nat$'|)) (= (= (|tptp.'pair$g'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$g'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a55 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (= (= (|tptp.'pair$h'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$h'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a56 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v3 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (= (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a57 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_b_vec_c_vec$'|)) (= (= (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$a'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a58 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (= (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a59 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|)) (= (= (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a60 (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| |tptp.'a$a'|)) (|tptp.'fst$d'| |tptp.'b$'|)))
% 0.60/1.00 (assume a61 (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$a'| (|tptp.'snd$'| |tptp.'a$a'|))) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$d'| |tptp.'b$'|)))))
% 0.60/1.00 (assume a62 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray$'|)) (=> (and (= (|tptp.'pair$i'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$i'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.60/1.00 (assume a63 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (= (|tptp.'pair$e'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$e'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.60/1.00 (assume a64 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 Int)) (=> (and (= (|tptp.'pair$f'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$f'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.60/1.00 (assume a65 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 Int) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (= (|tptp.'pair$g'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$g'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.60/1.00 (assume a66 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (= (|tptp.'pair$h'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$h'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.60/1.00 (assume a67 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v3 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (and (= (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.60/1.00 (assume a68 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_b_vec_c_vec$'|)) (=> (and (= (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$a'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.60/1.00 (assume a69 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (and (= (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.60/1.00 (assume a70 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|)) (=> (and (= (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.60/1.00 (assume a71 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray$'|)) (|tptp.'fun_app$c'| A__questionmark_v0 (|tptp.'pair$i'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$c'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a72 (forall ((A__questionmark_v0 |tptp.'Nat_nat_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat_nat_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (|tptp.'fun_app$d'| A__questionmark_v0 (|tptp.'pair$e'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$d'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a73 (forall ((A__questionmark_v0 |tptp.'Nat_int_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat_int_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 Int)) (|tptp.'fun_app$e'| A__questionmark_v0 (|tptp.'pair$f'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a74 (forall ((A__questionmark_v0 |tptp.'Int_nat_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'Int_nat_prod$'|)) (=> (forall ((A__questionmark_v2 Int) (A__questionmark_v3 |tptp.'Nat$'|)) (|tptp.'fun_app$f'| A__questionmark_v0 (|tptp.'pair$g'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$f'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a75 (forall ((A__questionmark_v0 |tptp.'Int_int_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'Int_int_prod$'|)) (=> (forall ((A__questionmark_v2 Int) (A__questionmark_v3 Int)) (|tptp.'fun_app$g'| A__questionmark_v0 (|tptp.'pair$h'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$g'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a76 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v3 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (|tptp.'fun_app$h'| A__questionmark_v0 (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$h'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a77 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_b_vec_c_vec$'|)) (|tptp.'fun_app$i'| A__questionmark_v0 (|tptp.'pair$a'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$i'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a78 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A_iarray_iarray$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_iarray_prod$'|)) (|tptp.'fun_app$j'| A__questionmark_v0 (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a79 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|)) (|tptp.'fun_app$k'| A__questionmark_v0 (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$k'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a80 (forall ((A__questionmark_v0 |tptp.'Int_int_prod$'|)) (exists ((A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= A__questionmark_v0 (|tptp.'pair$h'| A__questionmark_v1 A__questionmark_v2)))))
% 0.60/1.00 (assume a81 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (exists ((A__questionmark_v1 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$'| A__questionmark_v1 A__questionmark_v2)))))
% 0.60/1.00 (assume a82 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (exists ((A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v0 (|tptp.'pair$a'| A__questionmark_v1 A__questionmark_v2)))))
% 0.60/1.00 (assume a83 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (exists ((A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$d'| A__questionmark_v1 A__questionmark_v2)))))
% 0.60/1.00 (assume a84 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|)) (exists ((A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v0 (|tptp.'pair$b'| A__questionmark_v1 A__questionmark_v2)))))
% 0.60/1.00 (assume a85 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$'| A__questionmark_v1 A__questionmark_v2)) false)) false)))
% 0.60/1.00 (assume a86 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$a'| A__questionmark_v1 A__questionmark_v2)) false)) false)))
% 0.60/1.00 (assume a87 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$d'| A__questionmark_v1 A__questionmark_v2)) false)) false)))
% 0.60/1.00 (assume a88 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$b'| A__questionmark_v1 A__questionmark_v2)) false)) false)))
% 0.60/1.00 (assume a89 (= |tptp.'zero$h'| (|tptp.'pair$'| |tptp.'zero$a'| |tptp.'zero$i'|)))
% 0.60/1.00 (assume a90 (= |tptp.'zero$i'| (|tptp.'pair$a'| |tptp.'zero$d'| |tptp.'zero$j'|)))
% 0.60/1.00 (assume a91 (= |tptp.'zero$g'| (|tptp.'pair$h'| 0 0)))
% 0.60/1.00 (assume a92 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'snd$'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.60/1.00 (assume a93 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'snd$d'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.60/1.00 (assume a94 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'snd$c'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.60/1.00 (assume a95 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'snd$a'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.60/1.00 (assume a96 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'snd$b'| (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.60/1.00 (assume a97 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (= (|tptp.'snd$'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a98 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (= (|tptp.'snd$d'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a99 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (=> (= (|tptp.'snd$c'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a100 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|)) (=> (= (|tptp.'snd$a'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a101 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (=> (= (|tptp.'snd$b'| (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a102 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'fst$'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.60/1.00 (assume a103 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'fst$d'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.60/1.00 (assume a104 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'fst$c'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.60/1.00 (assume a105 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'fst$a'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.60/1.00 (assume a106 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'fst$b'| (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.60/1.00 (assume a107 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'A_c_vec_c_vec$'|)) (=> (= (|tptp.'fst$'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a108 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (=> (= (|tptp.'fst$d'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a109 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (=> (= (|tptp.'fst$c'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a110 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (= (|tptp.'fst$a'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a111 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (= (|tptp.'fst$b'| (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a112 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'A_b_vec_c_vec$'|)) (|tptp.'fun_app$h'| A__questionmark_v0 (|tptp.'pair$'| A__questionmark_v2 (|tptp.'pair$a'| A__questionmark_v3 A__questionmark_v4)))) (|tptp.'fun_app$h'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a113 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A_iarray_iarray$'|) (A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'A_iarray_iarray$'|)) (|tptp.'fun_app$j'| A__questionmark_v0 (|tptp.'pair$d'| A__questionmark_v2 (|tptp.'pair$b'| A__questionmark_v3 A__questionmark_v4)))) (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a114 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_b_vec_c_vec$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$'| A__questionmark_v1 (|tptp.'pair$a'| A__questionmark_v2 A__questionmark_v3))) false)) false)))
% 0.60/1.00 (assume a115 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$d'| A__questionmark_v1 (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v3))) false)) false)))
% 0.60/1.00 (assume a116 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (= (|tptp.'fst$'| A__questionmark_v0) (|tptp.'fst$'| A__questionmark_v1)) (= (|tptp.'snd$'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v1))))))
% 0.60/1.00 (assume a117 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (= (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'fst$d'| A__questionmark_v1)) (= (|tptp.'snd$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v1))))))
% 0.60/1.00 (assume a118 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (= (|tptp.'fst$c'| A__questionmark_v0) (|tptp.'fst$c'| A__questionmark_v1)) (= (|tptp.'snd$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v1))))))
% 0.60/1.00 (assume a119 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (= (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'fst$a'| A__questionmark_v1)) (= (|tptp.'snd$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v1))))))
% 0.60/1.00 (assume a120 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (= (|tptp.'fst$b'| A__questionmark_v0) (|tptp.'fst$b'| A__questionmark_v1)) (= (|tptp.'snd$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v1))))))
% 0.60/1.00 (assume a121 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (and (= (|tptp.'fst$'| A__questionmark_v0) (|tptp.'fst$'| A__questionmark_v1)) (= (|tptp.'snd$'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a122 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (=> (and (= (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'fst$d'| A__questionmark_v1)) (= (|tptp.'snd$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a123 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (=> (and (= (|tptp.'fst$c'| A__questionmark_v0) (|tptp.'fst$c'| A__questionmark_v1)) (= (|tptp.'snd$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a124 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (and (= (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'fst$a'| A__questionmark_v1)) (= (|tptp.'snd$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a125 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (and (= (|tptp.'fst$b'| A__questionmark_v0) (|tptp.'fst$b'| A__questionmark_v1)) (= (|tptp.'snd$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a126 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (and (= (|tptp.'fst$'| A__questionmark_v0) (|tptp.'fst$'| A__questionmark_v1)) (= (|tptp.'snd$'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a127 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (=> (and (= (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'fst$d'| A__questionmark_v1)) (= (|tptp.'snd$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a128 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (=> (and (= (|tptp.'fst$c'| A__questionmark_v0) (|tptp.'fst$c'| A__questionmark_v1)) (= (|tptp.'snd$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a129 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (and (= (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'fst$a'| A__questionmark_v1)) (= (|tptp.'snd$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a130 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (and (= (|tptp.'fst$b'| A__questionmark_v0) (|tptp.'fst$b'| A__questionmark_v1)) (= (|tptp.'snd$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a131 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$'| (|tptp.'fst$'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a132 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$d'| (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v0)))))
% 0.60/1.00 (assume a133 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$c'| (|tptp.'fst$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v0)))))
% 0.60/1.00 (assume a134 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$a'| (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v0)))))
% 0.60/1.00 (assume a135 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$b'| (|tptp.'fst$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v0)))))
