TSTP Solution File: ITP338_1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% 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 : n006.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 17:14:06 EDT 2024
% Result : Theorem 0.98s 1.17s
% Output : Proof 0.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.21 % 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 : n006.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
% 0.23/0.44 % CPULimit : 300
% 0.23/0.44 % WCLimit : 300
% 0.23/0.44 % DateTime : Sun May 26 03:58:54 EDT 2024
% 0.23/0.44 % CPUTime :
% 0.50/0.74 %----Proving TF0_ARI
% 0.98/1.17 --- Run --finite-model-find --decision=internal at 15...
% 0.98/1.17 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.P7bCphahst/cvc5---1.0.5_22502.smt2
% 0.98/1.17 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.P7bCphahst/cvc5---1.0.5_22502.smt2
% 0.98/1.17 (assume a0 (forall ((A__questionmark_v0 Int)) (= (|tptp.'fun_app$'| |tptp.'uub$'| A__questionmark_v0) (* 0 A__questionmark_v0))))
% 0.98/1.17 (assume a1 (forall ((A__questionmark_v0 Int)) (= (|tptp.'fun_app$'| |tptp.'uuf$'| A__questionmark_v0) (* 1 A__questionmark_v0))))
% 0.98/1.17 (assume a2 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| |tptp.'uug$'| A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a3 (forall ((A__questionmark_v0 Int)) (= (|tptp.'fun_app$'| |tptp.'uue$'| A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a4 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| |tptp.'uud$'| A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a5 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| |tptp.'uuc$'| A__questionmark_v0) |tptp.'zero$'|)))
% 0.98/1.17 (assume a6 (forall ((A__questionmark_v0 Int)) (= (|tptp.'fun_app$'| |tptp.'uua$'| A__questionmark_v0) 0)))
% 0.98/1.17 (assume a7 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| |tptp.'uu$'| A__questionmark_v0) |tptp.'zero$a'|)))
% 0.98/1.17 (assume a8 (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))))))
% 0.98/1.17 (assume a9 (<= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))
% 0.98/1.17 (assume a10 (not (< (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))
% 0.98/1.17 (assume a11 (< (|tptp.'of_nat$'| |tptp.'k$'|) (|tptp.'of_nat$'| (|tptp.'ncols$'| |tptp.'a$'|))))
% 0.98/1.17 (assume a12 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'pair$a'| (|tptp.'fst$b'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v0)) A__questionmark_v0)))
% 0.98/1.17 (assume a13 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_prod$'|)) (= (|tptp.'pair$b'| (|tptp.'fst$c'| A__questionmark_v0) (|tptp.'snd$f'| A__questionmark_v0)) A__questionmark_v0)))
% 0.98/1.17 (assume a14 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'pair$d'| (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v0)) A__questionmark_v0)))
% 0.98/1.17 (assume a15 (forall ((A__questionmark_v0 |tptp.'A_a_b_vec_c_vec_prod$'|)) (= (|tptp.'pair$e'| (|tptp.'fst$'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v0)) A__questionmark_v0)))
% 0.98/1.17 (assume a16 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (= (|tptp.'pair$'| (|tptp.'fst$e'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v0)) A__questionmark_v0)))
% 0.98/1.17 (assume a17 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (= (|tptp.'pair$c'| (|tptp.'fst$f'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v0)) A__questionmark_v0)))
% 0.98/1.17 (assume a18 (forall ((A__questionmark_v0 |tptp.'A_a_iarray_iarray_prod$'|)) (= (|tptp.'pair$f'| (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'snd$e'| A__questionmark_v0)) A__questionmark_v0)))
% 0.98/1.17 (assume a19 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (= A__questionmark_v0 (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1)) (or (= A__questionmark_v0 |tptp.'zero$a'|) (= A__questionmark_v1 |tptp.'one$'|)))))
% 0.98/1.17 (assume a20 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)) (or (= A__questionmark_v0 0) (= A__questionmark_v1 1)))))
% 0.98/1.17 (assume a21 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v0) (or (= A__questionmark_v0 |tptp.'zero$a'|) (= A__questionmark_v1 |tptp.'one$'|)))))
% 0.98/1.17 (assume a22 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v0) (or (= A__questionmark_v0 0) (= A__questionmark_v1 1)))))
% 0.98/1.17 (assume a23 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (= A__questionmark_v0 (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v0)) (or (= A__questionmark_v0 |tptp.'zero$a'|) (= A__questionmark_v1 |tptp.'one$'|)))))
% 0.98/1.17 (assume a24 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v0)) (or (= A__questionmark_v0 0) (= A__questionmark_v1 1)))))
% 0.98/1.17 (assume a25 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v1) (or (= A__questionmark_v1 |tptp.'zero$a'|) (= A__questionmark_v0 |tptp.'one$'|)))))
% 0.98/1.17 (assume a26 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v1) (or (= A__questionmark_v1 0) (= A__questionmark_v0 1)))))
% 0.98/1.17 (assume a27 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= (+ (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v1)) 0) (and (= A__questionmark_v0 0) (= A__questionmark_v1 0)))))
% 0.98/1.17 (assume a28 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v0) (<= A__questionmark_v1 0))))
% 0.98/1.17 (assume a29 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v1) (<= A__questionmark_v0 0))))
% 0.98/1.17 (assume a30 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 (+ A__questionmark_v0 A__questionmark_v1)) (<= 0 A__questionmark_v1))))
% 0.98/1.17 (assume a31 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v0)) (<= 0 A__questionmark_v1))))
% 0.98/1.17 (assume a32 (forall ((A__questionmark_v0 Int)) (= (<= (+ A__questionmark_v0 A__questionmark_v0) 0) (<= A__questionmark_v0 0))))
% 0.98/1.17 (assume a33 (forall ((A__questionmark_v0 Int)) (= (<= 0 (+ A__questionmark_v0 A__questionmark_v0)) (<= 0 A__questionmark_v0))))
% 0.98/1.17 (assume a34 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v2 A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v2))))
% 0.98/1.17 (assume a35 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a36 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (= (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a37 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (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$a'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a38 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray$'|)) (= (= (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a39 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (= (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$c'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a40 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|)) (= (= (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a41 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (= (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a42 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (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$a'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a43 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray$'|)) (= (= (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a44 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (= (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$c'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a45 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|)) (= (= (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v3)) (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a46 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (<= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v2 A__questionmark_v1)) (<= A__questionmark_v0 A__questionmark_v2))))
% 0.98/1.17 (assume a47 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (<= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v0 A__questionmark_v2)) (<= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a48 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v2) A__questionmark_v1)) (or (= A__questionmark_v1 |tptp.'zero$a'|) (= A__questionmark_v0 A__questionmark_v2)))))
% 0.98/1.17 (assume a49 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1)) (or (= A__questionmark_v1 0) (= A__questionmark_v0 A__questionmark_v2)))))
% 0.98/1.17 (assume a50 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v1)) (or (= A__questionmark_v1 |tptp.'zero$'|) (= A__questionmark_v0 A__questionmark_v2)))))
% 0.98/1.17 (assume a51 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)) (or (= A__questionmark_v0 |tptp.'zero$a'|) (= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a52 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (or (= A__questionmark_v0 0) (= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a53 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (or (= A__questionmark_v0 |tptp.'zero$'|) (= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a54 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$a'|) (or (= A__questionmark_v0 |tptp.'zero$a'|) (= A__questionmark_v1 |tptp.'zero$a'|)))))
% 0.98/1.17 (assume a55 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 0) (or (= A__questionmark_v0 0) (= A__questionmark_v1 0)))))
% 0.98/1.17 (assume a56 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$'|) (or (= A__questionmark_v0 |tptp.'zero$'|) (= A__questionmark_v1 |tptp.'zero$'|)))))
% 0.98/1.17 (assume a57 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) |tptp.'zero$a'|) |tptp.'zero$a'|)))
% 0.98/1.17 (assume a58 (forall ((A__questionmark_v0 Int)) (= (* A__questionmark_v0 0) 0)))
% 0.98/1.17 (assume a59 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) |tptp.'zero$'|) |tptp.'zero$'|)))
% 0.98/1.17 (assume a60 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| |tptp.'zero$a'|) A__questionmark_v0) |tptp.'zero$a'|)))
% 0.98/1.17 (assume a61 (forall ((A__questionmark_v0 Int)) (= (* 0 A__questionmark_v0) 0)))
% 0.98/1.17 (assume a62 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| |tptp.'zero$'|) A__questionmark_v0) |tptp.'zero$'|)))
% 0.98/1.17 (assume a63 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'plus$'| |tptp.'zero$a'|) A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a64 (forall ((A__questionmark_v0 Int)) (= (+ 0 A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a65 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (= A__questionmark_v0 (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) (= A__questionmark_v1 |tptp.'zero$a'|))))
% 0.98/1.17 (assume a66 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 (+ A__questionmark_v0 A__questionmark_v1)) (= A__questionmark_v1 0))))
% 0.98/1.17 (assume a67 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (= A__questionmark_v0 (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v0)) (= A__questionmark_v1 |tptp.'zero$a'|))))
% 0.98/1.17 (assume a68 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v0)) (= A__questionmark_v1 0))))
% 0.98/1.17 (assume a69 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v0) (= A__questionmark_v1 |tptp.'zero$a'|))))
% 0.98/1.17 (assume a70 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v0) (= A__questionmark_v1 0))))
% 0.98/1.17 (assume a71 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1) A__questionmark_v1) (= A__questionmark_v0 |tptp.'zero$a'|))))
% 0.98/1.17 (assume a72 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v1) (= A__questionmark_v0 0))))
% 0.98/1.17 (assume a73 (forall ((A__questionmark_v0 Int)) (= (= 0 (+ A__questionmark_v0 A__questionmark_v0)) (= A__questionmark_v0 0))))
% 0.98/1.17 (assume a74 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) |tptp.'zero$a'|) A__questionmark_v0)))
% 0.98/1.17 (assume a75 (forall ((A__questionmark_v0 Int)) (= (+ A__questionmark_v0 0) A__questionmark_v0)))
% 0.98/1.17 (assume a76 (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))))
% 0.98/1.17 (assume a77 (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))))
% 0.98/1.17 (assume a78 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| |tptp.'one$'|) A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a79 (forall ((A__questionmark_v0 Int)) (= (* 1 A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a80 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| |tptp.'one$a'|) A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a81 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) |tptp.'one$'|) A__questionmark_v0)))
% 0.98/1.17 (assume a82 (forall ((A__questionmark_v0 Int)) (= (* A__questionmark_v0 1) A__questionmark_v0)))
% 0.98/1.17 (assume a83 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) |tptp.'one$a'|) A__questionmark_v0)))
% 0.98/1.17 (assume a84 (forall ((A__questionmark_v0 Int)) (= (< 0 (+ A__questionmark_v0 A__questionmark_v0)) (< 0 A__questionmark_v0))))
% 0.98/1.17 (assume a85 (forall ((A__questionmark_v0 Int)) (= (< (+ A__questionmark_v0 A__questionmark_v0) 0) (< A__questionmark_v0 0))))
% 0.98/1.17 (assume a86 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v0)) (< 0 A__questionmark_v1))))
% 0.98/1.17 (assume a87 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 (+ A__questionmark_v0 A__questionmark_v1)) (< 0 A__questionmark_v1))))
% 0.98/1.17 (assume a88 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v1) (< A__questionmark_v0 0))))
% 0.98/1.17 (assume a89 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v0) (< A__questionmark_v1 0))))
% 0.98/1.17 (assume a90 (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)))
% 0.98/1.17 (assume a91 (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))))
% 0.98/1.17 (assume a92 (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))))
% 0.98/1.17 (assume a93 (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)))))
% 0.98/1.17 (assume a94 (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)))))
% 0.98/1.17 (assume a95 (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)))))
% 0.98/1.17 (assume a96 (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)))))
% 0.98/1.17 (assume a97 (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)))))
% 0.98/1.17 (assume a98 (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)))))
% 0.98/1.17 (assume a99 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (= |tptp.'zero$a'| A__questionmark_v0) (= A__questionmark_v0 |tptp.'zero$a'|))))
% 0.98/1.17 (assume a100 (forall ((A__questionmark_v0 Int)) (= (= 0 A__questionmark_v0) (= A__questionmark_v0 0))))
% 0.98/1.17 (assume a101 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)))))
% 0.98/1.17 (assume a102 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (|tptp.'times$a'| A__questionmark_v0 (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v2)) (|tptp.'times$a'| A__questionmark_v1 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)))))
% 0.98/1.17 (assume a103 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)))))
% 0.98/1.17 (assume a104 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v0))))
% 0.98/1.17 (assume a105 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v0))))
% 0.98/1.17 (assume a106 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v0))))
% 0.98/1.17 (assume a107 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a108 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (|tptp.'times$a'| (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v0 (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a109 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a110 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a111 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (|tptp.'times$a'| (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v0 (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a112 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a113 (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))))
% 0.98/1.17 (assume a114 (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))))
% 0.98/1.17 (assume a115 (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)))))
% 0.98/1.17 (assume a116 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (+ A__questionmark_v0 A__questionmark_v1) (+ A__questionmark_v1 A__questionmark_v0))))
% 0.98/1.17 (assume a117 (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))))
% 0.98/1.17 (assume a118 (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))))
% 0.98/1.17 (assume a119 (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)))))
% 0.98/1.17 (assume a120 (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))))))
% 0.98/1.17 (assume a121 (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))))))
% 0.98/1.17 (assume a122 (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)))))
% 0.98/1.17 (assume a123 (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)))))
% 0.98/1.17 (assume a124 (forall ((A__questionmark_v0 Int)) (= (= 1 A__questionmark_v0) (= A__questionmark_v0 1))))
% 0.98/1.17 (assume a125 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (and (= (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.98/1.17 (assume a126 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (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$a'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.98/1.17 (assume a127 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray$'|)) (=> (and (= (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.98/1.17 (assume a128 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (and (= (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$c'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.98/1.17 (assume a129 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|)) (=> (and (= (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v3)) (=> (and (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v3)) false)) false)))
% 0.98/1.17 (assume a130 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (|tptp.'fun_app$f'| A__questionmark_v0 (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$f'| A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a131 (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$g'| A__questionmark_v0 (|tptp.'pair$a'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$g'| A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a132 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray$'|)) (|tptp.'fun_app$e'| A__questionmark_v0 (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$e'| A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a133 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_iarray_prod$'|)) (|tptp.'fun_app$h'| A__questionmark_v0 (|tptp.'pair$c'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$h'| A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a134 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|)) (|tptp.'fun_app$i'| A__questionmark_v0 (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v3))) (|tptp.'fun_app$i'| A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a135 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (exists ((A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$'| A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a136 (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)))))
% 0.98/1.17 (assume a137 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_prod$'|)) (exists ((A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_iarray$'|)) (= A__questionmark_v0 (|tptp.'pair$b'| A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a138 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (exists ((A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$c'| A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a139 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|)) (exists ((A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v0 (|tptp.'pair$d'| A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a140 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$'| A__questionmark_v1 A__questionmark_v2)) false)) false)))
% 0.98/1.17 (assume a141 (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)))
% 0.98/1.17 (assume a142 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_iarray$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$b'| A__questionmark_v1 A__questionmark_v2)) false)) false)))
% 0.98/1.17 (assume a143 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$c'| A__questionmark_v1 A__questionmark_v2)) false)) false)))
% 0.98/1.17 (assume a144 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$d'| A__questionmark_v1 A__questionmark_v2)) false)) false)))
% 0.98/1.17 (assume a145 (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)))))
% 0.98/1.17 (assume a146 (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)))))
% 0.98/1.17 (assume a147 (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)))))
% 0.98/1.17 (assume a148 (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)))))
% 0.98/1.17 (assume a149 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v0)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v1)))))
% 0.98/1.17 (assume a150 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< 0 A__questionmark_v2)) (< (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1)))))
% 0.98/1.17 (assume a151 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1)) (or (and (< 0 A__questionmark_v1) (< A__questionmark_v0 A__questionmark_v2)) (and (< A__questionmark_v1 0) (< A__questionmark_v2 A__questionmark_v0))))))
% 0.98/1.17 (assume a152 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a153 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< 0 A__questionmark_v2)) (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a154 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v2 0)) (< (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)))))
% 0.98/1.17 (assume a155 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (or (and (< 0 A__questionmark_v0) (< A__questionmark_v1 A__questionmark_v2)) (and (< A__questionmark_v0 0) (< A__questionmark_v2 A__questionmark_v1))))))
% 0.98/1.17 (assume a156 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v0)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v1)))))
% 0.98/1.17 (assume a157 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< 0 A__questionmark_v2)) (< (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1)))))
% 0.98/1.17 (assume a158 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v2 0)) (< (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v0)))))
% 0.98/1.17 (assume a159 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (< 0 A__questionmark_v0) (= (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (< A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a160 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (< A__questionmark_v0 0) (= (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (< A__questionmark_v2 A__questionmark_v1)))))
% 0.98/1.17 (assume a161 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v0))))
% 0.98/1.17 (assume a162 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< 0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)) (< 0 A__questionmark_v1)) (< 0 A__questionmark_v0))))
% 0.98/1.17 (assume a163 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v0)) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v1))))
% 0.98/1.17 (assume a164 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< 0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)) (< 0 A__questionmark_v0)) (< 0 A__questionmark_v1))))
% 0.98/1.17 (assume a165 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< 0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)) (or (and (< 0 A__questionmark_v0) (< 0 A__questionmark_v1)) (and (< A__questionmark_v0 0) (< A__questionmark_v1 0))))))
% 0.98/1.17 (assume a166 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less$'| A__questionmark_v1) |tptp.'zero$'|)) (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v0)) |tptp.'zero$'|))))
% 0.98/1.17 (assume a167 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< 0 A__questionmark_v0) (< A__questionmark_v1 0)) (< (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v0) 0))))
% 0.98/1.17 (assume a168 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)))))
% 0.98/1.17 (assume a169 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< 0 A__questionmark_v0) (< 0 A__questionmark_v1)) (< 0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (assume a170 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less$'| A__questionmark_v1) |tptp.'zero$'|)) (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) |tptp.'zero$'|))))
% 0.98/1.17 (assume a171 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< 0 A__questionmark_v0) (< A__questionmark_v1 0)) (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 0))))
% 0.98/1.17 (assume a172 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| A__questionmark_v0) |tptp.'zero$'|) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) |tptp.'zero$'|))))
% 0.98/1.17 (assume a173 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< A__questionmark_v0 0) (< 0 A__questionmark_v1)) (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 0))))
% 0.98/1.17 (assume a174 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 0) (or (and (< 0 A__questionmark_v0) (< A__questionmark_v1 0)) (and (< A__questionmark_v0 0) (< 0 A__questionmark_v1))))))
% 0.98/1.17 (assume a175 (forall ((A__questionmark_v0 Int)) (not (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v0) 0))))
% 0.98/1.17 (assume a176 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< A__questionmark_v0 0) (< A__questionmark_v1 0)) (< 0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (assume a177 (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)))))
% 0.98/1.17 (assume a178 (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)))))
% 0.98/1.17 (assume a179 (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))))
% 0.98/1.17 (assume a180 (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)))))
% 0.98/1.17 (assume a181 (not (< 1 0)))
% 0.98/1.17 (assume a182 (< 0 1))
% 0.98/1.17 (assume a183 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'one$a'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'one$a'|) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'one$a'|) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)))))
% 0.98/1.17 (assume a184 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (< 1 A__questionmark_v0) (< 1 A__questionmark_v1)) (< 1 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (assume a185 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (< A__questionmark_v0 A__questionmark_v1) (< (+ A__questionmark_v0 1) (+ A__questionmark_v1 1)))))
% 0.98/1.17 (assume a186 (forall ((A__questionmark_v0 Int)) (< A__questionmark_v0 (+ A__questionmark_v0 1))))
% 0.98/1.17 (assume a187 (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$j'| (|tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v3)))))
% 0.98/1.17 (assume a188 (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) (<= 0 A__questionmark_v0) (< 0 A__questionmark_v2)) (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a189 (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$j'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less$'| A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v3)))))
% 0.98/1.17 (assume a190 (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) (< 0 A__questionmark_v0) (<= 0 A__questionmark_v2)) (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a191 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v2))))
% 0.98/1.17 (assume a192 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1)) (< 0 A__questionmark_v1)) (<= A__questionmark_v0 A__questionmark_v2))))
% 0.98/1.17 (assume a193 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v0)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v1) A__questionmark_v2))))
% 0.98/1.17 (assume a194 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (< 0 A__questionmark_v0)) (<= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a195 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (< 0 A__questionmark_v0) (= (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (<= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a196 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (< A__questionmark_v0 0) (= (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (<= A__questionmark_v2 A__questionmark_v1)))))
% 0.98/1.17 (assume a197 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1)) (and (=> (<= 0 A__questionmark_v1) (< A__questionmark_v0 A__questionmark_v2)) (=> (<= A__questionmark_v1 0) (< A__questionmark_v2 A__questionmark_v0))))))
% 0.98/1.17 (assume a198 (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$j'| (|tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less$'| A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v3)))))
% 0.98/1.17 (assume a199 (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) (<= 0 A__questionmark_v0) (<= 0 A__questionmark_v2)) (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a200 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less$'| A__questionmark_v0) A__questionmark_v2))))
% 0.98/1.17 (assume a201 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1)) (<= 0 A__questionmark_v1)) (< A__questionmark_v0 A__questionmark_v2))))
% 0.98/1.17 (assume a202 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (and (=> (<= 0 A__questionmark_v0) (< A__questionmark_v1 A__questionmark_v2)) (=> (<= A__questionmark_v0 0) (< A__questionmark_v2 A__questionmark_v1))))))
% 0.98/1.17 (assume a203 (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$j'| (|tptp.'less$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less$'| A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$j'| (|tptp.'less$'| |tptp.'zero$'|) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v3)))))
% 0.98/1.17 (assume a204 (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) (< 0 A__questionmark_v1) (<= 0 A__questionmark_v2)) (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a205 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less$'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v0)) (|tptp.'fun_app$j'| (|tptp.'less$'| A__questionmark_v1) A__questionmark_v2))))
% 0.98/1.17 (assume a206 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (<= 0 A__questionmark_v0)) (< A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a207 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1)) (and (=> (< 0 A__questionmark_v1) (<= A__questionmark_v0 A__questionmark_v2)) (=> (< A__questionmark_v1 0) (<= A__questionmark_v2 A__questionmark_v0))))))
% 0.98/1.17 (assume a208 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (and (=> (< 0 A__questionmark_v0) (<= A__questionmark_v1 A__questionmark_v2)) (=> (< A__questionmark_v0 0) (<= A__questionmark_v2 A__questionmark_v1))))))
% 0.98/1.17 (assume a209 (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)))))
% 0.98/1.17 (assume a210 (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)))))
% 0.98/1.17 (assume a211 (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)))))
% 0.98/1.17 (assume a212 (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))))
% 0.98/1.17 (assume a213 (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)))))
% 0.98/1.17 (assume a214 (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))))
% 0.98/1.17 (assume a215 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< 0 (+ (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v1))) (or (not (= A__questionmark_v0 0)) (not (= A__questionmark_v1 0))))))
% 0.98/1.17 (assume a216 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (not (< (+ (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v1)) 0))))
% 0.98/1.17 (assume a217 (< 0 (+ 1 1)))
% 0.98/1.17 (assume a218 (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))))
% 0.98/1.17 (assume a219 (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))))
% 0.98/1.17 (assume a220 (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)))))
% 0.98/1.17 (assume a221 (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)))))
% 0.98/1.17 (assume a222 (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)))))
% 0.98/1.17 (assume a223 (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)))))
% 0.98/1.17 (assume a224 (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)))))
% 0.98/1.17 (assume a225 (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)))))
% 0.98/1.17 (assume a226 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (=> (not (= A__questionmark_v0 |tptp.'zero$a'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v2) A__questionmark_v0)) (= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a227 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (not (= A__questionmark_v0 0)) (= (= (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v0)) (= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a228 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (not (= A__questionmark_v0 |tptp.'zero$'|)) (= (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v0)) (= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a229 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (=> (not (= A__questionmark_v0 |tptp.'zero$a'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a230 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (not (= A__questionmark_v0 0)) (= (= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a231 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (not (= A__questionmark_v0 |tptp.'zero$'|)) (= (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a232 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (and (not (= A__questionmark_v0 |tptp.'zero$a'|)) (not (= A__questionmark_v1 |tptp.'zero$a'|))) (not (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$a'|)))))
% 0.98/1.17 (assume a233 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (not (= A__questionmark_v0 0)) (not (= A__questionmark_v1 0))) (not (= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 0)))))
% 0.98/1.17 (assume a234 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (not (= A__questionmark_v0 |tptp.'zero$'|)) (not (= A__questionmark_v1 |tptp.'zero$'|))) (not (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$'|)))))
% 0.98/1.17 (assume a235 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$a'|) (or (= A__questionmark_v0 |tptp.'zero$a'|) (= A__questionmark_v1 |tptp.'zero$a'|)))))
% 0.98/1.17 (assume a236 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 0) (or (= A__questionmark_v0 0) (= A__questionmark_v1 0)))))
% 0.98/1.17 (assume a237 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$'|) (or (= A__questionmark_v0 |tptp.'zero$'|) (= A__questionmark_v1 |tptp.'zero$'|)))))
% 0.98/1.17 (assume a238 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (=> (not (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$a'|)) (and (not (= A__questionmark_v0 |tptp.'zero$a'|)) (not (= A__questionmark_v1 |tptp.'zero$a'|))))))
% 0.98/1.17 (assume a239 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (not (= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 0)) (and (not (= A__questionmark_v0 0)) (not (= A__questionmark_v1 0))))))
% 0.98/1.17 (assume a240 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (not (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$'|)) (and (not (= A__questionmark_v0 |tptp.'zero$'|)) (not (= A__questionmark_v1 |tptp.'zero$'|))))))
% 0.98/1.17 (assume a241 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'plus$'| |tptp.'zero$a'|) A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a242 (forall ((A__questionmark_v0 Int)) (= (+ 0 A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a243 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) |tptp.'zero$a'|) A__questionmark_v0)))
% 0.98/1.17 (assume a244 (forall ((A__questionmark_v0 Int)) (= (+ A__questionmark_v0 0) A__questionmark_v0)))
% 0.98/1.17 (assume a245 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'plus$'| |tptp.'zero$a'|) A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a246 (forall ((A__questionmark_v0 Int)) (= (+ 0 A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a247 (not (= |tptp.'zero$a'| |tptp.'one$'|)))
% 0.98/1.17 (assume a248 (not (= 0 1)))
% 0.98/1.17 (assume a249 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v2) A__questionmark_v1)) A__questionmark_v3)) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2)) A__questionmark_v1)) A__questionmark_v3))))
% 0.98/1.17 (assume a250 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (= (+ (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (+ (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1) A__questionmark_v3)) (+ (|tptp.'times$a'| (+ A__questionmark_v0 A__questionmark_v2) A__questionmark_v1) A__questionmark_v3))))
% 0.98/1.17 (assume a251 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'plus$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$a'| (|tptp.'plus$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v1)) A__questionmark_v3)) (|tptp.'fun_app$a'| (|tptp.'plus$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| (|tptp.'fun_app$a'| (|tptp.'plus$a'| A__questionmark_v0) A__questionmark_v2)) A__questionmark_v1)) A__questionmark_v3))))
% 0.98/1.17 (assume a252 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a253 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (|tptp.'times$a'| (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (+ (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a254 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| (|tptp.'fun_app$a'| (|tptp.'plus$a'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$a'| (|tptp.'plus$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a255 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)))))
% 0.98/1.17 (assume a256 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (|tptp.'times$a'| A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v2)) (+ (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)))))
% 0.98/1.17 (assume a257 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) (|tptp.'fun_app$a'| (|tptp.'plus$a'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'plus$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)))))
% 0.98/1.17 (assume a258 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a259 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (|tptp.'times$a'| (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (+ (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a260 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| (|tptp.'fun_app$a'| (|tptp.'plus$a'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$a'| (|tptp.'plus$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a261 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)))))