% 0.60/1.00 (assume a136 (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$'| |tptp.'a$'|))) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))
% 0.60/1.00 (assume a137 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a138 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0))))
% 0.60/1.00 (assume a139 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0))))
% 0.60/1.00 (assume a140 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v3 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (and (|tptp.'fun_app$i'| (|tptp.'fun_app$l'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'pair$'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$i'| (|tptp.'fun_app$l'| A__questionmark_v0 (|tptp.'fst$'| A__questionmark_v3)) (|tptp.'snd$'| A__questionmark_v3)))))
% 0.60/1.00 (assume a141 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (=> (and (|tptp.'fun_app$k'| (|tptp.'fun_app$m'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'pair$d'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$k'| (|tptp.'fun_app$m'| A__questionmark_v0 (|tptp.'fst$d'| A__questionmark_v3)) (|tptp.'snd$d'| A__questionmark_v3)))))
% 0.60/1.00 (assume a142 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (=> (and (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'pair$c'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$n'| (|tptp.'fun_app$o'| A__questionmark_v0 (|tptp.'fst$c'| A__questionmark_v3)) (|tptp.'snd$c'| A__questionmark_v3)))))
% 0.60/1.00 (assume a143 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v3 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (and (|tptp.'fun_app$p'| (|tptp.'fun_app$q'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'pair$a'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$p'| (|tptp.'fun_app$q'| A__questionmark_v0 (|tptp.'fst$a'| A__questionmark_v3)) (|tptp.'snd$a'| A__questionmark_v3)))))
% 0.60/1.00 (assume a144 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (and (|tptp.'fun_app$n'| (|tptp.'fun_app$r'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'pair$b'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$n'| (|tptp.'fun_app$r'| A__questionmark_v0 (|tptp.'fst$b'| A__questionmark_v3)) (|tptp.'snd$b'| A__questionmark_v3)))))
% 0.60/1.00 (assume a145 (forall ((A__questionmark_v0 |tptp.'Nat_int_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (<= (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v3) (|tptp.'fun_app$b'| A__questionmark_v0 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1))))) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))) (<= (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v2)))))
% 0.60/1.00 (assume a146 (forall ((A__questionmark_v0 |tptp.'Nat_int_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (<= (|tptp.'fun_app$b'| A__questionmark_v0 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1))) (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v3))) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))) (<= (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a147 (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'k$'|) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$'| |tptp.'a$'|))))
% 0.60/1.00 (assume a148 (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$'| |tptp.'a$'|))))
% 0.60/1.00 (assume a149 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a150 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a151 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0)) (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a152 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0)) (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a153 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) false)))
% 0.60/1.00 (assume a154 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1))))
% 0.60/1.00 (assume a155 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)))))
% 0.60/1.00 (assume a156 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a157 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ 0 1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.60/1.00 (assume a158 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (< 0 (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1))))
% 0.60/1.00 (assume a159 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) false) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) false)) false)))
% 0.60/1.00 (assume a160 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (not (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v2)) (exists ((A__questionmark_v3 |tptp.'Nat$'|)) (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (not (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v3)))))) (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a161 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v3))) (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v2))) (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a162 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) false)))
% 0.60/1.00 (assume a163 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))))))
% 0.60/1.00 (assume a164 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0))))))
% 0.60/1.00 (assume a165 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a166 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))) (or (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0))))))
% 0.60/1.00 (assume a167 (forall ((A__questionmark_v0 |tptp.'Nat_int_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (< (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v3) (|tptp.'fun_app$b'| A__questionmark_v0 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1))))) (= (< (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v2)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))))))
% 0.60/1.00 (assume a168 (forall ((A__questionmark_v0 |tptp.'Nat_int_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (< (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v3) (|tptp.'fun_app$b'| A__questionmark_v0 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1))))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))) (< (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$b'| A__questionmark_v0 A__questionmark_v2)))))
% 0.60/1.00 (assume a169 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.60/1.00 (assume a170 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) false) (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a171 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (not (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0))) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.60/1.00 (assume a172 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.60/1.00 (assume a173 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) false)))
% 0.60/1.00 (assume a174 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 0)))))
% 0.60/1.00 (assume a175 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'nat$'| 0)) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (not (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v2))) (exists ((A__questionmark_v3 |tptp.'Nat$'|)) (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (not (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v3))))))) (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a176 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)) false) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1))) false))) false)))
% 0.60/1.00 (assume a177 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a178 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1))) false))) false)))
% 0.60/1.00 (assume a179 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (not (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))) (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a180 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) false) (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) false)) false)))
% 0.60/1.00 (assume a181 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)))))
% 0.60/1.00 (assume a182 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_bool_fun$'|)) (= (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)) (|tptp.'fun_app$s'| A__questionmark_v1 A__questionmark_v2))) (or (|tptp.'fun_app$s'| A__questionmark_v1 A__questionmark_v0) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) (|tptp.'fun_app$s'| A__questionmark_v1 A__questionmark_v2)))))))
% 0.60/1.00 (assume a183 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (or (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))))))
% 0.60/1.00 (assume a184 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (not (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)))))
% 0.60/1.00 (assume a185 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_bool_fun$'|)) (= (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)) (|tptp.'fun_app$s'| A__questionmark_v1 A__questionmark_v2))) (and (|tptp.'fun_app$s'| A__questionmark_v1 A__questionmark_v0) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) (|tptp.'fun_app$s'| A__questionmark_v1 A__questionmark_v2)))))))
% 0.60/1.00 (assume a186 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)))))))
% 0.60/1.00 (assume a187 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (not (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1))) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a188 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a189 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))) (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)))))
% 0.60/1.00 (assume a190 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat_nat_bool_fun_fun$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v2 A__questionmark_v3) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1)))) (forall ((A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'Nat$'|) (A__questionmark_v5 |tptp.'Nat$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v4)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v4) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v5)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v2 A__questionmark_v3) A__questionmark_v4) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v2 A__questionmark_v4) A__questionmark_v5)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v2 A__questionmark_v3) A__questionmark_v5)))) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v1))))
% 0.60/1.00 (assume a191 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1)) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v3))) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$s'| A__questionmark_v2 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1)))) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v3)))) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v0))))
% 0.60/1.00 (assume a192 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (not (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))) (= (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))))))
% 0.60/1.00 (assume a193 (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (forall ((A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v4)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fun_app$u'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fun_app$u'| A__questionmark_v0 A__questionmark_v4))))) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fun_app$u'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fun_app$u'| A__questionmark_v0 A__questionmark_v2))))))
% 0.60/1.00 (assume a194 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a195 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (or (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a196 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (or (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))))))
% 0.60/1.00 (assume a197 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a198 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))))
% 0.60/1.00 (assume a199 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_bool_fun$'|)) (= (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)) (|tptp.'fun_app$s'| A__questionmark_v1 A__questionmark_v2))) (or (|tptp.'fun_app$s'| A__questionmark_v1 (|tptp.'nat$'| 0)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) (|tptp.'fun_app$s'| A__questionmark_v1 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1)))))))))
% 0.60/1.00 (assume a200 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) (exists ((A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1))))))
% 0.60/1.00 (assume a201 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_bool_fun$'|)) (= (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)) (|tptp.'fun_app$s'| A__questionmark_v1 A__questionmark_v2))) (and (|tptp.'fun_app$s'| A__questionmark_v1 (|tptp.'nat$'| 0)) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) (|tptp.'fun_app$s'| A__questionmark_v1 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1)))))))))
% 0.60/1.00 (assume a202 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) (exists ((A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1))))))
% 0.60/1.00 (assume a203 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (or (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))))))))
% 0.60/1.00 (assume a204 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v1) (not (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'nat$'| 0)))) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (not (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v3)))) (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v2))))))
% 0.60/1.00 (assume a205 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)))))
% 0.60/1.00 (assume a206 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a207 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a208 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (= (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0))))))
% 0.60/1.00 (assume a209 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a210 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v1) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$s'| A__questionmark_v2 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1)))) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v3)))) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v0))))
% 0.60/1.00 (assume a211 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v0) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'fun_app$s'| A__questionmark_v2 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1)))))) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v1))))
% 0.60/1.00 (assume a212 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a213 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a214 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v1) (not (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'nat$'| 0)))) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (not (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v3)))) (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1))))))))