% 0.98/1.17 (assume a262 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (|tptp.'times$a'| A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v2)) (+ (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)))))
% 0.98/1.17 (assume a263 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a264 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (|tptp.'times$a'| (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (+ (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a265 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) |tptp.'one$'|) A__questionmark_v0)))
% 0.98/1.17 (assume a266 (forall ((A__questionmark_v0 Int)) (= (* A__questionmark_v0 1) A__questionmark_v0)))
% 0.98/1.17 (assume a267 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) |tptp.'one$a'|) A__questionmark_v0)))
% 0.98/1.17 (assume a268 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| |tptp.'one$'|) A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a269 (forall ((A__questionmark_v0 Int)) (= (* 1 A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a270 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| |tptp.'one$a'|) A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a271 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.98/1.17 (assume a272 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray$'|)) (= (|tptp.'snd$f'| (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.98/1.17 (assume a273 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.98/1.17 (assume a274 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'snd$b'| (|tptp.'pair$e'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.98/1.17 (assume a275 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.98/1.17 (assume a276 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.98/1.17 (assume a277 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'snd$e'| (|tptp.'pair$f'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)))
% 0.98/1.17 (assume a278 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|)) (=> (= (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a279 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray$'|) (A__questionmark_v2 |tptp.'A_iarray$'|)) (=> (= (|tptp.'snd$f'| (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a280 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (=> (= (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a281 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|)) (=> (= (|tptp.'snd$b'| (|tptp.'pair$e'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a282 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (= (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a283 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (= (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a284 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|)) (=> (= (|tptp.'snd$e'| (|tptp.'pair$f'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a285 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'fst$e'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.98/1.17 (assume a286 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'fst$b'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.98/1.17 (assume a287 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray$'|)) (= (|tptp.'fst$c'| (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.98/1.17 (assume a288 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'fst$f'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.98/1.17 (assume a289 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'fst$d'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.98/1.17 (assume a290 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'fst$'| (|tptp.'pair$e'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.98/1.17 (assume a291 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'fst$a'| (|tptp.'pair$f'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v0)))
% 0.98/1.17 (assume a292 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'A$'|)) (=> (= (|tptp.'fst$e'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.98/1.17 (assume a293 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (= (|tptp.'fst$b'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.98/1.17 (assume a294 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (= (|tptp.'fst$c'| (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.98/1.17 (assume a295 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'A$'|)) (=> (= (|tptp.'fst$f'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.98/1.17 (assume a296 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (= (|tptp.'fst$d'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.98/1.17 (assume a297 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'A$'|)) (=> (= (|tptp.'fst$'| (|tptp.'pair$e'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.98/1.17 (assume a298 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (A__questionmark_v2 |tptp.'A$'|)) (=> (= (|tptp.'fst$a'| (|tptp.'pair$f'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (= A__questionmark_v0 A__questionmark_v2))))
% 0.98/1.17 (assume a299 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v1) (and (=> (<= 0 A__questionmark_v1) (< A__questionmark_v0 1)) (=> (<= A__questionmark_v1 0) (< 1 A__questionmark_v0))))))
% 0.98/1.17 (assume a300 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v0)) (and (=> (<= 0 A__questionmark_v0) (< 1 A__questionmark_v1)) (=> (<= A__questionmark_v0 0) (< A__questionmark_v1 1))))))
% 0.98/1.17 (assume a301 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v0) (and (=> (<= 0 A__questionmark_v0) (< A__questionmark_v1 1)) (=> (<= A__questionmark_v0 0) (< 1 A__questionmark_v1))))))
% 0.98/1.17 (assume a302 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)) (and (=> (<= 0 A__questionmark_v0) (< 1 A__questionmark_v1)) (=> (<= A__questionmark_v0 0) (< A__questionmark_v1 1))))))
% 0.98/1.17 (assume a303 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v1) (and (=> (< 0 A__questionmark_v1) (<= A__questionmark_v0 1)) (=> (< A__questionmark_v1 0) (<= 1 A__questionmark_v0))))))
% 0.98/1.17 (assume a304 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v0)) (and (=> (< 0 A__questionmark_v0) (<= 1 A__questionmark_v1)) (=> (< A__questionmark_v0 0) (<= A__questionmark_v1 1))))))
% 0.98/1.17 (assume a305 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v0) (and (=> (< 0 A__questionmark_v0) (<= A__questionmark_v1 1)) (=> (< A__questionmark_v0 0) (<= 1 A__questionmark_v1))))))
% 0.98/1.17 (assume a306 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= A__questionmark_v0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)) (and (=> (< 0 A__questionmark_v0) (<= 1 A__questionmark_v1)) (=> (< A__questionmark_v0 0) (<= A__questionmark_v1 1))))))
% 0.98/1.17 (assume a307 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'A_b_vec_c_vec$'|)) (|tptp.'fun_app$f'| A__questionmark_v0 (|tptp.'pair$'| A__questionmark_v2 (|tptp.'pair$a'| A__questionmark_v3 A__questionmark_v4)))) (|tptp.'fun_app$f'| A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a308 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod_bool_fun$'|) (A__questionmark_v1 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (=> (forall ((A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'A_iarray_iarray$'|)) (|tptp.'fun_app$h'| A__questionmark_v0 (|tptp.'pair$c'| A__questionmark_v2 (|tptp.'pair$d'| A__questionmark_v3 A__questionmark_v4)))) (|tptp.'fun_app$h'| A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a309 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_b_vec_c_vec$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$'| A__questionmark_v1 (|tptp.'pair$a'| A__questionmark_v2 A__questionmark_v3))) false)) false)))
% 0.98/1.17 (assume a310 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (=> (forall ((A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray_iarray$'|)) (=> (= A__questionmark_v0 (|tptp.'pair$c'| A__questionmark_v1 (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v3))) false)) false)))
% 0.98/1.17 (assume a311 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (= (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'fst$d'| A__questionmark_v1)) (= (|tptp.'snd$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v1))))))
% 0.98/1.17 (assume a312 (forall ((A__questionmark_v0 |tptp.'A_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'A_a_b_vec_c_vec_prod$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (= (|tptp.'fst$'| A__questionmark_v0) (|tptp.'fst$'| A__questionmark_v1)) (= (|tptp.'snd$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v1))))))
% 0.98/1.17 (assume a313 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (= (|tptp.'fst$e'| A__questionmark_v0) (|tptp.'fst$e'| A__questionmark_v1)) (= (|tptp.'snd$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v1))))))
% 0.98/1.17 (assume a314 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (= (|tptp.'fst$f'| A__questionmark_v0) (|tptp.'fst$f'| A__questionmark_v1)) (= (|tptp.'snd$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v1))))))
% 0.98/1.17 (assume a315 (forall ((A__questionmark_v0 |tptp.'A_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_a_iarray_iarray_prod$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (and (= (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'fst$a'| A__questionmark_v1)) (= (|tptp.'snd$e'| A__questionmark_v0) (|tptp.'snd$e'| A__questionmark_v1))))))
% 0.98/1.17 (assume a316 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (and (= (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'fst$d'| A__questionmark_v1)) (= (|tptp.'snd$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a317 (forall ((A__questionmark_v0 |tptp.'A_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'A_a_b_vec_c_vec_prod$'|)) (=> (and (= (|tptp.'fst$'| A__questionmark_v0) (|tptp.'fst$'| A__questionmark_v1)) (= (|tptp.'snd$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a318 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (and (= (|tptp.'fst$e'| A__questionmark_v0) (|tptp.'fst$e'| A__questionmark_v1)) (= (|tptp.'snd$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a319 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (=> (and (= (|tptp.'fst$f'| A__questionmark_v0) (|tptp.'fst$f'| A__questionmark_v1)) (= (|tptp.'snd$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a320 (forall ((A__questionmark_v0 |tptp.'A_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_a_iarray_iarray_prod$'|)) (=> (and (= (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'fst$a'| A__questionmark_v1)) (= (|tptp.'snd$e'| A__questionmark_v0) (|tptp.'snd$e'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a321 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (and (= (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'fst$d'| A__questionmark_v1)) (= (|tptp.'snd$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a322 (forall ((A__questionmark_v0 |tptp.'A_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'A_a_b_vec_c_vec_prod$'|)) (=> (and (= (|tptp.'fst$'| A__questionmark_v0) (|tptp.'fst$'| A__questionmark_v1)) (= (|tptp.'snd$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a323 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (and (= (|tptp.'fst$e'| A__questionmark_v0) (|tptp.'fst$e'| A__questionmark_v1)) (= (|tptp.'snd$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a324 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (=> (and (= (|tptp.'fst$f'| A__questionmark_v0) (|tptp.'fst$f'| A__questionmark_v1)) (= (|tptp.'snd$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a325 (forall ((A__questionmark_v0 |tptp.'A_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_a_iarray_iarray_prod$'|)) (=> (and (= (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'fst$a'| A__questionmark_v1)) (= (|tptp.'snd$e'| A__questionmark_v0) (|tptp.'snd$e'| A__questionmark_v1))) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a326 (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))
% 0.98/1.17 (assume a327 (= |tptp.'uua$'| |tptp.'uub$'|))
% 0.98/1.17 (assume a328 (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)))
% 0.98/1.17 (assume a329 (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)))
% 0.98/1.17 (assume a330 (= |tptp.'uue$'| |tptp.'uuf$'|))
% 0.98/1.17 (assume a331 (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)))
% 0.98/1.17 (assume a332 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int) (A__questionmark_v4 Int)) (=> (and (< A__questionmark_v0 A__questionmark_v1) (< A__questionmark_v2 A__questionmark_v1) (<= 0 A__questionmark_v3) (<= 0 A__questionmark_v4) (= (+ A__questionmark_v3 A__questionmark_v4) 1)) (< (+ (|tptp.'times$a'| A__questionmark_v3 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v4 A__questionmark_v2)) A__questionmark_v1))))
% 0.98/1.17 (assume a333 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v0)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v1)))))
% 0.98/1.17 (assume a334 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= 0 A__questionmark_v2)) (<= (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1)))))
% 0.98/1.17 (assume a335 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= 0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)) (or (and (<= 0 A__questionmark_v0) (<= 0 A__questionmark_v1)) (and (<= A__questionmark_v0 0) (<= A__questionmark_v1 0))))))
% 0.98/1.17 (assume a336 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v1) |tptp.'zero$'|)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v0)) |tptp.'zero$'|))))
% 0.98/1.17 (assume a337 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= 0 A__questionmark_v0) (<= A__questionmark_v1 0)) (<= (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v0) 0))))
% 0.98/1.17 (assume a338 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v0) |tptp.'zero$'|) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) |tptp.'zero$'|))))
% 0.98/1.17 (assume a339 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 0) (<= 0 A__questionmark_v1)) (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 0))))
% 0.98/1.17 (assume a340 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v1) |tptp.'zero$'|)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) |tptp.'zero$'|))))
% 0.98/1.17 (assume a341 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= 0 A__questionmark_v0) (<= A__questionmark_v1 0)) (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 0))))
% 0.98/1.17 (assume a342 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)))))
% 0.98/1.17 (assume a343 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= 0 A__questionmark_v0) (<= 0 A__questionmark_v1)) (<= 0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (assume a344 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (or (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v1) |tptp.'zero$'|)) (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v0) |tptp.'zero$'|) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v1))) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) |tptp.'zero$'|))))
% 0.98/1.17 (assume a345 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (or (and (<= 0 A__questionmark_v0) (<= A__questionmark_v1 0)) (and (<= A__questionmark_v0 0) (<= 0 A__questionmark_v1))) (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 0))))
% 0.98/1.17 (assume a346 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 0) (or (and (<= 0 A__questionmark_v0) (<= A__questionmark_v1 0)) (and (<= A__questionmark_v0 0) (<= 0 A__questionmark_v1))))))
% 0.98/1.17 (assume a347 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a348 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= 0 A__questionmark_v2)) (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a349 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 0)) (<= (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)))))
% 0.98/1.17 (assume a350 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v0)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v2) A__questionmark_v1)))))
% 0.98/1.17 (assume a351 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= 0 A__questionmark_v2)) (<= (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1)))))
% 0.98/1.17 (assume a352 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 0) (<= A__questionmark_v1 0)) (<= 0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (assume a353 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 0)) (<= (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v0)))))
% 0.98/1.17 (assume a354 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (or (and (<= 0 A__questionmark_v0) (<= 0 A__questionmark_v1)) (and (<= A__questionmark_v0 0) (<= A__questionmark_v1 0))) (<= 0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (assume a355 (forall ((A__questionmark_v0 Int)) (<= 0 (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v0))))
% 0.98/1.17 (assume a356 (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$j'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v3)))))
% 0.98/1.17 (assume a357 (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) (<= 0 A__questionmark_v0) (<= 0 A__questionmark_v2)) (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a358 (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$j'| (|tptp.'less_eq$a'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v2)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v3)))))
% 0.98/1.17 (assume a359 (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) (<= 0 A__questionmark_v1) (<= 0 A__questionmark_v2)) (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a360 (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))))))
% 0.98/1.17 (assume a361 (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))))))
% 0.98/1.17 (assume a362 (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))))
% 0.98/1.17 (assume a363 (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)))))
% 0.98/1.17 (assume a364 (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)))))
% 0.98/1.17 (assume a365 (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))))
% 0.98/1.17 (assume a366 (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)))))
% 0.98/1.17 (assume a367 (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))))
% 0.98/1.17 (assume a368 (not (<= 1 0)))
% 0.98/1.17 (assume a369 (<= 0 1))
% 0.98/1.17 (assume a370 (<= 0 1))
% 0.98/1.17 (assume a371 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$a'| (|tptp.'fst$b'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v0)))))
% 0.98/1.17 (assume a372 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$b'| (|tptp.'fst$c'| A__questionmark_v0) (|tptp.'snd$f'| A__questionmark_v0)))))
% 0.98/1.17 (assume a373 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$d'| (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v0)))))
% 0.98/1.17 (assume a374 (forall ((A__questionmark_v0 |tptp.'A_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$e'| (|tptp.'fst$'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v0)))))
% 0.98/1.17 (assume a375 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$'| (|tptp.'fst$e'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v0)))))
% 0.98/1.17 (assume a376 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$c'| (|tptp.'fst$f'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v0)))))