% 0.60/1.00 (assume a215 (forall ((A__questionmark_v0 Int)) (= (= 0 A__questionmark_v0) (= A__questionmark_v0 0))))
% 0.60/1.00 (assume a216 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (= |tptp.'one$'| A__questionmark_v0) (= A__questionmark_v0 |tptp.'one$'|))))
% 0.60/1.00 (assume a217 (forall ((A__questionmark_v0 Int)) (= (= 1 A__questionmark_v0) (= A__questionmark_v0 1))))
% 0.60/1.00 (assume a218 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (and (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) false) (=> (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0)) false)) false)))
% 0.60/1.00 (assume a219 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a220 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)))))
% 0.60/1.00 (assume a221 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v1) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v3) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))))) (exists ((A__questionmark_v3 |tptp.'Nat$'|)) (and (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v4) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v4) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3)))))))))
% 0.60/1.00 (assume a222 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (or (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a223 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0))) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a224 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a225 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)))))
% 0.60/1.00 (assume a226 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0))))
% 0.60/1.00 (assume a227 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (= 0 (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)))))
% 0.60/1.00 (assume a228 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) 0))))
% 0.60/1.00 (assume a229 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (= 0 (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)))))
% 0.60/1.00 (assume a230 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0)))))
% 0.60/1.00 (assume a231 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (and (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) false) (forall ((A__questionmark_v1 |tptp.'Nat$'|)) (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) false))) false)))
% 0.60/1.00 (assume a232 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'nat$'| 0)) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1)))))) (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a233 (forall ((A__questionmark_v0 |tptp.'Nat_nat_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v0 A__questionmark_v3) (|tptp.'nat$'| 0))) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v0 (|tptp.'nat$'| 0)) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1)))) (forall ((A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v0 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v4) 1)))))) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))))
% 0.60/1.00 (assume a234 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1))) (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v2)))) (|tptp.'fun_app$s'| A__questionmark_v0 (|tptp.'nat$'| 0)))))
% 0.60/1.00 (assume a235 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) 0) false)))
% 0.60/1.00 (assume a236 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (= 0 (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)) false)))
% 0.60/1.00 (assume a237 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (= 0 (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1)))))
% 0.60/1.00 (assume a238 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (not (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0)) (exists ((A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1))))))
% 0.60/1.00 (assume a239 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (<= 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) true)))
% 0.60/1.00 (assume a240 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.60/1.00 (assume a241 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.60/1.00 (assume a242 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.60/1.00 (assume a243 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a244 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (=> (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) false) (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) false)) false)))
% 0.60/1.00 (assume a245 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)))))
% 0.60/1.00 (assume a246 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1))))))
% 0.60/1.00 (assume a247 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (or (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1))))))
% 0.60/1.00 (assume a248 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a249 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (not (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))) (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a250 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v3))) (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v2))) (|tptp.'fun_app$s'| A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a251 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat_bool_fun$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v0) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3)) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'fun_app$s'| A__questionmark_v2 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1)))))) (|tptp.'fun_app$s'| A__questionmark_v2 A__questionmark_v1))))
% 0.60/1.00 (assume a252 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat_nat_bool_fun_fun$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v2 A__questionmark_v3) A__questionmark_v3)) (forall ((A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'Nat$'|) (A__questionmark_v5 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v2 A__questionmark_v3) A__questionmark_v4) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v2 A__questionmark_v4) A__questionmark_v5)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v2 A__questionmark_v3) A__questionmark_v5))) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v2 A__questionmark_v3) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) 1))))) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v1))))
% 0.60/1.00 (assume a253 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_c_vec_c_vec$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows$a'| A__questionmark_v1))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$a'| A__questionmark_v1)))) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$j'| (|tptp.'snd$k'| (|tptp.'gauss_Jordan_column_k_PA$a'| (|tptp.'pair$j'| A__questionmark_v3 (|tptp.'pair$k'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2)))) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$d'| (|tptp.'fun_app$v'| (|tptp.'fun_app$w'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| (|tptp.'pair$d'| (|tptp.'matrix_to_iarray$'| A__questionmark_v3) (|tptp.'pair$b'| A__questionmark_v0 (|tptp.'matrix_to_iarray$'| A__questionmark_v1)))) A__questionmark_v2))))))))
% 0.60/1.00 (assume a254 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_c_vec_c_vec$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v1))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$'| A__questionmark_v1)))) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| A__questionmark_v3 (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1))) A__questionmark_v2)))) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$d'| (|tptp.'fun_app$v'| (|tptp.'fun_app$w'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| (|tptp.'pair$d'| (|tptp.'matrix_to_iarray$'| A__questionmark_v3) (|tptp.'pair$b'| A__questionmark_v0 (|tptp.'matrix_to_iarray$a'| A__questionmark_v1)))) A__questionmark_v2))))))))
% 0.60/1.00 (assume a255 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_c_vec_c_vec$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows$a'| A__questionmark_v1))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$a'| A__questionmark_v1)))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$j'| (|tptp.'snd$k'| (|tptp.'gauss_Jordan_column_k_PA$a'| (|tptp.'pair$j'| A__questionmark_v3 (|tptp.'pair$k'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2)))) (|tptp.'snd$b'| (|tptp.'snd$d'| (|tptp.'fun_app$v'| (|tptp.'fun_app$w'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| (|tptp.'pair$d'| (|tptp.'matrix_to_iarray$'| A__questionmark_v3) (|tptp.'pair$b'| A__questionmark_v0 (|tptp.'matrix_to_iarray$'| A__questionmark_v1)))) A__questionmark_v2)))))))
% 0.60/1.00 (assume a256 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_c_vec_c_vec$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v1))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$'| A__questionmark_v1)))) (= (|tptp.'matrix_to_iarray$a'| (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| A__questionmark_v3 (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1))) A__questionmark_v2)))) (|tptp.'snd$b'| (|tptp.'snd$d'| (|tptp.'fun_app$v'| (|tptp.'fun_app$w'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| (|tptp.'pair$d'| (|tptp.'matrix_to_iarray$'| A__questionmark_v3) (|tptp.'pair$b'| A__questionmark_v0 (|tptp.'matrix_to_iarray$a'| A__questionmark_v1)))) A__questionmark_v2)))))))
% 0.60/1.00 (assume a257 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_c_vec_c_vec$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows$a'| A__questionmark_v1))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$a'| A__questionmark_v1)))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$l'| (|tptp.'gauss_Jordan_column_k_PA$a'| (|tptp.'pair$j'| A__questionmark_v3 (|tptp.'pair$k'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2))) (|tptp.'fst$d'| (|tptp.'fun_app$v'| (|tptp.'fun_app$w'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| (|tptp.'pair$d'| (|tptp.'matrix_to_iarray$'| A__questionmark_v3) (|tptp.'pair$b'| A__questionmark_v0 (|tptp.'matrix_to_iarray$'| A__questionmark_v1)))) A__questionmark_v2))))))
% 0.60/1.00 (assume a258 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_c_vec_c_vec$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v1))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$'| A__questionmark_v1)))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| A__questionmark_v3 (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1))) A__questionmark_v2))) (|tptp.'fst$d'| (|tptp.'fun_app$v'| (|tptp.'fun_app$w'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| (|tptp.'pair$d'| (|tptp.'matrix_to_iarray$'| A__questionmark_v3) (|tptp.'pair$b'| A__questionmark_v0 (|tptp.'matrix_to_iarray$a'| A__questionmark_v1)))) A__questionmark_v2))))))
% 0.60/1.00 (assume a259 (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$'| |tptp.'a$'|))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$k'| (|tptp.'gauss_Jordan_upt_k_PA$'| |tptp.'a$'| |tptp.'ka$'|))) (|tptp.'fst$c'| (|tptp.'gauss_Jordan_upt_k_iarrays_PA$'| (|tptp.'matrix_to_iarray$a'| |tptp.'a$'|) |tptp.'ka$'|)))))
% 0.60/1.00 (assume a260 (= (|tptp.'matrix_to_iarray$a'| (|tptp.'snd$a'| (|tptp.'snd$'| |tptp.'a$a'|))) (|tptp.'snd$b'| (|tptp.'snd$d'| |tptp.'b$'|))))
% 0.60/1.00 (assume a261 (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$'| |tptp.'a$'|))) (= (|tptp.'matrix_to_iarray$a'| (|tptp.'snd$l'| (|tptp.'gauss_Jordan_upt_k_PA$'| |tptp.'a$'| |tptp.'ka$'|))) (|tptp.'snd$c'| (|tptp.'gauss_Jordan_upt_k_iarrays_PA$'| (|tptp.'matrix_to_iarray$a'| |tptp.'a$'|) |tptp.'ka$'|)))))
% 0.60/1.00 (assume a262 (< 0 1))
% 0.60/1.00 (assume a263 (< 0 1))
% 0.60/1.00 (assume a264 (not (< 1 0)))
% 0.60/1.00 (assume a265 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.60/1.00 (assume a266 (= (|tptp.'matrix_to_iarray$a'| (|tptp.'snd$l'| (|tptp.'gauss_Jordan_upt_k_PA$'| |tptp.'a$'| |tptp.'ka$'|))) (|tptp.'snd$c'| (|tptp.'gauss_Jordan_upt_k_iarrays_PA$'| (|tptp.'matrix_to_iarray$a'| |tptp.'a$'|) |tptp.'ka$'|))))
% 0.60/1.00 (assume a267 (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$k'| (|tptp.'gauss_Jordan_upt_k_PA$'| |tptp.'a$'| |tptp.'ka$'|))) (|tptp.'fst$c'| (|tptp.'gauss_Jordan_upt_k_iarrays_PA$'| (|tptp.'matrix_to_iarray$a'| |tptp.'a$'|) |tptp.'ka$'|))))
% 0.60/1.00 (assume a268 (= 1 (+ 0 1)))
% 0.60/1.00 (assume a269 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (not (= A__questionmark_v0 A__questionmark_v1)) (=> (< A__questionmark_v0 A__questionmark_v1) false) (=> (< A__questionmark_v1 A__questionmark_v0) false)) false)))
% 0.60/1.00 (assume a270 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_bool_fun$'|)) (=> (and (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) (|tptp.'fun_app$s'| A__questionmark_v1 (|tptp.'nat$'| 1)) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'fun_app$s'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'fun_app$s'| A__questionmark_v1 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1)))))) (|tptp.'fun_app$s'| A__questionmark_v1 A__questionmark_v0))))
% 0.60/1.00 (assume a271 (<= 0 0))
% 0.60/1.00 (assume a272 (not (< 0 0)))
% 0.60/1.00 (assume a273 (<= 1 1))
% 0.60/1.00 (assume a274 (not (= |tptp.'zero$'| |tptp.'one$'|)))
% 0.60/1.00 (assume a275 (not (= 0 1)))
% 0.60/1.00 (assume a276 (not (< 1 1)))
% 0.60/1.00 (assume a277 (not (<= 1 0)))
% 0.60/1.00 (assume a278 (<= 0 1))
% 0.60/1.00 (assume a279 (<= 0 1))
% 0.60/1.00 (assume a280 (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$'| |tptp.'a$'|))) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$d'| (|tptp.'foldl$a'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| (|tptp.'pair$d'| (|tptp.'mat_iarray$'| |tptp.'one$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$a'| |tptp.'a$'|))) (|tptp.'pair$b'| (|tptp.'nat$'| 0) (|tptp.'matrix_to_iarray$a'| |tptp.'a$'|))) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))))))
% 0.60/1.00 (assume a281 (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$d'| (|tptp.'foldl$a'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| (|tptp.'pair$d'| (|tptp.'mat_iarray$'| |tptp.'one$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$a'| |tptp.'a$'|))) (|tptp.'pair$b'| (|tptp.'nat$'| 0) (|tptp.'matrix_to_iarray$a'| |tptp.'a$'|))) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))))))
% 0.60/1.00 (assume a282 (= |tptp.'b$'| (|tptp.'foldl$a'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| (|tptp.'pair$d'| (|tptp.'mat_iarray$'| |tptp.'one$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$a'| |tptp.'a$'|))) (|tptp.'pair$b'| (|tptp.'nat$'| 0) (|tptp.'matrix_to_iarray$a'| |tptp.'a$'|))) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))
% 0.60/1.00 (assume a283 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows$a'| A__questionmark_v0)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))))