% 0.98/1.17 (assume a377 (forall ((A__questionmark_v0 |tptp.'A_a_iarray_iarray_prod$'|)) (= A__questionmark_v0 (|tptp.'pair$f'| (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'snd$e'| A__questionmark_v0)))))
% 0.98/1.17 (assume a378 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$a'| (|tptp.'fst$b'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v0))) false) false)))
% 0.98/1.17 (assume a379 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$b'| (|tptp.'fst$c'| A__questionmark_v0) (|tptp.'snd$f'| A__questionmark_v0))) false) false)))
% 0.98/1.17 (assume a380 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$d'| (|tptp.'fst$d'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v0))) false) false)))
% 0.98/1.17 (assume a381 (forall ((A__questionmark_v0 |tptp.'A_a_b_vec_c_vec_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$e'| (|tptp.'fst$'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v0))) false) false)))
% 0.98/1.17 (assume a382 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$'| (|tptp.'fst$e'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v0))) false) false)))
% 0.98/1.17 (assume a383 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$c'| (|tptp.'fst$f'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v0))) false) false)))
% 0.98/1.17 (assume a384 (forall ((A__questionmark_v0 |tptp.'A_a_iarray_iarray_prod$'|)) (=> (=> (= A__questionmark_v0 (|tptp.'pair$f'| (|tptp.'fst$a'| A__questionmark_v0) (|tptp.'snd$e'| A__questionmark_v0))) false) false)))
% 0.98/1.17 (assume a385 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (<= (+ (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v1)) 0) (and (= A__questionmark_v0 0) (= A__questionmark_v1 0)))))
% 0.98/1.17 (assume a386 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (<= 0 (+ (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v1)))))
% 0.98/1.17 (assume a387 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v0) |tptp.'one$a'|) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v1)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v1) A__questionmark_v0)) A__questionmark_v1))))
% 0.98/1.17 (assume a388 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 1) (<= 0 A__questionmark_v1)) (<= (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v0) A__questionmark_v1))))
% 0.98/1.17 (assume a389 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v0) |tptp.'one$a'|) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v1) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v1) |tptp.'one$a'|)) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1)) |tptp.'one$a'|))))
% 0.98/1.17 (assume a390 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= A__questionmark_v0 1) (<= 0 A__questionmark_v1) (<= A__questionmark_v1 1)) (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 1))))
% 0.98/1.17 (assume a391 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= 0 A__questionmark_v0) (<= 0 A__questionmark_v1) (<= A__questionmark_v1 1)) (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v0))))
% 0.98/1.17 (assume a392 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= 0 A__questionmark_v0) (<= 0 A__questionmark_v1) (<= A__questionmark_v1 1)) (<= (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v0) A__questionmark_v0))))
% 0.98/1.17 (assume a393 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int) (A__questionmark_v4 Int)) (=> (and (<= A__questionmark_v0 A__questionmark_v1) (<= A__questionmark_v2 A__questionmark_v1) (<= 0 A__questionmark_v3) (<= 0 A__questionmark_v4) (= (+ A__questionmark_v3 A__questionmark_v4) 1)) (<= (+ (|tptp.'times$a'| A__questionmark_v3 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v4 A__questionmark_v2)) A__questionmark_v1))))
% 0.98/1.17 (assume a394 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| (|tptp.'fst$d'| (|tptp.'snd$d'| A__questionmark_v0)) (|tptp.'column_iarray$'| A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'snd$d'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'fst$d'| (|tptp.'snd$d'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'snd$c'| (|tptp.'snd$d'| A__questionmark_v0)))))) (= (|tptp.'gauss_Jordan_column_k_det_P_iarrays$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$c'| (|tptp.'fst$f'| A__questionmark_v0) (|tptp.'pair$d'| (|tptp.'fst$d'| (|tptp.'snd$d'| A__questionmark_v0)) (|tptp.'snd$c'| (|tptp.'snd$d'| A__questionmark_v0)))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| (|tptp.'fst$d'| (|tptp.'snd$d'| A__questionmark_v0)) (|tptp.'column_iarray$'| A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'snd$d'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'fst$d'| (|tptp.'snd$d'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'snd$c'| (|tptp.'snd$d'| A__questionmark_v0))))))) (= (|tptp.'gauss_Jordan_column_k_det_P_iarrays$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'snd$c'| (|tptp.'snd$d'| A__questionmark_v0)) (|tptp.'fst$d'| (|tptp.'snd$d'| A__questionmark_v0)) A__questionmark_v1))) (|tptp.'fst$f'| A__questionmark_v0)) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| (|tptp.'fst$d'| (|tptp.'snd$d'| A__questionmark_v0))) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'snd$c'| (|tptp.'snd$d'| A__questionmark_v0)) (|tptp.'fst$d'| (|tptp.'snd$d'| A__questionmark_v0)) A__questionmark_v1)))))))))
% 0.98/1.17 (assume a395 (forall ((A__questionmark_v0 |tptp.'A_nat_a_c_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (and (=> (or (forall ((A__questionmark_v2 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| (|tptp.'fst$g'| (|tptp.'snd$g'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'vec_nth$b'| (|tptp.'vec_nth$c'| (|tptp.'snd$h'| (|tptp.'snd$g'| A__questionmark_v0)) A__questionmark_v2) (|tptp.'from_nat$'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$g'| (|tptp.'snd$g'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$a'| (|tptp.'snd$h'| (|tptp.'snd$g'| A__questionmark_v0)))))) (= (|tptp.'gauss_Jordan_column_k_det_P$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$g'| (|tptp.'fst$h'| A__questionmark_v0) (|tptp.'pair$h'| (|tptp.'fst$g'| (|tptp.'snd$g'| A__questionmark_v0)) (|tptp.'snd$h'| (|tptp.'snd$g'| A__questionmark_v0)))))) (=> (not (or (forall ((A__questionmark_v2 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| (|tptp.'fst$g'| (|tptp.'snd$g'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'vec_nth$b'| (|tptp.'vec_nth$c'| (|tptp.'snd$h'| (|tptp.'snd$g'| A__questionmark_v0)) A__questionmark_v2) (|tptp.'from_nat$'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$g'| (|tptp.'snd$g'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$a'| (|tptp.'snd$h'| (|tptp.'snd$g'| A__questionmark_v0))))))) (= (|tptp.'gauss_Jordan_column_k_det_P$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$g'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$i'| (|tptp.'gauss_Jordan_in_ij_det_P$a'| (|tptp.'snd$h'| (|tptp.'snd$g'| A__questionmark_v0)) (|tptp.'from_nat$'| (|tptp.'fst$g'| (|tptp.'snd$g'| A__questionmark_v0))) (|tptp.'from_nat$'| A__questionmark_v1)))) (|tptp.'fst$h'| A__questionmark_v0)) (|tptp.'pair$h'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| (|tptp.'fst$g'| (|tptp.'snd$g'| A__questionmark_v0))) 1)) (|tptp.'snd$i'| (|tptp.'gauss_Jordan_in_ij_det_P$a'| (|tptp.'snd$h'| (|tptp.'snd$g'| A__questionmark_v0)) (|tptp.'from_nat$'| (|tptp.'fst$g'| (|tptp.'snd$g'| A__questionmark_v0))) (|tptp.'from_nat$'| A__questionmark_v1))))))))))
% 0.98/1.17 (assume a396 (forall ((A__questionmark_v0 |tptp.'A_nat_a_c_vec_b_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (and (=> (or (forall ((A__questionmark_v2 |tptp.'B$'|)) (=> (|tptp.'less_eq$b'| (|tptp.'from_nat$a'| (|tptp.'fst$j'| (|tptp.'snd$j'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'vec_nth$b'| (|tptp.'vec_nth$d'| (|tptp.'snd$k'| (|tptp.'snd$j'| A__questionmark_v0)) A__questionmark_v2) (|tptp.'from_nat$'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$j'| (|tptp.'snd$j'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$b'| (|tptp.'snd$k'| (|tptp.'snd$j'| A__questionmark_v0)))))) (= (|tptp.'gauss_Jordan_column_k_det_P$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$i'| (|tptp.'fst$k'| A__questionmark_v0) (|tptp.'pair$j'| (|tptp.'fst$j'| (|tptp.'snd$j'| A__questionmark_v0)) (|tptp.'snd$k'| (|tptp.'snd$j'| A__questionmark_v0)))))) (=> (not (or (forall ((A__questionmark_v2 |tptp.'B$'|)) (=> (|tptp.'less_eq$b'| (|tptp.'from_nat$a'| (|tptp.'fst$j'| (|tptp.'snd$j'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'vec_nth$b'| (|tptp.'vec_nth$d'| (|tptp.'snd$k'| (|tptp.'snd$j'| A__questionmark_v0)) A__questionmark_v2) (|tptp.'from_nat$'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$j'| (|tptp.'snd$j'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$b'| (|tptp.'snd$k'| (|tptp.'snd$j'| A__questionmark_v0))))))) (= (|tptp.'gauss_Jordan_column_k_det_P$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$i'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$l'| (|tptp.'gauss_Jordan_in_ij_det_P$b'| (|tptp.'snd$k'| (|tptp.'snd$j'| A__questionmark_v0)) (|tptp.'from_nat$a'| (|tptp.'fst$j'| (|tptp.'snd$j'| A__questionmark_v0))) (|tptp.'from_nat$'| A__questionmark_v1)))) (|tptp.'fst$k'| A__questionmark_v0)) (|tptp.'pair$j'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| (|tptp.'fst$j'| (|tptp.'snd$j'| A__questionmark_v0))) 1)) (|tptp.'snd$l'| (|tptp.'gauss_Jordan_in_ij_det_P$b'| (|tptp.'snd$k'| (|tptp.'snd$j'| A__questionmark_v0)) (|tptp.'from_nat$a'| (|tptp.'fst$j'| (|tptp.'snd$j'| A__questionmark_v0))) (|tptp.'from_nat$'| A__questionmark_v1))))))))))
% 0.98/1.17 (assume a397 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_b_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (and (=> (or (forall ((A__questionmark_v2 |tptp.'B$'|)) (=> (|tptp.'less_eq$b'| (|tptp.'from_nat$a'| (|tptp.'fst$m'| (|tptp.'snd$m'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'vec_nth$e'| (|tptp.'snd$n'| (|tptp.'snd$m'| A__questionmark_v0)) A__questionmark_v2)) (|tptp.'from_nat$a'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$m'| (|tptp.'snd$m'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$c'| (|tptp.'snd$n'| (|tptp.'snd$m'| A__questionmark_v0)))))) (= (|tptp.'gauss_Jordan_column_k_det_P$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$k'| (|tptp.'fst$n'| A__questionmark_v0) (|tptp.'pair$l'| (|tptp.'fst$m'| (|tptp.'snd$m'| A__questionmark_v0)) (|tptp.'snd$n'| (|tptp.'snd$m'| A__questionmark_v0)))))) (=> (not (or (forall ((A__questionmark_v2 |tptp.'B$'|)) (=> (|tptp.'less_eq$b'| (|tptp.'from_nat$a'| (|tptp.'fst$m'| (|tptp.'snd$m'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'vec_nth$e'| (|tptp.'snd$n'| (|tptp.'snd$m'| A__questionmark_v0)) A__questionmark_v2)) (|tptp.'from_nat$a'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$m'| (|tptp.'snd$m'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$c'| (|tptp.'snd$n'| (|tptp.'snd$m'| A__questionmark_v0))))))) (= (|tptp.'gauss_Jordan_column_k_det_P$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$k'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$o'| (|tptp.'gauss_Jordan_in_ij_det_P$c'| (|tptp.'snd$n'| (|tptp.'snd$m'| A__questionmark_v0)) (|tptp.'from_nat$a'| (|tptp.'fst$m'| (|tptp.'snd$m'| A__questionmark_v0))) (|tptp.'from_nat$a'| A__questionmark_v1)))) (|tptp.'fst$n'| A__questionmark_v0)) (|tptp.'pair$l'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| (|tptp.'fst$m'| (|tptp.'snd$m'| A__questionmark_v0))) 1)) (|tptp.'snd$o'| (|tptp.'gauss_Jordan_in_ij_det_P$c'| (|tptp.'snd$n'| (|tptp.'snd$m'| A__questionmark_v0)) (|tptp.'from_nat$a'| (|tptp.'fst$m'| (|tptp.'snd$m'| A__questionmark_v0))) (|tptp.'from_nat$a'| A__questionmark_v1))))))))))
% 0.98/1.17 (assume a398 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (and (=> (or (forall ((A__questionmark_v2 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| (|tptp.'fst$b'| (|tptp.'snd$a'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| (|tptp.'snd$'| (|tptp.'snd$a'| A__questionmark_v0))) A__questionmark_v2)) (|tptp.'from_nat$a'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$a'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$'| (|tptp.'snd$'| (|tptp.'snd$a'| A__questionmark_v0)))))) (= (|tptp.'gauss_Jordan_column_k_det_P$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| (|tptp.'fst$e'| A__questionmark_v0) (|tptp.'pair$a'| (|tptp.'fst$b'| (|tptp.'snd$a'| A__questionmark_v0)) (|tptp.'snd$'| (|tptp.'snd$a'| A__questionmark_v0)))))) (=> (not (or (forall ((A__questionmark_v2 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| (|tptp.'fst$b'| (|tptp.'snd$a'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| (|tptp.'snd$'| (|tptp.'snd$a'| A__questionmark_v0))) A__questionmark_v2)) (|tptp.'from_nat$a'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$a'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$'| (|tptp.'snd$'| (|tptp.'snd$a'| A__questionmark_v0))))))) (= (|tptp.'gauss_Jordan_column_k_det_P$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| (|tptp.'snd$'| (|tptp.'snd$a'| A__questionmark_v0)) (|tptp.'from_nat$'| (|tptp.'fst$b'| (|tptp.'snd$a'| A__questionmark_v0))) (|tptp.'from_nat$a'| A__questionmark_v1)))) (|tptp.'fst$e'| A__questionmark_v0)) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$a'| A__questionmark_v0))) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| (|tptp.'snd$'| (|tptp.'snd$a'| A__questionmark_v0)) (|tptp.'from_nat$'| (|tptp.'fst$b'| (|tptp.'snd$a'| A__questionmark_v0))) (|tptp.'from_nat$a'| A__questionmark_v1))))))))))
% 0.98/1.17 (assume a399 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'from_nat$'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| A__questionmark_v0) 1))) (|tptp.'plus$b'| (|tptp.'from_nat$'| A__questionmark_v0) |tptp.'one$b'|))))
% 0.98/1.17 (assume a400 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'from_nat$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| A__questionmark_v0) 1))) (|tptp.'plus$c'| (|tptp.'from_nat$a'| A__questionmark_v0) |tptp.'one$c'|))))
% 0.98/1.17 (assume a401 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (< (|tptp.'of_nat$'| A__questionmark_v0) 1) (= (|tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.98/1.17 (assume a402 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (<= (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))) (<= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2)))))
% 0.98/1.17 (assume a403 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< 0 (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1))) (or (< 0 (|tptp.'of_nat$'| A__questionmark_v0)) (< 0 (|tptp.'of_nat$'| A__questionmark_v1))))))
% 0.98/1.17 (assume a404 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (< (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))) (< (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2)))))
% 0.98/1.17 (assume a405 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (<= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v1))) (=> (< 0 (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a406 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (<= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))) (=> (< 0 (|tptp.'of_nat$'| A__questionmark_v0)) (<= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a407 (forall ((A__questionmark_v0 |tptp.'A_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'A_a_b_vec_c_vec_prod$'|)) (= (|tptp.'fst$'| (|tptp.'plus$d'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fst$'| A__questionmark_v0)) (|tptp.'fst$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a408 (forall ((A__questionmark_v0 |tptp.'A_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_a_iarray_iarray_prod$'|)) (= (|tptp.'fst$a'| (|tptp.'plus$e'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fst$a'| A__questionmark_v0)) (|tptp.'fst$a'| A__questionmark_v1)))))
% 0.98/1.17 (assume a409 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'snd$c'| (|tptp.'plus$f'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$g'| (|tptp.'snd$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v1)))))
% 0.98/1.17 (assume a410 (forall ((A__questionmark_v0 |tptp.'A_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'A_a_b_vec_c_vec_prod$'|)) (= (|tptp.'snd$b'| (|tptp.'plus$d'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$h'| (|tptp.'snd$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v1)))))
% 0.98/1.17 (assume a411 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (= (|tptp.'snd$a'| (|tptp.'plus$i'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$j'| (|tptp.'snd$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v1)))))
% 0.98/1.17 (assume a412 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (= (|tptp.'snd$d'| (|tptp.'plus$k'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$f'| (|tptp.'snd$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v1)))))
% 0.98/1.17 (assume a413 (forall ((A__questionmark_v0 |tptp.'A_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_a_iarray_iarray_prod$'|)) (= (|tptp.'snd$e'| (|tptp.'plus$e'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$g'| (|tptp.'snd$e'| A__questionmark_v0) (|tptp.'snd$e'| A__questionmark_v1)))))
% 0.98/1.17 (assume a414 (= (|tptp.'snd$b'| |tptp.'zero$b'|) |tptp.'zero$c'|))
% 0.98/1.17 (assume a415 (= (|tptp.'snd$a'| |tptp.'zero$d'|) |tptp.'zero$e'|))
% 0.98/1.17 (assume a416 (= (|tptp.'fst$'| |tptp.'zero$b'|) |tptp.'zero$a'|))
% 0.98/1.17 (assume a417 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (< (|tptp.'of_nat$'| A__questionmark_v0) 0) false)))
% 0.98/1.17 (assume a418 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (not (= (|tptp.'of_nat$'| A__questionmark_v0) 0)) (< 0 (|tptp.'of_nat$'| A__questionmark_v0)))))
% 0.98/1.17 (assume a419 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (not (= (|tptp.'of_nat$'| A__questionmark_v0) 0)) (< 0 (|tptp.'of_nat$'| A__questionmark_v0)))))
% 0.98/1.17 (assume a420 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= 0 (|tptp.'of_nat$'| A__questionmark_v0))))
% 0.98/1.17 (assume a421 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= 0 (|tptp.'of_nat$'| A__questionmark_v0))))
% 0.98/1.17 (assume a422 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) 0) (and (= (|tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'of_nat$'| A__questionmark_v1) 0)))))
% 0.98/1.17 (assume a423 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (+ (|tptp.'of_nat$'| A__questionmark_v0) 0) (|tptp.'of_nat$'| A__questionmark_v0))))
% 0.98/1.17 (assume a424 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) 0) (or (= (|tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'of_nat$'| A__questionmark_v1) 0)))))
% 0.98/1.17 (assume a425 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (* (|tptp.'of_nat$'| A__questionmark_v0) 0) 0)))
% 0.98/1.17 (assume a426 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))) (or (= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2)) (= (|tptp.'of_nat$'| A__questionmark_v0) 0)))))
% 0.98/1.17 (assume a427 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v1))) (or (= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (= (|tptp.'of_nat$'| A__questionmark_v1) 0)))))
% 0.98/1.17 (assume a428 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= 1 (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1))) (and (= (|tptp.'of_nat$'| A__questionmark_v0) 1) (= (|tptp.'of_nat$'| A__questionmark_v1) 1)))))
% 0.98/1.17 (assume a429 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) 1) (and (= (|tptp.'of_nat$'| A__questionmark_v0) 1) (= (|tptp.'of_nat$'| A__questionmark_v1) 1)))))
% 0.98/1.17 (assume a430 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (< (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))) (and (< 0 (|tptp.'of_nat$'| A__questionmark_v0)) (< (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a431 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< 0 (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1))) (and (< 0 (|tptp.'of_nat$'| A__questionmark_v0)) (< 0 (|tptp.'of_nat$'| A__questionmark_v1))))))
% 0.98/1.17 (assume a432 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (< (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v1))) (and (< 0 (|tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a433 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'plus$i'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2) (|tptp.'plus$j'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a434 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'plus$j'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$a'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$a'| (|tptp.'fun_app$a'| (|tptp.'plus$a'| A__questionmark_v0) A__questionmark_v2) (|tptp.'plus$h'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a435 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A_iarray$'|)) (= (|tptp.'plus$l'| (|tptp.'pair$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$b'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$b'| (|tptp.'fun_app$a'| (|tptp.'plus$a'| A__questionmark_v0) A__questionmark_v2) (|tptp.'plus$m'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a436 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'plus$k'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$c'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v2) (|tptp.'plus$f'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a437 (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$f'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$d'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$d'| (|tptp.'fun_app$a'| (|tptp.'plus$a'| A__questionmark_v0) A__questionmark_v2) (|tptp.'plus$g'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a438 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int) (A__questionmark_v3 Int)) (= (|tptp.'plus$n'| (|tptp.'pair$m'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$m'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'pair$m'| (+ A__questionmark_v0 A__questionmark_v2) (+ A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a439 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (and (=> (= (|tptp.'of_nat$'| A__questionmark_v0) 0) false) (=> (not (= (|tptp.'of_nat$'| A__questionmark_v0) 0)) false)) false)))
% 0.98/1.17 (assume a440 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (* 0 (|tptp.'of_nat$'| A__questionmark_v0)) 0)))
% 0.98/1.17 (assume a441 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))) (or (= (|tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a442 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (< 0 (|tptp.'of_nat$'| A__questionmark_v0)) (= (< (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))) (< (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a443 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (< 0 (|tptp.'of_nat$'| A__questionmark_v0)) (= (= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))) (= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a444 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (not (= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1))) (=> (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) false) (=> (< (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v0)) false)) false)))
% 0.98/1.17 (assume a445 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| A__questionmark_v0 (|tptp.'nat$'| 0)) (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (< 0 (|tptp.'of_nat$'| A__questionmark_v2)) (not (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v2))) (exists ((A__questionmark_v3 |tptp.'Nat$'|)) (and (< (|tptp.'of_nat$'| A__questionmark_v3) (|tptp.'of_nat$'| A__questionmark_v2)) (not (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v3))))))) (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a446 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (not (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v2)) (exists ((A__questionmark_v3 |tptp.'Nat$'|)) (and (< (|tptp.'of_nat$'| A__questionmark_v3) (|tptp.'of_nat$'| A__questionmark_v2)) (not (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v3)))))) (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a447 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v2 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v3) (|tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v3))) (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v2))) (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a448 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (< 0 (|tptp.'of_nat$'| A__questionmark_v2))) (< (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v0)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v1))))))
% 0.98/1.17 (assume a449 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (< 0 (|tptp.'of_nat$'| A__questionmark_v2))) (< (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a450 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v0)) false)))
% 0.98/1.17 (assume a451 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (not (= (|tptp.'of_nat$'| A__questionmark_v1) 0)))))
% 0.98/1.17 (assume a452 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (not (= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1))))))
% 0.98/1.17 (assume a453 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (not (= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v0))))))
% 0.98/1.17 (assume a454 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v0)))))
% 0.98/1.17 (assume a455 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (not (= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1))) (or (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v0))))))
% 0.98/1.17 (assume a456 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v0) 0) false)))
% 0.98/1.17 (assume a457 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (< (|tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.98/1.17 (assume a458 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (not (< 0 (|tptp.'of_nat$'| A__questionmark_v0))) (= (|tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.98/1.17 (assume a459 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (=> (= (|tptp.'of_nat$'| A__questionmark_v0) 0) false) (< 0 (|tptp.'of_nat$'| A__questionmark_v0)))))
% 0.98/1.17 (assume a460 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (not (< (|tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.98/1.17 (assume a461 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v1) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v3) (<= (|tptp.'of_nat$'| A__questionmark_v3) (|tptp.'of_nat$'| A__questionmark_v2))))) (exists ((A__questionmark_v3 |tptp.'Nat$'|)) (and (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v3) (forall ((A__questionmark_v4 |tptp.'Nat$'|)) (=> (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v4) (<= (|tptp.'of_nat$'| A__questionmark_v4) (|tptp.'of_nat$'| A__questionmark_v3)))))))))
% 0.98/1.17 (assume a462 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (or (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v0)))))
% 0.98/1.17 (assume a463 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v0)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v1))))))
% 0.98/1.17 (assume a464 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a465 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v3))) (<= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v3))))))
% 0.98/1.17 (assume a466 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v0))) (= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a467 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v0)))))
% 0.98/1.17 (assume a468 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a469 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))) (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)))))
% 0.98/1.17 (assume a470 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v0))))
% 0.98/1.17 (assume a471 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v0))))))
% 0.98/1.17 (assume a472 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (<= (|tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.98/1.17 (assume a473 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (=> (<= (|tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.98/1.17 (assume a474 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (<= (|tptp.'of_nat$'| A__questionmark_v0) 0) (= (|tptp.'of_nat$'| A__questionmark_v0) 0))))
% 0.98/1.17 (assume a475 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (<= 0 (|tptp.'of_nat$'| A__questionmark_v0)) true)))
% 0.98/1.17 (assume a476 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (+ 0 (|tptp.'of_nat$'| A__questionmark_v0)) (|tptp.'of_nat$'| A__questionmark_v0))))
% 0.98/1.17 (assume a477 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (= (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'of_nat$'| A__questionmark_v0)) (= (|tptp.'of_nat$'| A__questionmark_v1) 0))))
% 0.98/1.17 (assume a478 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'times$a'| (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'of_nat$'| A__questionmark_v2)) (+ (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a479 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))) (+ (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a480 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (= (+ (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (+ (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'of_nat$'| A__questionmark_v3))) (+ (|tptp.'times$a'| (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'of_nat$'| A__questionmark_v3)))))
% 0.98/1.17 (assume a481 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (* 1 (|tptp.'of_nat$'| A__questionmark_v0)) (|tptp.'of_nat$'| A__questionmark_v0))))
% 0.98/1.17 (assume a482 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (* (|tptp.'of_nat$'| A__questionmark_v0) 1) (|tptp.'of_nat$'| A__questionmark_v0))))
% 0.98/1.17 (assume a483 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1))) (or (= (|tptp.'of_nat$'| A__questionmark_v1) 1) (= (|tptp.'of_nat$'| A__questionmark_v0) 0)))))
% 0.98/1.17 (assume a484 (forall ((A__questionmark_v0 |tptp.'C$'|)) (|tptp.'less_eq$'| |tptp.'zero$f'| A__questionmark_v0)))
% 0.98/1.17 (assume a485 (= |tptp.'zero$e'| (|tptp.'pair$a'| |tptp.'zero$'| |tptp.'zero$c'|)))
% 0.98/1.17 (assume a486 (= |tptp.'zero$d'| (|tptp.'pair$'| |tptp.'zero$a'| |tptp.'zero$e'|)))
% 0.98/1.17 (assume a487 (= |tptp.'zero$g'| (|tptp.'pair$n'| |tptp.'zero$a'| |tptp.'zero$a'|)))
% 0.98/1.17 (assume a488 (= |tptp.'zero$h'| (|tptp.'pair$o'| |tptp.'zero$a'| 0)))
% 0.98/1.17 (assume a489 (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 |tptp.'zero$a'|)))
% 0.98/1.17 (assume a490 (= |tptp.'zero$j'| (|tptp.'pair$m'| 0 0)))
% 0.98/1.17 (assume a491 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (< 0 (|tptp.'of_nat$'| A__questionmark_v0)) (= (<= (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'times$a'| (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2))) (<= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a492 (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$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v3) (|tptp.'of_nat$'| A__questionmark_v4)) (< (|tptp.'of_nat$'| (|tptp.'fun_app$a'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'of_nat$'| (|tptp.'fun_app$a'| A__questionmark_v0 A__questionmark_v4))))) (<= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))) (<= (|tptp.'of_nat$'| (|tptp.'fun_app$a'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'of_nat$'| (|tptp.'fun_app$a'| A__questionmark_v0 A__questionmark_v2))))))
% 0.98/1.17 (assume a493 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (not (= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)))) (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a494 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (or (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1))) (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a495 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (or (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1))))))
% 0.98/1.17 (assume a496 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a497 (forall ((A__questionmark_v0 |tptp.'Nat_bool_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v1) (not (|tptp.'fun_app$j'| A__questionmark_v0 (|tptp.'nat$'| 0)))) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (<= (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v1)) (forall ((A__questionmark_v3 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v3) (|tptp.'of_nat$'| A__questionmark_v2)) (not (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v3)))) (|tptp.'fun_app$j'| A__questionmark_v0 A__questionmark_v2))))))
% 0.98/1.17 (assume a498 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (and (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (not (= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)))))))
% 0.98/1.17 (assume a499 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'of_nat$'| A__questionmark_v2)) (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)))))
% 0.98/1.17 (assume a500 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v3))) (< (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (+ (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v3))))))
% 0.98/1.17 (assume a501 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (not (< (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'of_nat$'| A__questionmark_v0)))))
% 0.98/1.17 (assume a502 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (not (< (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'of_nat$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a503 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (< (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (+ (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a504 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a505 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (< (|tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v1))))))
% 0.98/1.17 (assume a506 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (= (+ (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v1)) (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v3)))) (< (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v3)))))
% 0.98/1.17 (assume a507 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (and (< 0 (|tptp.'of_nat$'| A__questionmark_v2)) (= (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'of_nat$'| A__questionmark_v1)))))))
% 0.98/1.17 (assume a508 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (and (<= (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'of_nat$'| A__questionmark_v2)) (=> (and (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (<= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))) false)) false)))
% 0.98/1.17 (assume a509 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (<= (|tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a510 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (<= (|tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v0)))))
% 0.98/1.17 (assume a511 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'of_nat$'| A__questionmark_v2)) (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)))))
% 0.98/1.17 (assume a512 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (|tptp.'of_nat$'| A__questionmark_v2)) (<= (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2)))))
% 0.98/1.17 (assume a513 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)))))))
% 0.98/1.17 (assume a514 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat$'|)) (=> (and (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v3))) (<= (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (+ (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v3))))))
% 0.98/1.17 (assume a515 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)) (+ (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a516 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2))))))
% 0.98/1.17 (assume a517 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (<= (|tptp.'of_nat$'| A__questionmark_v0) (+ (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| A__questionmark_v1))))))
% 0.98/1.17 (assume a518 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v1)) (exists ((A__questionmark_v2 |tptp.'Nat$'|)) (= (|tptp.'of_nat$'| A__questionmark_v1) (+ (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| A__questionmark_v2)))))))
% 0.98/1.17 (assume a519 (= (|tptp.'from_nat$'| (|tptp.'nat$'| 0)) |tptp.'zero$f'|))
% 0.98/1.17 (assume a520 (= (|tptp.'from_nat$a'| (|tptp.'nat$'| 0)) |tptp.'zero$k'|))
% 0.98/1.17 (assume a521 (forall ((A__questionmark_v0 |tptp.'Nat_nat_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'Nat$'|)) (=> (forall ((A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'Nat$'|)) (=> (< (|tptp.'of_nat$'| A__questionmark_v3) (|tptp.'of_nat$'| A__questionmark_v4)) (< (|tptp.'of_nat$'| (|tptp.'fun_app$a'| A__questionmark_v0 A__questionmark_v3)) (|tptp.'of_nat$'| (|tptp.'fun_app$a'| A__questionmark_v0 A__questionmark_v4))))) (<= (+ (|tptp.'of_nat$'| (|tptp.'fun_app$a'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'of_nat$'| A__questionmark_v2)) (|tptp.'of_nat$'| (|tptp.'fun_app$a'| A__questionmark_v0 (|tptp.'nat$'| (+ (|tptp.'of_nat$'| A__questionmark_v1) (|tptp.'of_nat$'| A__questionmark_v2)))))))))
% 0.98/1.17 (assume a522 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v1))) (< (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| (|tptp.'ncols$'| A__questionmark_v1)))) (= (|tptp.'fst$e'| (|tptp.'gauss_Jordan_column_k_det_P$c'| (|tptp.'pair$'| A__questionmark_v3 (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2)) (|tptp.'fst$f'| (|tptp.'gauss_Jordan_column_k_det_P_iarrays$'| (|tptp.'pair$c'| A__questionmark_v3 (|tptp.'pair$d'| A__questionmark_v0 (|tptp.'matrix_to_iarray$'| A__questionmark_v1))) A__questionmark_v2))))))
% 0.98/1.17 (assume a523 (forall ((A__questionmark_v0 |tptp.'C$'|) (A__questionmark_v1 |tptp.'C$'|)) (=> (|tptp.'less$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'less_eq$'| (|tptp.'plus$b'| A__questionmark_v0 |tptp.'one$b'|) A__questionmark_v1))))
% 0.98/1.17 (assume a524 (forall ((A__questionmark_v0 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'plus$j'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$a'| (|tptp.'fun_app$a'| (|tptp.'plus$a'| (|tptp.'fst$b'| A__questionmark_v0)) (|tptp.'fst$b'| A__questionmark_v1)) (|tptp.'plus$h'| (|tptp.'snd$'| A__questionmark_v0) (|tptp.'snd$'| A__questionmark_v1))))))
% 0.98/1.17 (assume a525 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_prod$'|)) (= (|tptp.'plus$l'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$b'| (|tptp.'fun_app$a'| (|tptp.'plus$a'| (|tptp.'fst$c'| A__questionmark_v0)) (|tptp.'fst$c'| A__questionmark_v1)) (|tptp.'plus$m'| (|tptp.'snd$f'| A__questionmark_v0) (|tptp.'snd$f'| A__questionmark_v1))))))