% 0.60/1.00 (assume a284 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$a'| A__questionmark_v0))))))
% 0.60/1.00 (assume a285 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'gauss_Jordan_upt_k_iarrays_PA$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$c'| (|tptp.'fst$d'| (|tptp.'foldl$a'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| (|tptp.'pair$d'| (|tptp.'mat_iarray$'| |tptp.'one$'| (|tptp.'nrows_iarray$'| A__questionmark_v0)) (|tptp.'pair$b'| (|tptp.'nat$'| 0) A__questionmark_v0)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1))))) (|tptp.'snd$b'| (|tptp.'snd$d'| (|tptp.'foldl$a'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| (|tptp.'pair$d'| (|tptp.'mat_iarray$'| |tptp.'one$'| (|tptp.'nrows_iarray$'| A__questionmark_v0)) (|tptp.'pair$b'| (|tptp.'nat$'| 0) A__questionmark_v0)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1))))))))))
% 0.60/1.00 (assume a286 (forall ((A__questionmark_v0 Int)) (<= A__questionmark_v0 A__questionmark_v0)))
% 0.60/1.00 (assume a287 (forall ((A__questionmark_v0 Int)) (<= A__questionmark_v0 A__questionmark_v0)))
% 0.60/1.00 (assume a288 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (not (<= A__questionmark_v0 A__questionmark_v1)) (and (<= A__questionmark_v1 A__questionmark_v0) (not (= A__questionmark_v1 A__questionmark_v0))))))
% 0.60/1.00 (assume a289 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v2)) false) (=> (and (<= A__questionmark_v1 A__questionmark_v0) (<= A__questionmark_v0 A__questionmark_v2)) false) (=> (and (<= A__questionmark_v0 A__questionmark_v2) (<= A__questionmark_v2 A__questionmark_v1)) false) (=> (and (<= A__questionmark_v2 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0)) false) (=> (and (<= A__questionmark_v1 A__questionmark_v2) (<= A__questionmark_v2 A__questionmark_v0)) false) (=> (and (<= A__questionmark_v2 A__questionmark_v0) (<= A__questionmark_v0 A__questionmark_v1)) false)) false)))
% 0.60/1.00 (assume a290 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0)))))
% 0.60/1.00 (assume a291 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a292 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a293 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0)) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a294 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a295 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a296 (forall ((A__questionmark_v0 |tptp.'Int_int_bool_fun_fun$'|) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (forall ((A__questionmark_v3 Int) (A__questionmark_v4 Int)) (=> (<= A__questionmark_v3 A__questionmark_v4) (|tptp.'fun_app$x'| (|tptp.'fun_app$y'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4))) (forall ((A__questionmark_v3 Int) (A__questionmark_v4 Int)) (=> (|tptp.'fun_app$x'| (|tptp.'fun_app$y'| A__questionmark_v0 A__questionmark_v4) A__questionmark_v3) (|tptp.'fun_app$x'| (|tptp.'fun_app$y'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4)))) (|tptp.'fun_app$x'| (|tptp.'fun_app$y'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))))
% 0.60/1.00 (assume a297 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v1 A__questionmark_v0) (<= A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a298 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0)) (= A__questionmark_v1 A__questionmark_v0))))
% 0.60/1.00 (assume a299 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 A__questionmark_v0)) (<= A__questionmark_v2 A__questionmark_v1))))
% 0.60/1.00 (assume a300 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0)) (= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a301 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0)))))
% 0.60/1.00 (assume a302 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_int_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (<= (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v5))))) (<= A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a303 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (<= (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v5))))) (<= (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))))
% 0.60/1.00 (assume a304 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a305 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (or (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v0))))
% 0.60/1.00 (assume a306 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_int_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (<= (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v5))))) (<= A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a307 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (<= (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v5))))) (<= (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))))
% 0.60/1.00 (assume a308 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (=> (<= A__questionmark_v0 A__questionmark_v1) false) (=> (<= A__questionmark_v1 A__questionmark_v0) false)) false)))
% 0.60/1.00 (assume a309 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (<= A__questionmark_v0 A__questionmark_v1) (= (<= A__questionmark_v1 A__questionmark_v0) (= A__questionmark_v1 A__questionmark_v0)))))
% 0.60/1.00 (assume a310 (forall ((A__questionmark_v0 Int)) (exists ((A__questionmark_v1 Int)) (< A__questionmark_v1 A__questionmark_v0))))
% 0.60/1.00 (assume a311 (forall ((A__questionmark_v0 Int)) (exists ((A__questionmark_v1 Int)) (< A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a312 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (not (= A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a313 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v0)) false)))
% 0.60/1.00 (assume a314 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a315 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a316 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (not (< A__questionmark_v0 A__questionmark_v1)) (= (not (< A__questionmark_v1 A__questionmark_v0)) (= A__questionmark_v1 A__questionmark_v0)))))
% 0.60/1.00 (assume a317 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (=> (< A__questionmark_v0 A__questionmark_v1) false) (=> (= A__questionmark_v0 A__questionmark_v1) false) (=> (< A__questionmark_v1 A__questionmark_v0) false)) false)))
% 0.60/1.00 (assume a318 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v0)) false)))
% 0.60/1.00 (assume a319 (forall ((A__questionmark_v0 Int)) (not (< A__questionmark_v0 A__questionmark_v0))))
% 0.60/1.00 (assume a320 (forall ((A__questionmark_v0 |tptp.'Int_int_bool_fun_fun$'|) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (forall ((A__questionmark_v3 Int) (A__questionmark_v4 Int)) (=> (< A__questionmark_v3 A__questionmark_v4) (|tptp.'fun_app$x'| (|tptp.'fun_app$y'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4))) (forall ((A__questionmark_v3 Int)) (|tptp.'fun_app$x'| (|tptp.'fun_app$y'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v3)) (forall ((A__questionmark_v3 Int) (A__questionmark_v4 Int)) (=> (|tptp.'fun_app$x'| (|tptp.'fun_app$y'| A__questionmark_v0 A__questionmark_v4) A__questionmark_v3) (|tptp.'fun_app$x'| (|tptp.'fun_app$y'| A__questionmark_v0 A__questionmark_v3) A__questionmark_v4)))) (|tptp.'fun_app$x'| (|tptp.'fun_app$y'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))))
% 0.60/1.00 (assume a321 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a322 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (not (< A__questionmark_v0 A__questionmark_v1)) (or (< A__questionmark_v1 A__questionmark_v0) (= A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a323 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v2 A__questionmark_v0)) (< A__questionmark_v2 A__questionmark_v1))))
% 0.60/1.00 (assume a324 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (not (= A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a325 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (not (= A__questionmark_v1 A__questionmark_v0)))))
% 0.60/1.00 (assume a326 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (not (= A__questionmark_v0 A__questionmark_v1)) (=> (< A__questionmark_v0 A__questionmark_v1) false) (=> (< A__questionmark_v1 A__questionmark_v0) false)) false)))
% 0.60/1.00 (assume a327 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v0)) false)))
% 0.60/1.00 (assume a328 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (not (= A__questionmark_v0 A__questionmark_v1)) (or (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v0)))))
% 0.60/1.00 (assume a329 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v0)) false)))
% 0.60/1.00 (assume a330 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a331 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_int_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (< A__questionmark_v4 A__questionmark_v5) (< (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v5))))) (< A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a332 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (= (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (< A__questionmark_v4 A__questionmark_v5) (< (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v5))))) (< (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))))
% 0.60/1.00 (assume a333 (forall ((A__questionmark_v0 Int)) (not (< A__questionmark_v0 A__questionmark_v0))))
% 0.60/1.00 (assume a334 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_int_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (< A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (< A__questionmark_v4 A__questionmark_v5) (< (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v5))))) (< A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a335 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (< A__questionmark_v4 A__questionmark_v5) (< (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v5))))) (< (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))))
% 0.60/1.00 (assume a336 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (not (< A__questionmark_v1 A__questionmark_v0)))))
% 0.60/1.00 (assume a337 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 tptp.tlbool)) (=> (< A__questionmark_v0 A__questionmark_v1) (= (=> (< A__questionmark_v1 A__questionmark_v0) (= A__questionmark_v2 tptp.tltrue)) true))))
% 0.60/1.00 (assume a338 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (or (< A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v0))))
% 0.60/1.00 (assume a339 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (= (= A__questionmark_v0 A__questionmark_v1) false))))
% 0.60/1.00 (assume a340 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (= (= A__questionmark_v1 A__questionmark_v0) false))))
% 0.60/1.00 (assume a341 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (= (not (< A__questionmark_v1 A__questionmark_v0)) true))))
% 0.60/1.00 (assume a342 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'matrix_to_iarray$'| A__questionmark_v0) (|tptp.'matrix_to_iarray$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a343 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'matrix_to_iarray$a'| A__questionmark_v0) (|tptp.'matrix_to_iarray$a'| A__questionmark_v1)))))
% 0.60/1.00 (assume a344 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (<= A__questionmark_v0 A__questionmark_v1) (not (< A__questionmark_v1 A__questionmark_v0)))))
% 0.60/1.00 (assume a345 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (not (< A__questionmark_v0 A__questionmark_v1)) (<= A__questionmark_v1 A__questionmark_v0))))
% 0.60/1.00 (assume a346 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (not (< A__questionmark_v0 A__questionmark_v1)) (or (not (<= A__questionmark_v0 A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a347 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (not (< A__questionmark_v0 A__questionmark_v1)) (= (<= A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a348 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (<= A__questionmark_v0 A__questionmark_v1) (= (not (< A__questionmark_v0 A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a349 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v0 A__questionmark_v1) (not (<= A__questionmark_v1 A__questionmark_v0))))))
% 0.60/1.00 (assume a350 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (not (<= A__questionmark_v0 A__questionmark_v1)) (< A__questionmark_v1 A__questionmark_v0))))
% 0.60/1.00 (assume a351 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 A__questionmark_v1) (or (< A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a352 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v0 A__questionmark_v1) (not (= A__questionmark_v0 A__questionmark_v1))))))
% 0.60/1.00 (assume a353 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a354 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a355 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v0 A__questionmark_v1) (not (<= A__questionmark_v1 A__questionmark_v0))))))
% 0.60/1.00 (assume a356 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 A__questionmark_v1) (or (< A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v1 A__questionmark_v0)))))
% 0.60/1.00 (assume a357 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v0 A__questionmark_v1) (not (= A__questionmark_v1 A__questionmark_v0))))))
% 0.60/1.00 (assume a358 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v2 A__questionmark_v0)) (< A__questionmark_v2 A__questionmark_v1))))
% 0.60/1.00 (assume a359 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 A__questionmark_v0)) (< A__questionmark_v2 A__questionmark_v1))))
% 0.60/1.00 (assume a360 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v0 A__questionmark_v1) (not (<= A__questionmark_v1 A__questionmark_v0))))))
% 0.60/1.00 (assume a361 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a362 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a363 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 A__questionmark_v1) (or (< A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a364 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 A__questionmark_v1) (and (<= A__questionmark_v0 A__questionmark_v1) (not (= A__questionmark_v0 A__questionmark_v1))))))
% 0.60/1.00 (assume a365 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (not (<= A__questionmark_v0 A__questionmark_v1)) (< A__questionmark_v1 A__questionmark_v0))))
% 0.60/1.00 (assume a366 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (not (< A__questionmark_v0 A__questionmark_v1)) (<= A__questionmark_v1 A__questionmark_v0))))
% 0.60/1.00 (assume a367 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a368 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (not (= A__questionmark_v0 A__questionmark_v1))) (< A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a369 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (not (= A__questionmark_v0 A__questionmark_v1)) (<= A__questionmark_v0 A__questionmark_v1)) (< A__questionmark_v0 A__questionmark_v1))))