% 0.98/1.17 (assume a526 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'plus$f'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$d'| (|tptp.'fun_app$a'| (|tptp.'plus$a'| (|tptp.'fst$d'| A__questionmark_v0)) (|tptp.'fst$d'| A__questionmark_v1)) (|tptp.'plus$g'| (|tptp.'snd$c'| A__questionmark_v0) (|tptp.'snd$c'| A__questionmark_v1))))))
% 0.98/1.17 (assume a527 (forall ((A__questionmark_v0 |tptp.'A_a_b_vec_c_vec_prod$'|) (A__questionmark_v1 |tptp.'A_a_b_vec_c_vec_prod$'|)) (= (|tptp.'plus$d'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$e'| (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fst$'| A__questionmark_v0)) (|tptp.'fst$'| A__questionmark_v1)) (|tptp.'plus$h'| (|tptp.'snd$b'| A__questionmark_v0) (|tptp.'snd$b'| A__questionmark_v1))))))
% 0.98/1.17 (assume a528 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (= (|tptp.'plus$i'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fst$e'| A__questionmark_v0)) (|tptp.'fst$e'| A__questionmark_v1)) (|tptp.'plus$j'| (|tptp.'snd$a'| A__questionmark_v0) (|tptp.'snd$a'| A__questionmark_v1))))))
% 0.98/1.17 (assume a529 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|) (A__questionmark_v1 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (= (|tptp.'plus$k'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fst$f'| A__questionmark_v0)) (|tptp.'fst$f'| A__questionmark_v1)) (|tptp.'plus$f'| (|tptp.'snd$d'| A__questionmark_v0) (|tptp.'snd$d'| A__questionmark_v1))))))
% 0.98/1.17 (assume a530 (forall ((A__questionmark_v0 |tptp.'A_a_iarray_iarray_prod$'|) (A__questionmark_v1 |tptp.'A_a_iarray_iarray_prod$'|)) (= (|tptp.'plus$e'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$f'| (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fst$a'| A__questionmark_v0)) (|tptp.'fst$a'| A__questionmark_v1)) (|tptp.'plus$g'| (|tptp.'snd$e'| A__questionmark_v0) (|tptp.'snd$e'| A__questionmark_v1))))))
% 0.98/1.17 (assume a531 (forall ((A__questionmark_v0 |tptp.'Int_int_prod$'|) (A__questionmark_v1 |tptp.'Int_int_prod$'|)) (= (|tptp.'plus$n'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$m'| (+ (|tptp.'fst$p'| A__questionmark_v0) (|tptp.'fst$p'| A__questionmark_v1)) (+ (|tptp.'snd$p'| A__questionmark_v0) (|tptp.'snd$p'| A__questionmark_v1))))))
% 0.98/1.17 (assume a532 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'A$'|)) (=> (and (<= (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v1))) (< (|tptp.'of_nat$'| A__questionmark_v2) (|tptp.'of_nat$'| (|tptp.'ncols$'| A__questionmark_v1)))) (= (|tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$a'| (|tptp.'gauss_Jordan_column_k_det_P$c'| (|tptp.'pair$'| A__questionmark_v3 (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2)))) (|tptp.'of_nat$'| (|tptp.'fst$d'| (|tptp.'snd$d'| (|tptp.'gauss_Jordan_column_k_det_P_iarrays$'| (|tptp.'pair$c'| A__questionmark_v3 (|tptp.'pair$d'| A__questionmark_v0 (|tptp.'matrix_to_iarray$'| A__questionmark_v1))) A__questionmark_v2))))))))
% 0.98/1.17 (assume a533 (forall ((A__questionmark_v0 |tptp.'B$'|)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| |tptp.'one$d'|) A__questionmark_v0) |tptp.'one$'|)))
% 0.98/1.17 (assume a534 (forall ((A__questionmark_v0 |tptp.'C$'|)) (= (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'one$e'|) A__questionmark_v0) |tptp.'one$d'|)))
% 0.98/1.17 (assume a535 (forall ((A__questionmark_v0 |tptp.'A_b_vec$'|) (A__questionmark_v1 |tptp.'A_b_vec$'|) (A__questionmark_v2 |tptp.'B$'|)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'plus$o'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a536 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'C$'|)) (= (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| (|tptp.'plus$h'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (|tptp.'plus$o'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v0) A__questionmark_v2) (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a537 (forall ((A__questionmark_v0 |tptp.'A_b_vec$'|) (A__questionmark_v1 |tptp.'A_b_vec$'|) (A__questionmark_v2 |tptp.'B$'|)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'times$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a538 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'C$'|)) (= (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| (|tptp.'times$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) (|tptp.'times$c'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v0) A__questionmark_v2) (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a539 (forall ((A__questionmark_v0 |tptp.'B$'|)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| |tptp.'zero$l'|) A__questionmark_v0) |tptp.'zero$a'|)))
% 0.98/1.17 (assume a540 (forall ((A__questionmark_v0 |tptp.'C$'|)) (= (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'zero$c'|) A__questionmark_v0) |tptp.'zero$l'|)))
% 0.98/1.17 (assume a541 (forall ((A__questionmark_v0 tptp.tlbool) (A__questionmark_v1 |tptp.'A_b_vec$'|) (A__questionmark_v2 |tptp.'A_b_vec$'|) (A__questionmark_v3 |tptp.'B$'|)) (and (=> (= A__questionmark_v0 tptp.tltrue) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v1) A__questionmark_v3) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v1) A__questionmark_v3))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v1) A__questionmark_v3) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v2) A__questionmark_v3))))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v1) A__questionmark_v3))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v2) A__questionmark_v3))))))))
% 0.98/1.17 (assume a542 (forall ((A__questionmark_v0 tptp.tlbool) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v3 |tptp.'C$'|)) (and (=> (= A__questionmark_v0 tptp.tltrue) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v1) A__questionmark_v3) (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v1) A__questionmark_v3))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v1) A__questionmark_v3) (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v2) A__questionmark_v3))))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v1) A__questionmark_v3))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v2) A__questionmark_v3) (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v2) A__questionmark_v3))))))))
% 0.98/1.17 (assume a543 (forall ((A__questionmark_v0 |tptp.'A_b_vec$'|) (A__questionmark_v1 |tptp.'A_b_vec$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'B$'|)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v0) A__questionmark_v2) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v1) A__questionmark_v2))))))
% 0.98/1.17 (assume a544 (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) (forall ((A__questionmark_v2 |tptp.'C$'|)) (= (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v0) A__questionmark_v2) (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v1) A__questionmark_v2))))))
% 0.98/1.17 (assume a545 (forall ((A__questionmark_v0 |tptp.'A_b_vec$'|) (A__questionmark_v1 |tptp.'A_b_vec$'|)) (= (= (|tptp.'vec_nth$'| A__questionmark_v0) (|tptp.'vec_nth$'| A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a546 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (= (|tptp.'vec_nth$a'| A__questionmark_v0) (|tptp.'vec_nth$a'| A__questionmark_v1)) (= A__questionmark_v0 A__questionmark_v1))))
% 0.98/1.17 (assume a547 (forall ((A__questionmark_v0 |tptp.'A_a_fun$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'C$'|) (A__questionmark_v3 |tptp.'B$'|)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| (|tptp.'map_matrix$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2)) A__questionmark_v3) (|tptp.'fun_app$b'| A__questionmark_v0 (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v1) A__questionmark_v2)) A__questionmark_v3)))))
% 0.98/1.17 (assume a548 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| |tptp.'one$'|) A__questionmark_v0) A__questionmark_v0)))
% 0.98/1.17 (assume a549 (forall ((A__questionmark_v0 Int)) (= (= (+ A__questionmark_v0 A__questionmark_v0) 0) (= A__questionmark_v0 0))))
% 0.98/1.17 (assume a550 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) |tptp.'zero$a'|) (or (= A__questionmark_v0 |tptp.'zero$a'|) (= A__questionmark_v1 |tptp.'zero$a'|)))))
% 0.98/1.17 (assume a551 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| |tptp.'zero$a'|) A__questionmark_v0) |tptp.'zero$a'|)))
% 0.98/1.17 (assume a552 (forall ((A__questionmark_v0 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) |tptp.'zero$a'|) |tptp.'zero$a'|)))
% 0.98/1.17 (assume a553 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)) (or (= A__questionmark_v1 A__questionmark_v2) (= A__questionmark_v0 |tptp.'zero$a'|)))))
% 0.98/1.17 (assume a554 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v2) A__questionmark_v1)) (or (= A__questionmark_v0 A__questionmark_v2) (= A__questionmark_v1 |tptp.'zero$a'|)))))
% 0.98/1.17 (assume a555 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2))))
% 0.98/1.17 (assume a556 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)))))
% 0.98/1.17 (assume a557 (forall ((A__questionmark_v0 |tptp.'B_a_bool_fun_fun$'|)) (= (forall ((A__questionmark_v1 |tptp.'B$'|)) (exists ((A__questionmark_v2 |tptp.'A$'|)) (|tptp.'fun_app$k'| (|tptp.'fun_app$l'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))) (exists ((A__questionmark_v1 |tptp.'A_b_vec$'|)) (forall ((A__questionmark_v2 |tptp.'B$'|)) (|tptp.'fun_app$k'| (|tptp.'fun_app$l'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| A__questionmark_v1) A__questionmark_v2)))))))
% 0.98/1.17 (assume a558 (forall ((A__questionmark_v0 |tptp.'C_a_b_vec_bool_fun_fun$'|)) (= (forall ((A__questionmark_v1 |tptp.'C$'|)) (exists ((A__questionmark_v2 |tptp.'A_b_vec$'|)) (|tptp.'fun_app$m'| (|tptp.'fun_app$n'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2))) (exists ((A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (forall ((A__questionmark_v2 |tptp.'C$'|)) (|tptp.'fun_app$m'| (|tptp.'fun_app$n'| A__questionmark_v0 A__questionmark_v2) (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v1) A__questionmark_v2)))))))
% 0.98/1.17 (assume a559 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (=> (and (not (= A__questionmark_v0 |tptp.'zero$a'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2))) (= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a560 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (=> (and (not (= A__questionmark_v0 |tptp.'zero$a'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v2) A__questionmark_v0))) (= A__questionmark_v1 A__questionmark_v2))))
% 0.98/1.17 (assume a561 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v0) A__questionmark_v1)) A__questionmark_v2) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v1) A__questionmark_v2)))))
% 0.98/1.17 (assume a562 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A$'|)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) (|tptp.'fun_app$b'| (|tptp.'plus$'| A__questionmark_v1) A__questionmark_v2)) (|tptp.'fun_app$b'| (|tptp.'plus$'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v1)) (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2)))))
% 0.98/1.17 (assume a563 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (< A__questionmark_v0 A__questionmark_v1) (<= (+ A__questionmark_v0 1) A__questionmark_v1))))
% 0.98/1.17 (assume a564 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (and (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| |tptp.'zero$'|) A__questionmark_v0) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v0) |tptp.'one$a'|) (|tptp.'fun_app$j'| (|tptp.'less_eq$a'| A__questionmark_v1) |tptp.'one$a'|)) (= (= (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v1) |tptp.'one$a'|) (and (= A__questionmark_v0 |tptp.'one$a'|) (= A__questionmark_v1 |tptp.'one$a'|))))))
% 0.98/1.17 (assume a565 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (and (<= 0 A__questionmark_v0) (<= A__questionmark_v0 1) (<= A__questionmark_v1 1)) (= (= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) 1) (and (= A__questionmark_v0 1) (= A__questionmark_v1 1))))))
% 0.98/1.17 (assume a566 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (= (|tptp.'divides_aux$'| (|tptp.'pair$m'| A__questionmark_v0 A__questionmark_v1)) (= A__questionmark_v1 0))))
% 0.98/1.17 (assume a567 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (< 0 A__questionmark_v0) (= (<= (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2)) (<= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a568 (forall ((A__questionmark_v0 |tptp.'Int_int_prod$'|)) (= (|tptp.'divides_aux$'| A__questionmark_v0) (= (|tptp.'snd$p'| A__questionmark_v0) 0))))
% 0.98/1.17 (assume a569 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (< 0 A__questionmark_v0) (= (< (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v0)) (< A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a570 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (=> (< 0 A__questionmark_v0) (= (<= (|tptp.'times$a'| A__questionmark_v1 A__questionmark_v0) (|tptp.'times$a'| A__questionmark_v2 A__questionmark_v0)) (<= A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a571 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))))
% 0.98/1.17 (assume a572 (forall ((A__questionmark_v0 |tptp.'A_b_vec_b_vec$'|)) (= (|tptp.'upper_triangular$'| A__questionmark_v0) (forall ((A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'B$'|)) (=> (|tptp.'less$b'| A__questionmark_v2 A__questionmark_v1) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'vec_nth$e'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) |tptp.'zero$a'|))))))
% 0.98/1.17 (assume a573 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec_c_vec$'|)) (= (|tptp.'upper_triangular$a'| A__questionmark_v0) (forall ((A__questionmark_v1 |tptp.'C$'|) (A__questionmark_v2 |tptp.'C$'|)) (=> (|tptp.'less$a'| A__questionmark_v2 A__questionmark_v1) (= (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| (|tptp.'vec_nth$f'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v2) |tptp.'zero$l'|))))))
% 0.98/1.17 (assume a574 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'matrix_to_iarray$'| (|tptp.'plus$h'| A__questionmark_v0 A__questionmark_v1)) (|tptp.'plus$g'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0) (|tptp.'matrix_to_iarray$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a575 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (= A__questionmark_v0 A__questionmark_v1) (= (|tptp.'matrix_to_iarray$'| A__questionmark_v0) (|tptp.'matrix_to_iarray$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a576 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'A_c_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$a'| (|tptp.'gauss_Jordan_column_k_det_P$c'| (|tptp.'pair$'| A__questionmark_v0 (|tptp.'pair$a'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v3)))) (|tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$q'| (|tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$q'| A__questionmark_v4 (|tptp.'pair$a'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v3)))))))
% 0.98/1.17 (assume a577 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'A_c_vec_c_vec$'|)) (= (|tptp.'snd$a'| (|tptp.'gauss_Jordan_column_k_det_P$c'| (|tptp.'pair$'| A__questionmark_v0 (|tptp.'pair$a'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v3)) (|tptp.'snd$q'| (|tptp.'gauss_Jordan_column_k_PA$'| (|tptp.'pair$q'| A__questionmark_v4 (|tptp.'pair$a'| A__questionmark_v1 A__questionmark_v2)) A__questionmark_v3)))))
% 0.98/1.17 (assume a578 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (and (=> (or (forall ((A__questionmark_v2 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| (|tptp.'fst$g'| (|tptp.'snd$r'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'vec_nth$b'| (|tptp.'vec_nth$c'| (|tptp.'snd$h'| (|tptp.'snd$r'| A__questionmark_v0)) A__questionmark_v2) (|tptp.'from_nat$'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$g'| (|tptp.'snd$r'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$a'| (|tptp.'snd$h'| (|tptp.'snd$r'| A__questionmark_v0)))))) (= (|tptp.'gauss_Jordan_column_k_PA$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$r'| (|tptp.'fst$q'| A__questionmark_v0) (|tptp.'pair$h'| (|tptp.'fst$g'| (|tptp.'snd$r'| A__questionmark_v0)) (|tptp.'snd$h'| (|tptp.'snd$r'| A__questionmark_v0)))))) (=> (not (or (forall ((A__questionmark_v2 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| (|tptp.'fst$g'| (|tptp.'snd$r'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'vec_nth$b'| (|tptp.'vec_nth$c'| (|tptp.'snd$h'| (|tptp.'snd$r'| A__questionmark_v0)) A__questionmark_v2) (|tptp.'from_nat$'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$g'| (|tptp.'snd$r'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$a'| (|tptp.'snd$h'| (|tptp.'snd$r'| A__questionmark_v0))))))) (= (|tptp.'gauss_Jordan_column_k_PA$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$r'| (|tptp.'fst$r'| (|tptp.'gauss_Jordan_in_ij_PA$'| (|tptp.'pair$s'| (|tptp.'fst$q'| A__questionmark_v0) (|tptp.'snd$h'| (|tptp.'snd$r'| A__questionmark_v0))) (|tptp.'from_nat$'| (|tptp.'fst$g'| (|tptp.'snd$r'| A__questionmark_v0))) (|tptp.'from_nat$'| A__questionmark_v1))) (|tptp.'pair$h'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| (|tptp.'fst$g'| (|tptp.'snd$r'| A__questionmark_v0))) 1)) (|tptp.'snd$s'| (|tptp.'gauss_Jordan_in_ij_PA$'| (|tptp.'pair$s'| (|tptp.'fst$q'| A__questionmark_v0) (|tptp.'snd$h'| (|tptp.'snd$r'| A__questionmark_v0))) (|tptp.'from_nat$'| (|tptp.'fst$g'| (|tptp.'snd$r'| A__questionmark_v0))) (|tptp.'from_nat$'| A__questionmark_v1))))))))))
% 0.98/1.17 (assume a579 (forall ((A__questionmark_v0 |tptp.'A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (and (=> (or (forall ((A__questionmark_v2 |tptp.'B$'|)) (=> (|tptp.'less_eq$b'| (|tptp.'from_nat$a'| (|tptp.'fst$j'| (|tptp.'snd$t'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'vec_nth$b'| (|tptp.'vec_nth$d'| (|tptp.'snd$k'| (|tptp.'snd$t'| A__questionmark_v0)) A__questionmark_v2) (|tptp.'from_nat$'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$j'| (|tptp.'snd$t'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$b'| (|tptp.'snd$k'| (|tptp.'snd$t'| A__questionmark_v0)))))) (= (|tptp.'gauss_Jordan_column_k_PA$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$t'| (|tptp.'fst$s'| A__questionmark_v0) (|tptp.'pair$j'| (|tptp.'fst$j'| (|tptp.'snd$t'| A__questionmark_v0)) (|tptp.'snd$k'| (|tptp.'snd$t'| A__questionmark_v0)))))) (=> (not (or (forall ((A__questionmark_v2 |tptp.'B$'|)) (=> (|tptp.'less_eq$b'| (|tptp.'from_nat$a'| (|tptp.'fst$j'| (|tptp.'snd$t'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'vec_nth$b'| (|tptp.'vec_nth$d'| (|tptp.'snd$k'| (|tptp.'snd$t'| A__questionmark_v0)) A__questionmark_v2) (|tptp.'from_nat$'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$j'| (|tptp.'snd$t'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$b'| (|tptp.'snd$k'| (|tptp.'snd$t'| A__questionmark_v0))))))) (= (|tptp.'gauss_Jordan_column_k_PA$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$t'| (|tptp.'fst$t'| (|tptp.'gauss_Jordan_in_ij_PA$a'| (|tptp.'pair$u'| (|tptp.'fst$s'| A__questionmark_v0) (|tptp.'snd$k'| (|tptp.'snd$t'| A__questionmark_v0))) (|tptp.'from_nat$a'| (|tptp.'fst$j'| (|tptp.'snd$t'| A__questionmark_v0))) (|tptp.'from_nat$'| A__questionmark_v1))) (|tptp.'pair$j'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| (|tptp.'fst$j'| (|tptp.'snd$t'| A__questionmark_v0))) 1)) (|tptp.'snd$u'| (|tptp.'gauss_Jordan_in_ij_PA$a'| (|tptp.'pair$u'| (|tptp.'fst$s'| A__questionmark_v0) (|tptp.'snd$k'| (|tptp.'snd$t'| A__questionmark_v0))) (|tptp.'from_nat$a'| (|tptp.'fst$j'| (|tptp.'snd$t'| A__questionmark_v0))) (|tptp.'from_nat$'| A__questionmark_v1))))))))))
% 0.98/1.17 (assume a580 (forall ((A__questionmark_v0 |tptp.'A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (and (=> (or (forall ((A__questionmark_v2 |tptp.'B$'|)) (=> (|tptp.'less_eq$b'| (|tptp.'from_nat$a'| (|tptp.'fst$m'| (|tptp.'snd$v'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'vec_nth$e'| (|tptp.'snd$n'| (|tptp.'snd$v'| A__questionmark_v0)) A__questionmark_v2)) (|tptp.'from_nat$a'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$m'| (|tptp.'snd$v'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$c'| (|tptp.'snd$n'| (|tptp.'snd$v'| A__questionmark_v0)))))) (= (|tptp.'gauss_Jordan_column_k_PA$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$v'| (|tptp.'fst$u'| A__questionmark_v0) (|tptp.'pair$l'| (|tptp.'fst$m'| (|tptp.'snd$v'| A__questionmark_v0)) (|tptp.'snd$n'| (|tptp.'snd$v'| A__questionmark_v0)))))) (=> (not (or (forall ((A__questionmark_v2 |tptp.'B$'|)) (=> (|tptp.'less_eq$b'| (|tptp.'from_nat$a'| (|tptp.'fst$m'| (|tptp.'snd$v'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'vec_nth$e'| (|tptp.'snd$n'| (|tptp.'snd$v'| A__questionmark_v0)) A__questionmark_v2)) (|tptp.'from_nat$a'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$m'| (|tptp.'snd$v'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$c'| (|tptp.'snd$n'| (|tptp.'snd$v'| A__questionmark_v0))))))) (= (|tptp.'gauss_Jordan_column_k_PA$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$v'| (|tptp.'fst$v'| (|tptp.'gauss_Jordan_in_ij_PA$b'| (|tptp.'pair$w'| (|tptp.'fst$u'| A__questionmark_v0) (|tptp.'snd$n'| (|tptp.'snd$v'| A__questionmark_v0))) (|tptp.'from_nat$a'| (|tptp.'fst$m'| (|tptp.'snd$v'| A__questionmark_v0))) (|tptp.'from_nat$a'| A__questionmark_v1))) (|tptp.'pair$l'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| (|tptp.'fst$m'| (|tptp.'snd$v'| A__questionmark_v0))) 1)) (|tptp.'snd$w'| (|tptp.'gauss_Jordan_in_ij_PA$b'| (|tptp.'pair$w'| (|tptp.'fst$u'| A__questionmark_v0) (|tptp.'snd$n'| (|tptp.'snd$v'| A__questionmark_v0))) (|tptp.'from_nat$a'| (|tptp.'fst$m'| (|tptp.'snd$v'| A__questionmark_v0))) (|tptp.'from_nat$a'| A__questionmark_v1))))))))))
% 0.98/1.17 (assume a581 (forall ((A__questionmark_v0 |tptp.'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (and (=> (or (forall ((A__questionmark_v2 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| (|tptp.'fst$b'| (|tptp.'snd$q'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| (|tptp.'snd$'| (|tptp.'snd$q'| A__questionmark_v0))) A__questionmark_v2)) (|tptp.'from_nat$a'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$q'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$'| (|tptp.'snd$'| (|tptp.'snd$q'| A__questionmark_v0)))))) (= (|tptp.'gauss_Jordan_column_k_PA$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$q'| (|tptp.'fst$w'| A__questionmark_v0) (|tptp.'pair$a'| (|tptp.'fst$b'| (|tptp.'snd$q'| A__questionmark_v0)) (|tptp.'snd$'| (|tptp.'snd$q'| A__questionmark_v0)))))) (=> (not (or (forall ((A__questionmark_v2 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| (|tptp.'fst$b'| (|tptp.'snd$q'| A__questionmark_v0))) A__questionmark_v2) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| (|tptp.'snd$'| (|tptp.'snd$q'| A__questionmark_v0))) A__questionmark_v2)) (|tptp.'from_nat$a'| A__questionmark_v1)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$q'| A__questionmark_v0))) (|tptp.'of_nat$'| (|tptp.'nrows$'| (|tptp.'snd$'| (|tptp.'snd$q'| A__questionmark_v0))))))) (= (|tptp.'gauss_Jordan_column_k_PA$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'pair$q'| (|tptp.'fst$x'| (|tptp.'gauss_Jordan_in_ij_PA$c'| (|tptp.'pair$x'| (|tptp.'fst$w'| A__questionmark_v0) (|tptp.'snd$'| (|tptp.'snd$q'| A__questionmark_v0))) (|tptp.'from_nat$'| (|tptp.'fst$b'| (|tptp.'snd$q'| A__questionmark_v0))) (|tptp.'from_nat$a'| A__questionmark_v1))) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| (|tptp.'fst$b'| (|tptp.'snd$q'| A__questionmark_v0))) 1)) (|tptp.'snd$x'| (|tptp.'gauss_Jordan_in_ij_PA$c'| (|tptp.'pair$x'| (|tptp.'fst$w'| A__questionmark_v0) (|tptp.'snd$'| (|tptp.'snd$q'| A__questionmark_v0))) (|tptp.'from_nat$'| (|tptp.'fst$b'| (|tptp.'snd$q'| A__questionmark_v0))) (|tptp.'from_nat$a'| A__questionmark_v1))))))))))
% 0.98/1.17 (assume a582 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'C$'|) (A__questionmark_v2 |tptp.'B$'|) (A__questionmark_v3 |tptp.'A_c_vec_c_vec$'|)) (= (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| A__questionmark_v0 A__questionmark_v1 A__questionmark_v2)) (|tptp.'snd$x'| (|tptp.'gauss_Jordan_in_ij_PA$c'| (|tptp.'pair$x'| A__questionmark_v3 A__questionmark_v0) A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a583 (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$o'| (|tptp.'fun_app$p'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'pair$a'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$o'| (|tptp.'fun_app$p'| A__questionmark_v0 (|tptp.'fst$b'| A__questionmark_v3)) (|tptp.'snd$'| A__questionmark_v3)))))
% 0.98/1.17 (assume a584 (forall ((A__questionmark_v0 |tptp.'Nat_a_iarray_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'Nat$'|) (A__questionmark_v2 |tptp.'A_iarray$'|) (A__questionmark_v3 |tptp.'Nat_a_iarray_prod$'|)) (=> (and (|tptp.'fun_app$q'| (|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$q'| (|tptp.'fun_app$r'| A__questionmark_v0 (|tptp.'fst$c'| A__questionmark_v3)) (|tptp.'snd$f'| A__questionmark_v3)))))
% 0.98/1.17 (assume a585 (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$s'| (|tptp.'fun_app$t'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'pair$d'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$s'| (|tptp.'fun_app$t'| A__questionmark_v0 (|tptp.'fst$d'| A__questionmark_v3)) (|tptp.'snd$c'| A__questionmark_v3)))))
% 0.98/1.17 (assume a586 (forall ((A__questionmark_v0 |tptp.'A_a_b_vec_c_vec_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v3 |tptp.'A_a_b_vec_c_vec_prod$'|)) (=> (and (|tptp.'fun_app$o'| (|tptp.'fun_app$u'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'pair$e'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$o'| (|tptp.'fun_app$u'| A__questionmark_v0 (|tptp.'fst$'| A__questionmark_v3)) (|tptp.'snd$b'| A__questionmark_v3)))))
% 0.98/1.17 (assume a587 (forall ((A__questionmark_v0 |tptp.'A_nat_a_b_vec_c_vec_prod_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (A__questionmark_v3 |tptp.'A_nat_a_b_vec_c_vec_prod_prod$'|)) (=> (and (|tptp.'fun_app$g'| (|tptp.'fun_app$v'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'pair$'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$g'| (|tptp.'fun_app$v'| A__questionmark_v0 (|tptp.'fst$e'| A__questionmark_v3)) (|tptp.'snd$a'| A__questionmark_v3)))))
% 0.98/1.17 (assume a588 (forall ((A__questionmark_v0 |tptp.'A_nat_a_iarray_iarray_prod_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'Nat_a_iarray_iarray_prod$'|) (A__questionmark_v3 |tptp.'A_nat_a_iarray_iarray_prod_prod$'|)) (=> (and (|tptp.'fun_app$i'| (|tptp.'fun_app$w'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'pair$c'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$i'| (|tptp.'fun_app$w'| A__questionmark_v0 (|tptp.'fst$f'| A__questionmark_v3)) (|tptp.'snd$d'| A__questionmark_v3)))))
% 0.98/1.17 (assume a589 (forall ((A__questionmark_v0 |tptp.'A_a_iarray_iarray_bool_fun_fun$'|) (A__questionmark_v1 |tptp.'A$'|) (A__questionmark_v2 |tptp.'A_iarray_iarray$'|) (A__questionmark_v3 |tptp.'A_a_iarray_iarray_prod$'|)) (=> (and (|tptp.'fun_app$s'| (|tptp.'fun_app$x'| A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (= A__questionmark_v3 (|tptp.'pair$f'| A__questionmark_v1 A__questionmark_v2))) (|tptp.'fun_app$s'| (|tptp.'fun_app$x'| A__questionmark_v0 (|tptp.'fst$a'| A__questionmark_v3)) (|tptp.'snd$e'| A__questionmark_v3)))))
% 0.98/1.17 (assume a590 (forall ((A__questionmark_v0 tptp.tlbool) (A__questionmark_v1 |tptp.'A$'|)) (and (=> (= A__questionmark_v0 tptp.tltrue) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'fun_app$b'| (|tptp.'times$'| |tptp.'one$'|) A__questionmark_v1) A__questionmark_v1)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| |tptp.'one$'|) A__questionmark_v1) |tptp.'zero$a'|)))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'fun_app$b'| (|tptp.'times$'| |tptp.'zero$a'|) A__questionmark_v1) A__questionmark_v1)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'fun_app$b'| (|tptp.'times$'| |tptp.'zero$a'|) A__questionmark_v1) |tptp.'zero$a'|)))))))
% 0.98/1.17 (assume a591 (forall ((A__questionmark_v0 tptp.tlbool) (A__questionmark_v1 Int)) (and (=> (= A__questionmark_v0 tptp.tltrue) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'times$a'| 1 A__questionmark_v1) A__questionmark_v1)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'times$a'| 1 A__questionmark_v1) 0)))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'times$a'| 0 A__questionmark_v1) A__questionmark_v1)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'times$a'| 0 A__questionmark_v1) 0)))))))
% 0.98/1.17 (assume a592 (forall ((A__questionmark_v0 tptp.tlbool) (A__questionmark_v1 |tptp.'Nat$'|)) (and (=> (= A__questionmark_v0 tptp.tltrue) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| |tptp.'one$a'|) A__questionmark_v1) A__questionmark_v1)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| |tptp.'one$a'|) A__questionmark_v1) |tptp.'zero$'|)))) (=> (not (= A__questionmark_v0 tptp.tltrue)) (and (=> (= A__questionmark_v0 tptp.tltrue) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| |tptp.'zero$'|) A__questionmark_v1) A__questionmark_v1)) (=> (not (= A__questionmark_v0 tptp.tltrue)) (= (|tptp.'fun_app$a'| (|tptp.'times$b'| |tptp.'zero$'|) A__questionmark_v1) |tptp.'zero$'|)))))))
% 0.98/1.17 (assume a593 (< 0 1))
% 0.98/1.17 (assume a594 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'C$'|)) (=> (exists ((A__questionmark_v3 |tptp.'C$'|)) (and (not (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v0) A__questionmark_v3)) A__questionmark_v1) |tptp.'zero$a'|)) (|tptp.'less_eq$'| A__questionmark_v2 A__questionmark_v3))) (= (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1)) (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0) (|tptp.'to_nat$'| A__questionmark_v2) (|tptp.'to_nat$a'| A__questionmark_v1)))))))
% 0.98/1.17 (assume a595 (forall ((A__questionmark_v0 |tptp.'C$'|)) (= (|tptp.'from_nat$'| (|tptp.'to_nat$'| A__questionmark_v0)) A__questionmark_v0)))
% 0.98/1.17 (assume a596 (forall ((A__questionmark_v0 |tptp.'B$'|)) (= (|tptp.'from_nat$a'| (|tptp.'to_nat$a'| A__questionmark_v0)) A__questionmark_v0)))
% 0.98/1.17 (assume a597 (forall ((A__questionmark_v0 |tptp.'C$'|) (A__questionmark_v1 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| A__questionmark_v0 A__questionmark_v1) (<= (|tptp.'of_nat$'| (|tptp.'to_nat$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'to_nat$'| A__questionmark_v1))))))
% 0.98/1.17 (assume a598 (forall ((A__questionmark_v0 |tptp.'C$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (= (|tptp.'of_nat$'| (|tptp.'to_nat$'| A__questionmark_v0)) (|tptp.'of_nat$'| A__questionmark_v1)) (= (|tptp.'from_nat$'| A__questionmark_v1) A__questionmark_v0))))
% 0.98/1.17 (assume a599 (forall ((A__questionmark_v0 |tptp.'B$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (= (|tptp.'of_nat$'| (|tptp.'to_nat$a'| A__questionmark_v0)) (|tptp.'of_nat$'| A__questionmark_v1)) (= (|tptp.'from_nat$a'| A__questionmark_v1) A__questionmark_v0))))
% 0.98/1.17 (assume a600 (forall ((A__questionmark_v0 |tptp.'C$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (|tptp.'less$a'| A__questionmark_v0 (|tptp.'from_nat$'| A__questionmark_v1)) (< (|tptp.'of_nat$'| (|tptp.'to_nat$'| A__questionmark_v0)) (|tptp.'of_nat$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a601 (forall ((A__questionmark_v0 |tptp.'B$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (=> (|tptp.'less$b'| A__questionmark_v0 (|tptp.'from_nat$a'| A__questionmark_v1)) (< (|tptp.'of_nat$'| (|tptp.'to_nat$a'| A__questionmark_v0)) (|tptp.'of_nat$'| A__questionmark_v1)))))
% 0.98/1.17 (assume a602 (forall ((A__questionmark_v0 |tptp.'C$'|) (A__questionmark_v1 |tptp.'C$'|)) (= (|tptp.'plus$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'from_nat$'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| (|tptp.'to_nat$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'to_nat$'| A__questionmark_v1))))))))
% 0.98/1.17 (assume a603 (forall ((A__questionmark_v0 |tptp.'B$'|) (A__questionmark_v1 |tptp.'B$'|)) (= (|tptp.'plus$c'| A__questionmark_v0 A__questionmark_v1) (|tptp.'from_nat$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| (|tptp.'to_nat$a'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'to_nat$a'| A__questionmark_v1))))))))
% 0.98/1.17 (assume a604 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int) (A__questionmark_v2 Int)) (= (+ (+ A__questionmark_v0 A__questionmark_v1) A__questionmark_v2) (+ A__questionmark_v0 (+ A__questionmark_v1 A__questionmark_v2)))))
% 0.98/1.17 (assume a605 (forall ((A__questionmark_v0 |tptp.'A_b_vec_b_vec$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$j'| (|tptp.'upper_triangular_upt_k$'| A__questionmark_v0) A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'B$'|) (A__questionmark_v3 |tptp.'B$'|)) (=> (and (|tptp.'less$b'| A__questionmark_v3 A__questionmark_v2) (< (|tptp.'of_nat$'| (|tptp.'to_nat$a'| A__questionmark_v3)) (|tptp.'of_nat$'| A__questionmark_v1))) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'vec_nth$e'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v3) |tptp.'zero$a'|))))))
% 0.98/1.17 (assume a606 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec_c_vec$'|) (A__questionmark_v1 |tptp.'Nat$'|)) (= (|tptp.'fun_app$j'| (|tptp.'upper_triangular_upt_k$a'| A__questionmark_v0) A__questionmark_v1) (forall ((A__questionmark_v2 |tptp.'C$'|) (A__questionmark_v3 |tptp.'C$'|)) (=> (and (|tptp.'less$a'| A__questionmark_v3 A__questionmark_v2) (< (|tptp.'of_nat$'| (|tptp.'to_nat$'| A__questionmark_v3)) (|tptp.'of_nat$'| A__questionmark_v1))) (= (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| (|tptp.'vec_nth$f'| A__questionmark_v0 A__questionmark_v2)) A__questionmark_v3) |tptp.'zero$l'|))))))
% 0.98/1.17 (assume a607 (<= 0 0))
% 0.98/1.17 (assume a608 (not (< 0 0)))
% 0.98/1.17 (assume a609 (<= 1 1))
% 0.98/1.17 (assume a610 (not (< 1 1)))
% 0.98/1.17 (assume a611 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v1 |tptp.'B$'|) (A__questionmark_v2 |tptp.'C$'|)) (=> (exists ((A__questionmark_v3 |tptp.'C$'|)) (and (not (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| A__questionmark_v0) A__questionmark_v3)) A__questionmark_v1) |tptp.'zero$a'|)) (|tptp.'less_eq$'| A__questionmark_v2 A__questionmark_v3))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| A__questionmark_v0 A__questionmark_v2 A__questionmark_v1))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0) (|tptp.'to_nat$'| A__questionmark_v2) (|tptp.'to_nat$a'| A__questionmark_v1)))))))
% 0.98/1.17 (assume a612 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'C$'|) (A__questionmark_v3 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v4 |tptp.'B$'|) (A__questionmark_v5 |tptp.'C$'|)) (=> (and (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v1))) (<= (|tptp.'of_nat$'| (|tptp.'to_nat$'| A__questionmark_v2)) (|tptp.'of_nat$'| A__questionmark_v0))) (= (|tptp.'vec_nth$b'| (|tptp.'vec_nth$c'| (|tptp.'fst$x'| (|tptp.'row_add_iterate_PA$'| (|tptp.'pair$x'| A__questionmark_v3 A__questionmark_v1) A__questionmark_v0 A__questionmark_v2 A__questionmark_v4)) A__questionmark_v2) A__questionmark_v5) (|tptp.'vec_nth$b'| (|tptp.'vec_nth$c'| A__questionmark_v3 A__questionmark_v2) A__questionmark_v5)))))
% 0.98/1.17 (assume a613 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (A__questionmark_v2 |tptp.'C$'|) (A__questionmark_v3 |tptp.'A_c_vec_c_vec$'|) (A__questionmark_v4 |tptp.'C$'|) (A__questionmark_v5 |tptp.'B$'|) (A__questionmark_v6 |tptp.'C$'|)) (=> (and (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v1))) (< (|tptp.'of_nat$'| A__questionmark_v0) (|tptp.'of_nat$'| (|tptp.'to_nat$'| A__questionmark_v2)))) (= (|tptp.'vec_nth$b'| (|tptp.'vec_nth$c'| (|tptp.'fst$x'| (|tptp.'row_add_iterate_PA$'| (|tptp.'pair$x'| A__questionmark_v3 A__questionmark_v1) A__questionmark_v0 A__questionmark_v4 A__questionmark_v5)) A__questionmark_v2) A__questionmark_v6) (|tptp.'vec_nth$b'| (|tptp.'vec_nth$c'| A__questionmark_v3 A__questionmark_v2) A__questionmark_v6)))))
% 0.98/1.17 (assume a614 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_set$'|) (A__questionmark_v2 Int) (A__questionmark_v3 |tptp.'Int_set$'|)) (=> (and (|tptp.'member$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'member$'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'member$'| (+ A__questionmark_v0 A__questionmark_v2) (|tptp.'plus$p'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a615 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_set$'|) (A__questionmark_v2 |tptp.'A$'|) (A__questionmark_v3 |tptp.'A_set$'|)) (=> (and (|tptp.'member$a'| A__questionmark_v0 A__questionmark_v1) (|tptp.'member$a'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'member$a'| (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v0) A__questionmark_v2) (|tptp.'times$e'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a616 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_set$'|) (A__questionmark_v2 Int) (A__questionmark_v3 |tptp.'Int_set$'|)) (=> (and (|tptp.'member$'| A__questionmark_v0 A__questionmark_v1) (|tptp.'member$'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'member$'| (|tptp.'times$a'| A__questionmark_v0 A__questionmark_v2) (|tptp.'times$f'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a617 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat$'|) (A__questionmark_v3 |tptp.'Nat_set$'|)) (=> (and (|tptp.'member$b'| A__questionmark_v0 A__questionmark_v1) (|tptp.'member$b'| A__questionmark_v2 A__questionmark_v3)) (|tptp.'member$b'| (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v0) A__questionmark_v2) (|tptp.'times$g'| A__questionmark_v1 A__questionmark_v3)))))
% 0.98/1.17 (assume a618 (forall ((A__questionmark_v0 |tptp.'A_set$'|) (A__questionmark_v1 |tptp.'A_set$'|)) (=> (|tptp.'member$a'| |tptp.'zero$a'| A__questionmark_v0) (|tptp.'less_eq$c'| A__questionmark_v1 (|tptp.'plus$q'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (assume a619 (forall ((A__questionmark_v0 |tptp.'Int_set$'|) (A__questionmark_v1 |tptp.'Int_set$'|)) (=> (|tptp.'member$'| 0 A__questionmark_v0) (|tptp.'less_eq$d'| A__questionmark_v1 (|tptp.'plus$p'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (assume a620 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'A_set$'|) (A__questionmark_v2 |tptp.'A_set$'|)) (=> (and (|tptp.'member$a'| A__questionmark_v0 (|tptp.'times$e'| A__questionmark_v1 A__questionmark_v2)) (forall ((A__questionmark_v3 |tptp.'A$'|) (A__questionmark_v4 |tptp.'A$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$b'| (|tptp.'times$'| A__questionmark_v3) A__questionmark_v4)) (|tptp.'member$a'| A__questionmark_v3 A__questionmark_v1) (|tptp.'member$a'| A__questionmark_v4 A__questionmark_v2)) false))) false)))