% 0.60/1.00 (assume a370 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a371 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a372 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_int_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (< A__questionmark_v4 A__questionmark_v5) (< (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v5))))) (< A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a373 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (< (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (<= (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v5))))) (< (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))))
% 0.60/1.00 (assume a374 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_int_fun$'|) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (< A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v2 A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (<= A__questionmark_v4 A__questionmark_v5) (<= (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v5))))) (< A__questionmark_v0 (|tptp.'fun_app$z'| A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a375 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Int_int_fun$'|) (A__questionmark_v3 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (<= (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3) (forall ((A__questionmark_v4 Int) (A__questionmark_v5 Int)) (=> (< A__questionmark_v4 A__questionmark_v5) (< (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v4) (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v5))))) (< (|tptp.'fun_app$z'| A__questionmark_v2 A__questionmark_v0) A__questionmark_v3))))
% 0.60/1.00 (assume a376 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (or (<= A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v1 A__questionmark_v0))))
% 0.60/1.00 (assume a377 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (<= A__questionmark_v0 A__questionmark_v1) (or (< A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a378 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'gauss_Jordan_upt_k_PA$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$l'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) A__questionmark_v0)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) A__questionmark_v0)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1))))))))))
% 0.60/1.00 (assume a379 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (not (= 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'ncols$'| A__questionmark_v0))))))
% 0.60/1.00 (assume a380 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (not (= 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0))))))
% 0.60/1.00 (assume a381 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (and (=> (or (|tptp.'fun_app$c'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$i'| (|tptp.'fst$b'| (|tptp.'snd$d'| A__questionmark_v0)) (|tptp.'column_iarray$'| A__questionmark_v1 (|tptp.'snd$b'| (|tptp.'snd$d'| A__questionmark_v0))))) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$d'| A__questionmark_v0))) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'snd$b'| (|tptp.'snd$d'| A__questionmark_v0)))))) (= (|tptp.'fun_app$v'| (|tptp.'fun_app$w'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'pair$d'| (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'pair$b'| (|tptp.'fst$b'| (|tptp.'snd$d'| A__questionmark_v0)) (|tptp.'snd$b'| (|tptp.'snd$d'| A__questionmark_v0)))))) (=> (not (or (|tptp.'fun_app$c'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$i'| (|tptp.'fst$b'| (|tptp.'snd$d'| A__questionmark_v0)) (|tptp.'column_iarray$'| A__questionmark_v1 (|tptp.'snd$b'| (|tptp.'snd$d'| A__questionmark_v0))))) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$d'| A__questionmark_v0))) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'snd$b'| (|tptp.'snd$d'| A__questionmark_v0))))))) (= (|tptp.'fun_app$v'| (|tptp.'fun_app$w'| |tptp.'gauss_Jordan_column_k_iarrays_PA$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'pair$d'| (|tptp.'fst$c'| (|tptp.'gauss_Jordan_in_ij_iarrays_PA$'| (|tptp.'pair$c'| (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'snd$b'| (|tptp.'snd$d'| A__questionmark_v0))) (|tptp.'fst$b'| (|tptp.'snd$d'| A__questionmark_v0)) A__questionmark_v1)) (|tptp.'pair$b'| (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$d'| A__questionmark_v0))) 1)) (|tptp.'snd$c'| (|tptp.'gauss_Jordan_in_ij_iarrays_PA$'| (|tptp.'pair$c'| (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'snd$b'| (|tptp.'snd$d'| A__questionmark_v0))) (|tptp.'fst$b'| (|tptp.'snd$d'| A__questionmark_v0)) A__questionmark_v1)))))))))
% 0.60/1.00 (assume a382 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (= (= A__questionmark_v0 (|tptp.'fst$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v2))))))
% 0.60/1.00 (assume a383 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (= (= A__questionmark_v0 (|tptp.'fst$d'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v2))))))
% 0.60/1.00 (assume a384 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (= (= A__questionmark_v0 (|tptp.'fst$c'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v2))))))
% 0.60/1.00 (assume a385 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (= A__questionmark_v0 (|tptp.'fst$a'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v2))))))
% 0.60/1.00 (assume a386 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (= A__questionmark_v0 (|tptp.'fst$b'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v2))))))
% 0.60/1.00 (assume a387 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a388 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a389 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v2 A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a390 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a391 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) A__questionmark_v2))))
% 0.60/1.00 (assume a392 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (<= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v0 A__questionmark_v2)) (<= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a393 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v1)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) A__questionmark_v2))))
% 0.60/1.00 (assume a394 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (<= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v2 A__questionmark_v1)) (<= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a395 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) |tptp.'zero$d'|) A__questionmark_v0)))
% 0.60/1.00 (assume a396 (forall ((A__questionmark_v0 Int)) (= (+ A__questionmark_v0 0) A__questionmark_v0)))
% 0.60/1.00 (assume a397 (forall ((A__questionmark_v0 Int)) (= (= 0 (+ A__questionmark_v0 A__questionmark_v0)) (= A__questionmark_v0 0))))
% 0.60/1.00 (assume a398 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v1) (= A__questionmark_v0 |tptp.'zero$d'|))))
% 0.60/1.00 (assume a399 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v1) (= A__questionmark_v0 0))))
% 0.60/1.00 (assume a400 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v0) (= A__questionmark_v1 |tptp.'zero$d'|))))
% 0.60/1.00 (assume a401 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v0) (= A__questionmark_v1 0))))
% 0.60/1.00 (assume a402 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= A__questionmark_v0 (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v0)) (= A__questionmark_v1 |tptp.'zero$d'|))))
% 0.60/1.00 (assume a403 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v0)) (= A__questionmark_v1 0))))
% 0.60/1.00 (assume a404 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= A__questionmark_v0 (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (= A__questionmark_v1 |tptp.'zero$d'|))))
% 0.60/1.00 (assume a405 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 (+ A__questionmark_v0 A__questionmark_v1)) (= A__questionmark_v1 0))))
% 0.60/1.00 (assume a406 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$d'|) (and (= A__questionmark_v0 |tptp.'zero$d'|) (= A__questionmark_v1 |tptp.'zero$d'|)))))
% 0.60/1.00 (assume a407 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= |tptp.'zero$d'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (and (= A__questionmark_v0 |tptp.'zero$d'|) (= A__questionmark_v1 |tptp.'zero$d'|)))))
% 0.60/1.00 (assume a408 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$u'| (|tptp.'plus$'| |tptp.'zero$d'|) A__questionmark_v0) A__questionmark_v0)))
% 0.60/1.00 (assume a409 (forall ((A__questionmark_v0 Int)) (= (+ 0 A__questionmark_v0) A__questionmark_v0)))
% 0.60/1.00 (assume a410 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v1) A__questionmark_v2))))
% 0.60/1.00 (assume a411 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (< (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v0 A__questionmark_v2)) (< A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a412 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v1)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v2))))
% 0.60/1.00 (assume a413 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (< (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v2 A__questionmark_v1)) (< A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a414 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v3 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'plus$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$'| (|tptp.'plus$b'| A__questionmark_v0 A__questionmark_v2) (|tptp.'plus$c'| A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a415 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'plus$d'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$d'| (|tptp.'plus$e'| A__questionmark_v0 A__questionmark_v2) (|tptp.'plus$f'| A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a416 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (= (|tptp.'plus$g'| (|tptp.'pair$h'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$h'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$h'| (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a417 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 Int) (A__questionmark_v3 |tptp.'Nat$'|)) (= (|tptp.'plus$h'| (|tptp.'pair$g'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$g'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$g'| (+ A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a418 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'plus$c'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$a'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$a'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2) (|tptp.'plus$i'| A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a419 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'plus$f'| (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$b'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2) (|tptp.'plus$e'| A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a420 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 Int) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 Int)) (= (|tptp.'plus$j'| (|tptp.'pair$f'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$f'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$f'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a421 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (= (|tptp.'plus$k'| (|tptp.'pair$e'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$e'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$e'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a422 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (= (|tptp.'snd$'| (|tptp.'plus$a'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$c'| (|tptp.'snd$'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a423 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (= (|tptp.'snd$d'| (|tptp.'plus$d'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$f'| (|tptp.'snd$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v1)))))
% 0.60/1.00 (assume a424 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (= (|tptp.'snd$c'| (|tptp.'plus$l'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$e'| (|tptp.'snd$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v1)))))
% 0.60/1.00 (assume a425 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'snd$a'| (|tptp.'plus$c'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$i'| (|tptp.'snd$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v1)))))
% 0.60/1.00 (assume a426 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'snd$b'| (|tptp.'plus$f'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$e'| (|tptp.'snd$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v1)))))
% 0.60/1.00 (assume a427 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (= (|tptp.'fst$'| (|tptp.'plus$a'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$b'| (|tptp.'fst$'| A__questionmark_v0) (|tptp.'fst$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a428 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (= (|tptp.'fst$d'| (|tptp.'plus$d'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$e'| (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'fst$d'| A__questionmark_v1)))))
% 0.60/1.00 (assume a429 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (= (|tptp.'fst$c'| (|tptp.'plus$l'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$e'| (|tptp.'fst$c'| A__questionmark_v0) (|tptp.'fst$c'| A__questionmark_v1)))))
% 0.60/1.00 (assume a430 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'fst$a'| (|tptp.'plus$c'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| (|tptp.'fst$a'| A__questionmark_v0)) (|tptp.'fst$a'| A__questionmark_v1)))))
% 0.60/1.00 (assume a431 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'fst$b'| (|tptp.'plus$f'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| (|tptp.'fst$b'| A__questionmark_v0)) (|tptp.'fst$b'| A__questionmark_v1)))))
% 0.60/1.00 (assume a432 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0))))
% 0.60/1.00 (assume a433 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) 0) (and (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 0)))))
% 0.60/1.00 (assume a434 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)) (+ (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) 1))))
% 0.60/1.00 (assume a435 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)))))
% 0.60/1.00 (assume a436 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)))))
% 0.60/1.00 (assume a437 (forall ((A__questionmark_v0 Int)) (= (<= 0 (+ A__questionmark_v0 A__questionmark_v0)) (<= 0 A__questionmark_v0))))
% 0.60/1.00 (assume a438 (forall ((A__questionmark_v0 Int)) (= (<= (+ A__questionmark_v0 A__questionmark_v0) 0) (<= A__questionmark_v0 0))))
% 0.60/1.00 (assume a439 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v0)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) A__questionmark_v1))))
% 0.60/1.00 (assume a440 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v0)) (<= 0 A__questionmark_v1))))
% 0.60/1.00 (assume a441 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) A__questionmark_v1))))
% 0.60/1.00 (assume a442 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 (+ A__questionmark_v0 A__questionmark_v1)) (<= 0 A__questionmark_v1))))
% 0.60/1.00 (assume a443 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) |tptp.'zero$d'|))))
% 0.60/1.00 (assume a444 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v1) (<= A__questionmark_v0 0))))
% 0.60/1.00 (assume a445 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) |tptp.'zero$d'|))))
% 0.60/1.00 (assume a446 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v0) (<= A__questionmark_v1 0))))
% 0.60/1.00 (assume a447 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v1) |tptp.'zero$d'|))))
% 0.60/1.00 (assume a448 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v0) (< A__questionmark_v1 0))))
% 0.60/1.00 (assume a449 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) |tptp.'zero$d'|))))
% 0.60/1.00 (assume a450 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v1) (< A__questionmark_v0 0))))
% 0.60/1.00 (assume a451 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) A__questionmark_v1))))
% 0.60/1.00 (assume a452 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 (+ A__questionmark_v0 A__questionmark_v1)) (< 0 A__questionmark_v1))))
% 0.60/1.00 (assume a453 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v0)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) A__questionmark_v1))))
% 0.60/1.00 (assume a454 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v0)) (< 0 A__questionmark_v1))))
% 0.60/1.00 (assume a455 (forall ((A__questionmark_v0 Int)) (= (< (+ A__questionmark_v0 A__questionmark_v0) 0) (< A__questionmark_v0 0))))
% 0.60/1.00 (assume a456 (forall ((A__questionmark_v0 Int)) (= (< 0 (+ A__questionmark_v0 A__questionmark_v0)) (< 0 A__questionmark_v0))))
% 0.60/1.00 (assume a457 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< 0 (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))) (or (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))))))
% 0.60/1.00 (assume a458 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (+ 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0))))
% 0.60/1.00 (assume a459 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 0))))
% 0.60/1.00 (assume a460 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$u'| (|tptp.'plus$'| |tptp.'zero$d'|) A__questionmark_v0) A__questionmark_v0)))
% 0.60/1.00 (assume a461 (forall ((A__questionmark_v0 Int)) (= (+ 0 A__questionmark_v0) A__questionmark_v0)))
% 0.60/1.00 (assume a462 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) |tptp.'zero$d'|) A__questionmark_v0)))
% 0.60/1.00 (assume a463 (forall ((A__questionmark_v0 Int)) (= (+ A__questionmark_v0 0) A__questionmark_v0)))
% 0.60/1.00 (assume a464 (forall ((A__questionmark_v0 Int)) (= (+ 0 A__questionmark_v0) A__questionmark_v0)))
% 0.60/1.00 (assume a465 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (+ (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (+ A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v2)))))
% 0.60/1.00 (assume a466 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) A__questionmark_v1) (= A__questionmark_v2 A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a467 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v2 A__questionmark_v3)) (<= (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a468 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a469 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 A__questionmark_v3)) (<= (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a470 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a471 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 A__questionmark_v3)) (<= (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a472 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a473 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 A__questionmark_v3)) (<= (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a474 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v0)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v1)))))
% 0.60/1.00 (assume a475 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (<= A__questionmark_v0 A__questionmark_v1) (<= (+ A__questionmark_v2 A__questionmark_v0) (+ A__questionmark_v2 A__questionmark_v1)))))
% 0.60/1.00 (assume a476 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (= A__questionmark_v1 (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) false))) false)))
% 0.60/1.00 (assume a477 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.60/1.00 (assume a478 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (<= A__questionmark_v0 A__questionmark_v1) (<= (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v2)))))
% 0.60/1.00 (assume a479 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) A__questionmark_v1) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (= A__questionmark_v1 (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2))))))
% 0.60/1.00 (assume a480 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) A__questionmark_v2))))
% 0.60/1.00 (assume a481 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (<= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v0 A__questionmark_v2)) (<= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a482 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v1)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) A__questionmark_v2))))
% 0.60/1.00 (assume a483 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (<= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v2 A__questionmark_v1)) (<= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a484 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a485 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v2 A__questionmark_v3)) (< (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a486 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a487 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v2 A__questionmark_v3)) (< (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a488 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (= A__questionmark_v2 A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a489 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v2 A__questionmark_v3)) (< (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a490 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a491 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v2 A__questionmark_v3)) (< (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a492 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v0)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v1)))))
% 0.60/1.00 (assume a493 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (< (+ A__questionmark_v2 A__questionmark_v0) (+ A__questionmark_v2 A__questionmark_v1)))))
% 0.60/1.00 (assume a494 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.60/1.00 (assume a495 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (< (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v2)))))
% 0.60/1.00 (assume a496 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v1) A__questionmark_v2))))
% 0.60/1.00 (assume a497 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (< (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v0 A__questionmark_v2)) (< A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a498 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v1)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v2))))
% 0.60/1.00 (assume a499 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (< (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v2 A__questionmark_v1)) (< A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a500 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (+ (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 1)))))
% 0.60/1.00 (assume a501 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (+ (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (+ (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) 1))))
% 0.60/1.00 (assume a502 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))) (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) 1))))))
% 0.60/1.00 (assume a503 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)))))
% 0.60/1.00 (assume a504 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3))) (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3))))))
% 0.60/1.00 (assume a505 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (not (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a506 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (not (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a507 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))))))
% 0.60/1.00 (assume a508 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))))))
% 0.60/1.00 (assume a509 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))))))
% 0.60/1.00 (assume a510 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3)))) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3)))))
% 0.60/1.00 (assume a511 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))) false)) false)))
% 0.60/1.00 (assume a512 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a513 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a514 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)))))
% 0.60/1.00 (assume a515 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)))))
% 0.60/1.00 (assume a516 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)))))))
% 0.60/1.00 (assume a517 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3))) (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3))))))
% 0.60/1.00 (assume a518 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))))))
% 0.60/1.00 (assume a519 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2))))))
% 0.60/1.00 (assume a520 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))))))
% 0.60/1.00 (assume a521 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (<= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)))))))
% 0.60/1.00 (assume a522 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (+ (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (+ A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v2)))))
% 0.60/1.00 (assume a523 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$u'| (|tptp.'plus$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.60/1.00 (assume a524 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v2 A__questionmark_v3)) (= (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a525 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (= A__questionmark_v0 A__questionmark_v1) (= A__questionmark_v2 A__questionmark_v3)) (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a526 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (= A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v2)) (= (+ A__questionmark_v0 A__questionmark_v3) (+ A__questionmark_v1 (+ A__questionmark_v2 A__questionmark_v3))))))
% 0.60/1.00 (assume a527 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (= A__questionmark_v0 (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v2)) (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v3) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v3))))))
% 0.60/1.00 (assume a528 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (= A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v2)) (= (+ A__questionmark_v3 A__questionmark_v0) (+ A__questionmark_v1 (+ A__questionmark_v3 A__questionmark_v2))))))
% 0.60/1.00 (assume a529 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (= A__questionmark_v0 (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v2)) (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v3) A__questionmark_v0) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v3) A__questionmark_v2))))))
% 0.60/1.00 (assume a530 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (+ (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (+ A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v2)))))
% 0.60/1.00 (assume a531 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$u'| (|tptp.'plus$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.60/1.00 (assume a532 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a533 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v2 A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a534 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v1 A__questionmark_v0))))
% 0.60/1.00 (assume a535 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v0))))
% 0.60/1.00 (assume a536 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (+ A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v2)) (+ A__questionmark_v1 (+ A__questionmark_v0 A__questionmark_v2)))))
% 0.60/1.00 (assume a537 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)))))
% 0.60/1.00 (assume a538 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a539 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))))
% 0.60/1.00 (assume a540 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v2 A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a541 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v2))))
% 0.60/1.00 (assume a542 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (= (|tptp.'plus$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| (|tptp.'plus$b'| (|tptp.'fst$'| A__questionmark_v0) (|tptp.'fst$'| A__questionmark_v1)) (|tptp.'plus$c'| (|tptp.'snd$'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v1))))))
% 0.60/1.00 (assume a543 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (= (|tptp.'plus$d'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$d'| (|tptp.'plus$e'| (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'fst$d'| A__questionmark_v1)) (|tptp.'plus$f'| (|tptp.'snd$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v1))))))
% 0.60/1.00 (assume a544 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (= (|tptp.'plus$l'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$c'| (|tptp.'plus$e'| (|tptp.'fst$c'| A__questionmark_v0) (|tptp.'fst$c'| A__questionmark_v1)) (|tptp.'plus$e'| (|tptp.'snd$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v1))))))
% 0.60/1.00 (assume a545 (forall ((A__questionmark_v0 |tptp.'Int_int_prod$'|) (A__questionmark_v1 |tptp.'Int_int_prod$'|)) (= (|tptp.'plus$g'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$h'| (+ (|tptp.'fst$h'| A__questionmark_v0) (|tptp.'fst$h'| A__questionmark_v1)) (+ (|tptp.'snd$h'| A__questionmark_v0) (|tptp.'snd$h'| A__questionmark_v1))))))
% 0.60/1.00 (assume a546 (forall ((A__questionmark_v0 |tptp.'Int_nat_prod$'|) (A__questionmark_v1 |tptp.'Int_nat_prod$'|)) (= (|tptp.'plus$h'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$g'| (+ (|tptp.'fst$g'| A__questionmark_v0) (|tptp.'fst$g'| A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| (|tptp.'snd$g'| A__questionmark_v0)) (|tptp.'snd$g'| A__questionmark_v1))))))
% 0.60/1.00 (assume a547 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'plus$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$a'| (|tptp.'fun_app$u'| (|tptp.'plus$'| (|tptp.'fst$a'| A__questionmark_v0)) (|tptp.'fst$a'| A__questionmark_v1)) (|tptp.'plus$i'| (|tptp.'snd$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v1))))))
% 0.60/1.00 (assume a548 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'plus$f'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$b'| (|tptp.'fun_app$u'| (|tptp.'plus$'| (|tptp.'fst$b'| A__questionmark_v0)) (|tptp.'fst$b'| A__questionmark_v1)) (|tptp.'plus$e'| (|tptp.'snd$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v1))))))
% 0.60/1.00 (assume a549 (forall ((A__questionmark_v0 |tptp.'Nat_int_prod$'|) (A__questionmark_v1 |tptp.'Nat_int_prod$'|)) (= (|tptp.'plus$j'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$f'| (|tptp.'fun_app$u'| (|tptp.'plus$'| (|tptp.'fst$f'| A__questionmark_v0)) (|tptp.'fst$f'| A__questionmark_v1)) (+ (|tptp.'snd$f'| A__questionmark_v0) (|tptp.'snd$f'| A__questionmark_v1))))))
% 0.60/1.00 (assume a550 (forall ((A__questionmark_v0 |tptp.'Nat_nat_prod$'|) (A__questionmark_v1 |tptp.'Nat_nat_prod$'|)) (= (|tptp.'plus$k'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$e'| (|tptp.'fun_app$u'| (|tptp.'plus$'| (|tptp.'fst$e'| A__questionmark_v0)) (|tptp.'fst$e'| A__questionmark_v1)) (|tptp.'fun_app$u'| (|tptp.'plus$'| (|tptp.'snd$e'| A__questionmark_v0)) (|tptp.'snd$e'| A__questionmark_v1))))))
% 0.60/1.00 (assume a551 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) |tptp.'zero$d'|) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) |tptp.'zero$d'|)) (= (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$d'|) (and (= A__questionmark_v0 |tptp.'zero$d'|) (= A__questionmark_v1 |tptp.'zero$d'|))))))
% 0.60/1.00 (assume a552 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 0) (<= A__questionmark_v1 0)) (= (= (+ A__questionmark_v0 A__questionmark_v1) 0) (and (= A__questionmark_v0 0) (= A__questionmark_v1 0))))))
% 0.60/1.00 (assume a553 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) A__questionmark_v1)) (= (= (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$d'|) (and (= A__questionmark_v0 |tptp.'zero$d'|) (= A__questionmark_v1 |tptp.'zero$d'|))))))
% 0.60/1.00 (assume a554 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= 0 A__questionmark_v0) (<= 0 A__questionmark_v1)) (= (= (+ A__questionmark_v0 A__questionmark_v1) 0) (and (= A__questionmark_v0 0) (= A__questionmark_v1 0))))))
% 0.60/1.00 (assume a555 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) |tptp.'zero$d'|) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) |tptp.'zero$d'|)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) |tptp.'zero$d'|))))
% 0.60/1.00 (assume a556 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 0) (<= A__questionmark_v1 0)) (<= (+ A__questionmark_v0 A__questionmark_v1) 0))))
% 0.60/1.00 (assume a557 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) A__questionmark_v1)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)))))
% 0.60/1.00 (assume a558 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= 0 A__questionmark_v0) (<= 0 A__questionmark_v1)) (<= 0 (+ A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a559 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v2) A__questionmark_v0)))))
% 0.60/1.00 (assume a560 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= 0 A__questionmark_v0) (<= A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v1 (+ A__questionmark_v2 A__questionmark_v0)))))
% 0.60/1.00 (assume a561 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) |tptp.'zero$d'|) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v0)) A__questionmark_v2))))
% 0.60/1.00 (assume a562 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 0) (<= A__questionmark_v1 A__questionmark_v2)) (<= (+ A__questionmark_v1 A__questionmark_v0) A__questionmark_v2))))
% 0.60/1.00 (assume a563 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)))))
% 0.60/1.00 (assume a564 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= 0 A__questionmark_v0) (<= A__questionmark_v1 A__questionmark_v2)) (<= A__questionmark_v1 (+ A__questionmark_v0 A__questionmark_v2)))))
% 0.60/1.00 (assume a565 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) |tptp.'zero$d'|) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2))))
% 0.60/1.00 (assume a566 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 0) (<= A__questionmark_v1 A__questionmark_v2)) (<= (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))))
% 0.60/1.00 (assume a567 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a568 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v2 A__questionmark_v3)) (< (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a569 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a570 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 A__questionmark_v3)) (< (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a571 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a572 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v2 A__questionmark_v3)) (< (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a573 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v2) A__questionmark_v3)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v3)))))
% 0.60/1.00 (assume a574 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 A__questionmark_v3)) (< (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.60/1.00 (assume a575 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) |tptp.'zero$d'|) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v1) |tptp.'zero$d'|)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) |tptp.'zero$d'|))))
% 0.60/1.00 (assume a576 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< A__questionmark_v0 0) (< A__questionmark_v1 0)) (< (+ A__questionmark_v0 A__questionmark_v1) 0))))
% 0.60/1.00 (assume a577 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) A__questionmark_v1)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)))))
% 0.60/1.00 (assume a578 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< 0 A__questionmark_v0) (< 0 A__questionmark_v1)) (< 0 (+ A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a579 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (= A__questionmark_v1 (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) (not (= A__questionmark_v2 |tptp.'zero$d'|))) false))) false)))
% 0.60/1.00 (assume a580 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)))))
% 0.60/1.00 (assume a581 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< 0 A__questionmark_v0) (< A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v1 (+ A__questionmark_v0 A__questionmark_v2)))))
% 0.60/1.00 (assume a582 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< (+ A__questionmark_v0 A__questionmark_v1) 0) (or (< A__questionmark_v0 0) (< A__questionmark_v1 0)))))
% 0.60/1.00 (assume a583 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) |tptp.'one$a'|)) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v1) |tptp.'one$a'|)))))
% 0.60/1.00 (assume a584 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (< (+ A__questionmark_v0 1) (+ A__questionmark_v1 1)))))
% 0.60/1.00 (assume a585 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) |tptp.'one$a'|))))
% 0.60/1.00 (assume a586 (forall ((A__questionmark_v0 Int)) (< A__questionmark_v0 (+ A__questionmark_v0 1))))
% 0.60/1.00 (assume a587 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (+ 0 1)) (or (and (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ 0 1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 0)) (and (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ 0 1)))))))
% 0.60/1.00 (assume a588 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (+ 0 1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1))) (or (and (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ 0 1)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) 0)) (and (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ 0 1)))))))
% 0.60/1.00 (assume a589 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (< 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)))))))
% 0.60/1.00 (assume a590 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) 1))))))
% 0.60/1.00 (assume a591 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) 1))))))
% 0.60/1.00 (assume a592 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) 1))))
% 0.60/1.00 (assume a593 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (+ (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) 1))))
% 0.60/1.00 (assume a594 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1)) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (+ (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) 1)) false))) false)))
% 0.60/1.00 (assume a595 (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'Nat$'|)) (=> (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v3) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v4)) (< (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fun_app$u'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fun_app$u'| A__questionmark_v0 A__questionmark_v4))))) (<= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fun_app$u'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'fun_app$u'| A__questionmark_v0 (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v1) (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v2)))))))))
% 0.60/1.00 (assume a596 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)))))
% 0.60/1.00 (assume a597 (= (|tptp.'plus$'| (|tptp.'nat$'| 1)) |tptp.'suc$'|))
% 0.60/1.00 (assume a598 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1) (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0) 1))))
% 0.60/1.00 (assume a599 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)))))
% 0.60/1.00 (assume a600 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= 0 A__questionmark_v0) (< A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v1 (+ A__questionmark_v0 A__questionmark_v2)))))
% 0.60/1.00 (assume a601 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v1) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)))))
% 0.60/1.00 (assume a602 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< 0 A__questionmark_v0) (<= A__questionmark_v1 A__questionmark_v2)) (< A__questionmark_v1 (+ A__questionmark_v0 A__questionmark_v2)))))
% 0.60/1.00 (assume a603 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) A__questionmark_v1)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)))))
% 0.60/1.00 (assume a604 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< 0 A__questionmark_v0) (<= 0 A__questionmark_v1)) (< 0 (+ A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a605 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v0) |tptp.'zero$d'|) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v1) |tptp.'zero$d'|)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) |tptp.'zero$d'|))))
% 0.60/1.00 (assume a606 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 0) (< A__questionmark_v1 0)) (< (+ A__questionmark_v0 A__questionmark_v1) 0))))
% 0.60/1.00 (assume a607 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| |tptp.'zero$d'|) A__questionmark_v0) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) A__questionmark_v1)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)))))
% 0.60/1.00 (assume a608 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= 0 A__questionmark_v0) (< 0 A__questionmark_v1)) (< 0 (+ A__questionmark_v0 A__questionmark_v1)))))
% 0.60/1.00 (assume a609 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) |tptp.'zero$d'|) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| A__questionmark_v1) |tptp.'zero$d'|)) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) |tptp.'zero$d'|))))
% 0.60/1.00 (assume a610 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< A__questionmark_v0 0) (<= A__questionmark_v1 0)) (< (+ A__questionmark_v0 A__questionmark_v1) 0))))
% 0.60/1.00 (assume a611 (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| |tptp.'zero$d'|) (|tptp.'fun_app$u'| (|tptp.'plus$'| |tptp.'one$a'|) |tptp.'one$a'|)))
% 0.60/1.00 (assume a612 (< 0 (+ 1 1)))
% 0.60/1.00 (assume a613 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|)) (= (= A__questionmark_v0 (|tptp.'snd$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'A_c_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v0))))))
% 0.60/1.00 (assume a614 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$'|)) (= (= A__questionmark_v0 (|tptp.'snd$d'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v0))))))
% 0.60/1.00 (assume a615 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray_a_iarray_iarray_prod$'|)) (= (= A__questionmark_v0 (|tptp.'snd$c'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'pair$c'| A__questionmark_v2 A__questionmark_v0))))))
% 0.60/1.00 (assume a616 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (= A__questionmark_v0 (|tptp.'snd$a'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (= A__questionmark_v1 (|tptp.'pair$a'| A__questionmark_v2 A__questionmark_v0))))))
% 0.60/1.00 (assume a617 (forall ((A__questionmark_v0 |tptp.'A_iarray_iarray$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (= A__questionmark_v0 (|tptp.'snd$b'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (= A__questionmark_v1 (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v0))))))
% 0.60/1.00 (assume a618 (forall ((A__questionmark_v0 tptp.tlbool) (A__questionmark_v1 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v3 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v4 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (and (=> (= A__questionmark_v0 tptp.tltrue) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'snd$'| (|tptp.'pair$'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v2)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'snd$'| (|tptp.'pair$'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v4)))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'snd$'| (|tptp.'pair$'| A__questionmark_v3 A__questionmark_v4)) A__questionmark_v2)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'snd$'| (|tptp.'pair$'| A__questionmark_v3 A__questionmark_v4)) A__questionmark_v4)))))))
% 0.60/1.00 (assume a619 (forall ((A__questionmark_v0 tptp.tlbool) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|) (A__questionmark_v4 |tptp.'Nat_a_iarray_iarray_prod$'|)) (and (=> (= A__questionmark_v0 tptp.tltrue) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'snd$d'| (|tptp.'pair$d'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v2)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'snd$d'| (|tptp.'pair$d'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v4)))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'snd$d'| (|tptp.'pair$d'| A__questionmark_v3 A__questionmark_v4)) A__questionmark_v2)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'snd$d'| (|tptp.'pair$d'| A__questionmark_v3 A__questionmark_v4)) A__questionmark_v4)))))))
% 0.60/1.00 (assume a620 (forall ((A__questionmark_v0 tptp.tlbool) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|) (A__questionmark_v4 |tptp.'A_iarray_iarray$'|)) (and (=> (= A__questionmark_v0 tptp.tltrue) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'snd$c'| (|tptp.'pair$c'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v2)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'snd$c'| (|tptp.'pair$c'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v4)))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'snd$c'| (|tptp.'pair$c'| A__questionmark_v3 A__questionmark_v4)) A__questionmark_v2)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'snd$c'| (|tptp.'pair$c'| A__questionmark_v3 A__questionmark_v4)) A__questionmark_v4)))))))
% 0.60/1.00 (assume a621 (forall ((A__questionmark_v0 tptp.tlbool) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'A_b_vec_c_vec$'|)) (and (=> (= A__questionmark_v0 tptp.tltrue) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'snd$a'| (|tptp.'pair$a'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v2)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'snd$a'| (|tptp.'pair$a'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v4)))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'snd$a'| (|tptp.'pair$a'| A__questionmark_v3 A__questionmark_v4)) A__questionmark_v2)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'snd$a'| (|tptp.'pair$a'| A__questionmark_v3 A__questionmark_v4)) A__questionmark_v4)))))))
% 0.60/1.00 (assume a622 (forall ((A__questionmark_v0 tptp.tlbool) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|) (A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'A_iarray_iarray$'|)) (and (=> (= A__questionmark_v0 tptp.tltrue) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'snd$b'| (|tptp.'pair$b'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v2)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'snd$b'| (|tptp.'pair$b'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v4)))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'snd$b'| (|tptp.'pair$b'| A__questionmark_v3 A__questionmark_v4)) A__questionmark_v2)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'snd$b'| (|tptp.'pair$b'| A__questionmark_v3 A__questionmark_v4)) A__questionmark_v4)))))))
% 0.60/1.00 (assume a623 (forall ((A__questionmark_v0 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v0) 0) (= A__questionmark_v0 0))))
% 0.60/1.00 (assume a624 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| |tptp.'less_eq$'| (|tptp.'fun_app$u'| (|tptp.'plus$'| A__questionmark_v0) |tptp.'one$a'|)) A__questionmark_v1))))
% 0.60/1.00 (assume a625 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 A__questionmark_v1) (<= (+ A__questionmark_v0 1) A__questionmark_v1))))
% 0.60/1.00 (assume a626 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'A_c_vec_c_vec$'|)) (= (|tptp.'matrix_to_iarray$'| (|tptp.'plus$b'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$e'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0) (|tptp.'matrix_to_iarray$'| A__questionmark_v1)))))
% 0.60/1.00 (assume a627 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'matrix_to_iarray$a'| (|tptp.'plus$i'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$e'| (|tptp.'matrix_to_iarray$a'| A__questionmark_v0) (|tptp.'matrix_to_iarray$a'| A__questionmark_v1)))))
% 0.60/1.00 (assume a628 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (|tptp.'fun_app$g'| |tptp.'divides_aux$'| (|tptp.'pair$h'| A__questionmark_v0 A__questionmark_v1)) (= A__questionmark_v1 0))))
% 0.60/1.00 (assume a629 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= 0 (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0))))
% 0.60/1.00 (assume a630 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'nat$'| (|tptp.'fun_app$b'| |tptp.'of_nat$'| A__questionmark_v0)) A__questionmark_v0)))
% 0.60/1.00 (assume a631 (forall ((A__questionmark_v0 Int)) (and (=> (<= 0 A__questionmark_v0) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nat$'| A__questionmark_v0)) A__questionmark_v0)) (=> (not (<= 0 A__questionmark_v0)) (= (|tptp.'fun_app$b'| |tptp.'of_nat$'| (|tptp.'nat$'| A__questionmark_v0)) 0)))))
% 0.60/1.00 (assume a632 (forall ((B tptp.tlbool)) (or (= B tptp.tltrue) (= B tptp.tlfalse))))
% 0.60/1.00 (assume a633 (not (= tptp.tltrue tptp.tlfalse)))
% 0.60/1.00 (assume a634 true)
% 0.60/1.00 (step t1 (cl (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))))) :rule implies_neg1)
% 0.60/1.00 (anchor :step t2)
% 0.60/1.00 (assume t2.a0 (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))))
% 0.60/1.00 (step t2.t1 (cl (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))))) :rule implies_neg1)
% 0.60/1.00 (anchor :step t2.t2)
% 0.60/1.00 (assume t2.t2.a0 (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))))
% 0.60/1.00 (step t2.t2.t1 (cl (= |tptp.'gauss_Jordan_column_k_PA$'| |tptp.'gauss_Jordan_column_k_PA$'|)) :rule refl)
% 0.60/1.00 (step t2.t2.t2 (cl (= (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) :rule symm :premises (t2.t2.a0))
% 0.60/1.00 (step t2.t2.t3 (cl (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))))) :rule symm :premises (t2.t2.t2))
% 0.60/1.00 (step t2.t2.t4 (cl (= (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))))) :rule cong :premises (t2.t2.t1 t2.t2.t3))
% 0.60/1.00 (step t2.t2.t5 (cl (= (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) :rule refl)
% 0.60/1.00 (step t2.t2.t6 (cl (= (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))) (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) :rule cong :premises (t2.t2.t4 t2.t2.t5))
% 0.60/1.00 (step t2.t2.t7 (cl (= (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) :rule cong :premises (t2.t2.t6))
% 0.60/1.00 (step t2.t2.t8 (cl (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule cong :premises (t2.t2.t7))
% 0.60/1.00 (step t2.t2 (cl (not (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule subproof :discharge (t2.t2.a0))
% 0.60/1.00 (step t2.t3 (cl (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule resolution :premises (t2.t1 t2.t2))
% 0.60/1.00 (step t2.t4 (cl (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) (not (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule implies_neg2)
% 0.60/1.00 (step t2.t5 (cl (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule resolution :premises (t2.t3 t2.t4))
% 0.60/1.00 (step t2.t6 (cl (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule contraction :premises (t2.t5))
% 0.60/1.00 (step t2.t7 (cl (not (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule implies :premises (t2.t6))
% 0.60/1.00 (step t2.t8 (cl (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule resolution :premises (t2.t7 t2.a0))
% 0.60/1.00 (step t2 (cl (not (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule subproof :discharge (t2.a0))
% 0.60/1.00 (step t3 (cl (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule resolution :premises (t1 t2))
% 0.60/1.00 (step t4 (cl (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) (not (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule implies_neg2)
% 0.60/1.00 (step t5 (cl (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule resolution :premises (t3 t4))
% 0.60/1.00 (step t6 (cl (=> (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule contraction :premises (t5))
% 0.60/1.00 (step t7 (cl (not (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule implies :premises (t6))
% 0.60/1.00 (step t8 (cl (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (not (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))))) :rule reordering :premises (t7))
% 0.60/1.00 (step t9 (cl (not (= (= |tptp.'a$a'| (|tptp.'pair$'| (|tptp.'fst$'| |tptp.'a$a'|) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| |tptp.'a$a'|)) (|tptp.'snd$a'| (|tptp.'snd$'| |tptp.'a$a'|))))) (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))))) (not (= |tptp.'a$a'| (|tptp.'pair$'| (|tptp.'fst$'| |tptp.'a$a'|) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| |tptp.'a$a'|)) (|tptp.'snd$a'| (|tptp.'snd$'| |tptp.'a$a'|)))))) (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))))) :rule equiv_pos2)
% 0.60/1.00 (step t10 (cl (not (= (= |tptp.'a$a'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (= |tptp.'a$a'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) (not (= |tptp.'a$a'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (= |tptp.'a$a'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) :rule equiv_pos2)
% 0.60/1.00 (step t11 (cl (= |tptp.'a$a'| |tptp.'a$a'|)) :rule refl)
% 0.60/1.00 (step t12 (cl (= |tptp.'gauss_Jordan_column_k_PA$'| |tptp.'gauss_Jordan_column_k_PA$'|)) :rule refl)
% 0.60/1.00 (step t13 (cl (= (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)))) :rule refl)
% 0.60/1.00 (step t14 (cl (= (|tptp.'nat$'| 0) (|tptp.'nat$'| 0))) :rule refl)
% 0.60/1.00 (step t15 (cl (= (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1) (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))) :rule all_simplify)
% 0.60/1.00 (step t16 (cl (= (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) :rule cong :premises (t15))
% 0.60/1.00 (step t17 (cl (= (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) :rule cong :premises (t14 t16))
% 0.60/1.00 (step t18 (cl (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))) (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) :rule cong :premises (t12 t13 t17))
% 0.60/1.00 (step t19 (cl (= (= |tptp.'a$a'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (= |tptp.'a$a'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule cong :premises (t11 t18))
% 0.60/1.00 (step t20 (cl (= |tptp.'a$a'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) :rule resolution :premises (t10 t19 a2))
% 0.60/1.00 (step t21 (cl (= (|tptp.'fst$'| |tptp.'a$a'|) (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule cong :premises (t20))
% 0.60/1.00 (step t22 (cl (= (|tptp.'snd$'| |tptp.'a$a'|) (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule cong :premises (t20))
% 0.60/1.00 (step t23 (cl (= (|tptp.'fst$a'| (|tptp.'snd$'| |tptp.'a$a'|)) (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule cong :premises (t22))
% 0.60/1.00 (step t24 (cl (= (|tptp.'snd$a'| (|tptp.'snd$'| |tptp.'a$a'|)) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule cong :premises (t22))
% 0.60/1.00 (step t25 (cl (= (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| |tptp.'a$a'|)) (|tptp.'snd$a'| (|tptp.'snd$'| |tptp.'a$a'|))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) :rule cong :premises (t23 t24))
% 0.60/1.00 (step t26 (cl (= (|tptp.'pair$'| (|tptp.'fst$'| |tptp.'a$a'|) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| |tptp.'a$a'|)) (|tptp.'snd$a'| (|tptp.'snd$'| |tptp.'a$a'|)))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))))) :rule cong :premises (t21 t25))
% 0.60/1.00 (step t27 (cl (= (= |tptp.'a$a'| (|tptp.'pair$'| (|tptp.'fst$'| |tptp.'a$a'|) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| |tptp.'a$a'|)) (|tptp.'snd$a'| (|tptp.'snd$'| |tptp.'a$a'|))))) (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))))) :rule cong :premises (t20 t26))
% 0.60/1.00 (step t28 (cl (= (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))))) :rule resolution :premises (t9 t27 a3))
% 0.60/1.00 (step t29 (cl (not (= (not (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))) (not (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (not (not (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))))) (not (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule equiv_pos2)
% 0.60/1.00 (step t30 (cl (= (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule cong :premises (t12 t18))
% 0.60/1.00 (step t31 (cl (= (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))) (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) :rule cong :premises (t30 t16))
% 0.60/1.00 (step t32 (cl (= (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))) (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) :rule cong :premises (t31))
% 0.60/1.00 (step t33 (cl (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule cong :premises (t32))
% 0.60/1.00 (step t34 (cl (= (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule cong :premises (t18))
% 0.60/1.00 (step t35 (cl (= (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule cong :premises (t18))
% 0.60/1.00 (step t36 (cl (= (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule cong :premises (t35))
% 0.60/1.00 (step t37 (cl (= (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule cong :premises (t35))
% 0.60/1.00 (step t38 (cl (= (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) :rule cong :premises (t36 t37))
% 0.60/1.00 (step t39 (cl (= (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))))) (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))))) :rule cong :premises (t34 t38))
% 0.60/1.00 (step t40 (cl (= (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))))) (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))))) :rule cong :premises (t12 t39))
% 0.60/1.00 (step t41 (cl (= (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))) (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) :rule cong :premises (t40 t16))
% 0.60/1.00 (step t42 (cl (= (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))) (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) :rule cong :premises (t41))
% 0.60/1.00 (step t43 (cl (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))) :rule cong :premises (t42))
% 0.60/1.00 (step t44 (cl (= (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule cong :premises (t33 t43))
% 0.60/1.00 (step t45 (cl (= (not (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1)))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))))) (|tptp.'nat$'| (+ (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|) 1))))))) (not (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) :rule cong :premises (t44))
% 0.60/1.00 (step t46 (cl (not (= (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'fst$'| (|tptp.'fun_app$'| (|tptp.'fun_app$a'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'fst$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))) (|tptp.'pair$a'| (|tptp.'fst$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))) (|tptp.'snd$a'| (|tptp.'snd$'| (|tptp.'foldl$'| |tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$'| (|tptp.'mat$'| |tptp.'one$'|) (|tptp.'pair$a'| (|tptp.'nat$'| 0) |tptp.'a$'|)) (|tptp.'upt$'| (|tptp.'nat$'| 0) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|)))))))))) (|tptp.'nat$'| (+ 1 (|tptp.'fun_app$b'| |tptp.'of_nat$'| |tptp.'ka$'|))))))))) :rule resolution :premises (t29 t45 a0))
% 0.60/1.00 (step t47 (cl) :rule resolution :premises (t8 t28 t46))
% 0.60/1.00
% 0.60/1.00 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.Rvl98d6hE4/cvc5---1.0.5_1917.smt2
% 0.60/1.00 % cvc5---1.0.5 exiting
% 0.60/1.01 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------