% 0.98/1.17 (assume a621 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_set$'|) (A__questionmark_v2 |tptp.'Int_set$'|)) (=> (and (|tptp.'member$'| A__questionmark_v0 (|tptp.'times$f'| A__questionmark_v1 A__questionmark_v2)) (forall ((A__questionmark_v3 Int) (A__questionmark_v4 Int)) (=> (and (= A__questionmark_v0 (|tptp.'times$a'| A__questionmark_v3 A__questionmark_v4)) (|tptp.'member$'| A__questionmark_v3 A__questionmark_v1) (|tptp.'member$'| A__questionmark_v4 A__questionmark_v2)) false))) false)))
% 0.98/1.17 (assume a622 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'Nat_set$'|) (A__questionmark_v2 |tptp.'Nat_set$'|)) (=> (and (|tptp.'member$b'| A__questionmark_v0 (|tptp.'times$g'| A__questionmark_v1 A__questionmark_v2)) (forall ((A__questionmark_v3 |tptp.'Nat$'|) (A__questionmark_v4 |tptp.'Nat$'|)) (=> (and (= A__questionmark_v0 (|tptp.'fun_app$a'| (|tptp.'times$b'| A__questionmark_v3) A__questionmark_v4)) (|tptp.'member$b'| A__questionmark_v3 A__questionmark_v1) (|tptp.'member$b'| A__questionmark_v4 A__questionmark_v2)) false))) false)))
% 0.98/1.17 (assume a623 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 |tptp.'Int_set$'|) (A__questionmark_v2 |tptp.'Int_set$'|)) (=> (and (|tptp.'member$'| A__questionmark_v0 (|tptp.'plus$p'| A__questionmark_v1 A__questionmark_v2)) (forall ((A__questionmark_v3 Int) (A__questionmark_v4 Int)) (=> (and (= A__questionmark_v0 (+ A__questionmark_v3 A__questionmark_v4)) (|tptp.'member$'| A__questionmark_v3 A__questionmark_v1) (|tptp.'member$'| A__questionmark_v4 A__questionmark_v2)) false))) false)))
% 0.98/1.17 (assume a624 (forall ((A__questionmark_v0 |tptp.'C$'|)) (|tptp.'less_eq$'| A__questionmark_v0 A__questionmark_v0)))
% 0.98/1.17 (assume a625 (forall ((A__questionmark_v0 Int)) (<= A__questionmark_v0 A__questionmark_v0)))
% 0.98/1.17 (assume a626 (forall ((A__questionmark_v0 |tptp.'C$'|)) (|tptp.'less_eq$'| A__questionmark_v0 A__questionmark_v0)))
% 0.98/1.17 (assume a627 (forall ((A__questionmark_v0 |tptp.'C$'|)) (|tptp.'less_eq$'| A__questionmark_v0 A__questionmark_v0)))
% 0.98/1.17 (assume a628 (forall ((A__questionmark_v0 Int)) (<= A__questionmark_v0 A__questionmark_v0)))
% 0.98/1.17 (assume a629 (forall ((A__questionmark_v0 Int) (A__questionmark_v1 Int)) (=> (<= A__questionmark_v0 A__questionmark_v1) (= (<= A__questionmark_v1 A__questionmark_v0) (= A__questionmark_v1 A__questionmark_v0)))))
% 0.98/1.17 (assume a630 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (<= 0 (|tptp.'of_nat$'| A__questionmark_v0))))
% 0.98/1.17 (assume a631 (forall ((A__questionmark_v0 |tptp.'Nat$'|)) (= (|tptp.'nat$'| (|tptp.'of_nat$'| A__questionmark_v0)) A__questionmark_v0)))
% 0.98/1.17 (assume a632 (forall ((A__questionmark_v0 Int)) (and (=> (<= 0 A__questionmark_v0) (= (|tptp.'of_nat$'| (|tptp.'nat$'| A__questionmark_v0)) A__questionmark_v0)) (=> (not (<= 0 A__questionmark_v0)) (= (|tptp.'of_nat$'| (|tptp.'nat$'| A__questionmark_v0)) 0)))))
% 0.98/1.17 (assume a633 (forall ((B tptp.tlbool)) (or (= B tptp.tltrue) (= B tptp.tlfalse))))
% 0.98/1.17 (assume a634 (not (= tptp.tltrue tptp.tlfalse)))
% 0.98/1.17 (assume a635 true)
% 0.98/1.17 (step t1 (cl (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t2)
% 0.98/1.17 (assume t2.a0 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (step t2.t1 (cl (or (not (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule forall_inst :args ((:= A__questionmark_v0 |tptp.'n$'|) (:= A__questionmark_v1 (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))
% 0.98/1.17 (step t2.t2 (cl (not (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule or :premises (t2.t1))
% 0.98/1.17 (step t2.t3 (cl (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule resolution :premises (t2.t2 t2.a0))
% 0.98/1.17 (step t2 (cl (not (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule subproof :discharge (t2.a0))
% 0.98/1.17 (step t3 (cl (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule resolution :premises (t1 t2))
% 0.98/1.17 (step t4 (cl (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule implies_neg2)
% 0.98/1.17 (step t5 (cl (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule resolution :premises (t3 t4))
% 0.98/1.17 (step t6 (cl (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule contraction :premises (t5))
% 0.98/1.17 (step t7 (cl (not (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule implies :premises (t6))
% 0.98/1.17 (step t8 (cl (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (not (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule and_neg)
% 0.98/1.17 (step t9 (cl (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t10)
% 0.98/1.17 (assume t10.a0 (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))
% 0.98/1.17 (assume t10.a1 (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))
% 0.98/1.17 (step t10.t1 (cl (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t10.t2)
% 0.98/1.17 (assume t10.t2.a0 (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))
% 0.98/1.17 (assume t10.t2.a1 (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))
% 0.98/1.17 (step t10.t2.t1 (cl (= (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)) |tptp.'a$'|)) :rule symm :premises (t10.t2.a1))
% 0.98/1.17 (step t10.t2.t2 (cl (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) :rule symm :premises (t10.t2.t1))
% 0.98/1.17 (step t10.t2.t3 (cl (= (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))) (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))) :rule symm :premises (t10.t2.a0))
% 0.98/1.17 (step t10.t2.t4 (cl (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule symm :premises (t10.t2.t3))
% 0.98/1.17 (step t10.t2.t5 (cl (= (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)) (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule cong :premises (t10.t2.t4))
% 0.98/1.17 (step t10.t2.t6 (cl (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule trans :premises (t10.t2.t2 t10.t2.t5))
% 0.98/1.17 (step t10.t2 (cl (not (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule subproof :discharge (t10.t2.a0 t10.t2.a1))
% 0.98/1.17 (step t10.t3 (cl (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule and_pos)
% 0.98/1.17 (step t10.t4 (cl (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) :rule and_pos)
% 0.98/1.17 (step t10.t5 (cl (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule resolution :premises (t10.t2 t10.t3 t10.t4))
% 0.98/1.17 (step t10.t6 (cl (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule reordering :premises (t10.t5))
% 0.98/1.17 (step t10.t7 (cl (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule contraction :premises (t10.t6))
% 0.98/1.17 (step t10.t8 (cl (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule resolution :premises (t10.t1 t10.t7))
% 0.98/1.17 (step t10.t9 (cl (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule implies_neg2)
% 0.98/1.17 (step t10.t10 (cl (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule resolution :premises (t10.t8 t10.t9))
% 0.98/1.17 (step t10.t11 (cl (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule contraction :premises (t10.t10))
% 0.98/1.17 (step t10.t12 (cl (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule implies :premises (t10.t11))
% 0.98/1.17 (step t10.t13 (cl (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (not (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule and_neg)
% 0.98/1.17 (step t10.t14 (cl (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule resolution :premises (t10.t13 t10.a0 t10.a1))
% 0.98/1.17 (step t10.t15 (cl (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule resolution :premises (t10.t12 t10.t14))
% 0.98/1.17 (step t10 (cl (not (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule subproof :discharge (t10.a0 t10.a1))
% 0.98/1.17 (step t11 (cl (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule and_pos)
% 0.98/1.17 (step t12 (cl (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) :rule and_pos)
% 0.98/1.17 (step t13 (cl (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule resolution :premises (t10 t11 t12))
% 0.98/1.17 (step t14 (cl (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule reordering :premises (t13))
% 0.98/1.17 (step t15 (cl (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule contraction :premises (t14))
% 0.98/1.17 (step t16 (cl (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule resolution :premises (t9 t15))
% 0.98/1.17 (step t17 (cl (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule implies_neg2)
% 0.98/1.17 (step t18 (cl (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule resolution :premises (t16 t17))
% 0.98/1.17 (step t19 (cl (=> (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule contraction :premises (t18))
% 0.98/1.17 (step t20 (cl (not (and (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule implies :premises (t19))
% 0.98/1.17 (step t21 (cl (not (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule resolution :premises (t8 t20))
% 0.98/1.17 (step t22 (cl (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule reordering :premises (t21))
% 0.98/1.17 (step t23 (cl (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule and_neg)
% 0.98/1.17 (step t24 (cl (=> (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t25)
% 0.98/1.17 (assume t25.a0 (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))
% 0.98/1.17 (assume t25.a1 (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))
% 0.98/1.17 (step t25.t1 (cl (=> (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t25.t2)
% 0.98/1.17 (assume t25.t2.a0 (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))
% 0.98/1.17 (assume t25.t2.a1 (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))
% 0.98/1.17 (step t25.t2.t1 (cl (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) :rule symm :premises (t25.t2.a1))
% 0.98/1.17 (step t25.t2.t2 (cl (= (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) |tptp.'a$'|)) :rule symm :premises (t25.t2.a0))
% 0.98/1.17 (step t25.t2.t3 (cl (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule symm :premises (t25.t2.t2))
% 0.98/1.17 (step t25.t2.t4 (cl (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule cong :premises (t25.t2.t3))
% 0.98/1.17 (step t25.t2.t5 (cl (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule trans :premises (t25.t2.t1 t25.t2.t4))
% 0.98/1.17 (step t25.t2 (cl (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule subproof :discharge (t25.t2.a0 t25.t2.a1))
% 0.98/1.17 (step t25.t3 (cl (not (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule and_pos)
% 0.98/1.17 (step t25.t4 (cl (not (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule and_pos)
% 0.98/1.17 (step t25.t5 (cl (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (not (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) (not (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))))) :rule resolution :premises (t25.t2 t25.t3 t25.t4))
% 0.98/1.17 (step t25.t6 (cl (not (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) (not (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule reordering :premises (t25.t5))
% 0.98/1.17 (step t25.t7 (cl (not (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule contraction :premises (t25.t6))
% 0.98/1.17 (step t25.t8 (cl (=> (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule resolution :premises (t25.t1 t25.t7))
% 0.98/1.17 (step t25.t9 (cl (=> (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (not (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))))) :rule implies_neg2)
% 0.98/1.17 (step t25.t10 (cl (=> (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))))) :rule resolution :premises (t25.t8 t25.t9))
% 0.98/1.17 (step t25.t11 (cl (=> (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))))) :rule contraction :premises (t25.t10))
% 0.98/1.17 (step t25.t12 (cl (not (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule implies :premises (t25.t11))
% 0.98/1.17 (step t25.t13 (cl (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) :rule and_neg)
% 0.98/1.17 (step t25.t14 (cl (and (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) :rule resolution :premises (t25.t13 t25.a1 t25.a0))
% 0.98/1.17 (step t25.t15 (cl (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule resolution :premises (t25.t12 t25.t14))
% 0.98/1.17 (step t25 (cl (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule subproof :discharge (t25.a0 t25.a1))
% 0.98/1.17 (step t26 (cl (not (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule and_pos)
% 0.98/1.17 (step t27 (cl (not (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule and_pos)
% 0.98/1.17 (step t28 (cl (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (not (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (not (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))))) :rule resolution :premises (t25 t26 t27))
% 0.98/1.17 (step t29 (cl (not (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (not (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule reordering :premises (t28))
% 0.98/1.17 (step t30 (cl (not (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule contraction :premises (t29))
% 0.98/1.17 (step t31 (cl (=> (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule resolution :premises (t24 t30))
% 0.98/1.17 (step t32 (cl (=> (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (not (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))))) :rule implies_neg2)
% 0.98/1.17 (step t33 (cl (=> (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))))) :rule resolution :premises (t31 t32))
% 0.98/1.17 (step t34 (cl (=> (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))))) :rule contraction :premises (t33))
% 0.98/1.17 (step t35 (cl (not (and (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule implies :premises (t34))
% 0.98/1.17 (step t36 (cl (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule resolution :premises (t23 t35))
% 0.98/1.17 (step t37 (cl (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule reordering :premises (t36))
% 0.98/1.17 (step t38 (cl (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (not (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))))) :rule implies_neg2)
% 0.98/1.17 (step t39 (cl (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))) (not (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))))) (not (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) :rule and_neg)
% 0.98/1.17 (step t40 (cl (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (not (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))))) :rule implies_neg2)
% 0.98/1.17 (step t41 (cl (not (= (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))))) (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))))) (not (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))))))) (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))))) :rule equiv_pos2)
% 0.98/1.17 (anchor :step t42 :args ((A__questionmark_v0 |tptp.'C$'|) (:= A__questionmark_v0 A__questionmark_v0)))
% 0.98/1.17 (step t42.t1 (cl (= A__questionmark_v0 A__questionmark_v0)) :rule refl)
% 0.98/1.17 (step t42.t2 (cl (= (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0))) :rule refl)
% 0.98/1.17 (step t42.t3 (cl (= (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) :rule all_simplify)
% 0.98/1.17 (step t42.t4 (cl (= (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)))))) :rule cong :premises (t42.t2 t42.t3))
% 0.98/1.17 (step t42 (cl (= (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))))) :rule bind)
% 0.98/1.17 (step t43 (cl (= (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))))) :rule all_simplify)
% 0.98/1.17 (step t44 (cl (= (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))))) :rule trans :premises (t42 t43))
% 0.98/1.17 (step t45 (cl (= (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule refl)
% 0.98/1.17 (step t46 (cl (= (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule cong :premises (t44 t45))
% 0.98/1.17 (step t47 (cl (= (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule refl)
% 0.98/1.17 (step t48 (cl (= (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))))) :rule all_simplify)
% 0.98/1.17 (step t49 (cl (= (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))))) :rule cong :premises (t47 t48))
% 0.98/1.17 (step t50 (cl (= (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) :rule refl)
% 0.98/1.17 (step t51 (cl (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule refl)
% 0.98/1.17 (step t52 (cl (= (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|))) :rule refl)
% 0.98/1.17 (step t53 (cl (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1) (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|)))) :rule all_simplify)
% 0.98/1.17 (step t54 (cl (= (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))))) :rule cong :premises (t53))
% 0.98/1.17 (step t55 (cl (= (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))) :rule refl)
% 0.98/1.17 (step t56 (cl (= (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))) :rule cong :premises (t54 t55))
% 0.98/1.17 (step t57 (cl (= (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))) (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) :rule cong :premises (t52 t56))
% 0.98/1.17 (step t58 (cl (= (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))) (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))) :rule cong :premises (t57))
% 0.98/1.17 (step t59 (cl (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))) :rule cong :premises (t58))
% 0.98/1.17 (step t60 (cl (= (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))) :rule cong :premises (t51 t59))
% 0.98/1.17 (step t61 (cl (= (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) :rule cong :premises (t50 t60))
% 0.98/1.17 (step t62 (cl (= (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))))) :rule cong :premises (t49 t61))
% 0.98/1.17 (step t63 (cl (= (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))))) :rule cong :premises (t46 t62))
% 0.98/1.17 (anchor :step t64 :args ((A__questionmark_v0 |tptp.'C$'|) (:= A__questionmark_v0 A__questionmark_v0)))
% 0.98/1.17 (step t64.t1 (cl (= A__questionmark_v0 A__questionmark_v0)) :rule refl)
% 0.98/1.17 (step t64.t2 (cl (= (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0))) :rule refl)
% 0.98/1.17 (step t64.t3 (cl (= (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) :rule all_simplify)
% 0.98/1.17 (step t64.t4 (cl (= (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)))))) :rule cong :premises (t64.t2 t64.t3))
% 0.98/1.17 (step t64 (cl (= (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))))) :rule bind)
% 0.98/1.17 (step t65 (cl (= (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))))) :rule all_simplify)
% 0.98/1.17 (step t66 (cl (= (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))))) :rule trans :premises (t64 t65))
% 0.98/1.17 (step t67 (cl (= (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule cong :premises (t66 t45))
% 0.98/1.17 (step t68 (cl (= (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))))) :rule cong :premises (t67))
% 0.98/1.17 (step t69 (cl (= (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|))) :rule refl)
% 0.98/1.17 (step t70 (cl (= (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))) :rule refl)
% 0.98/1.17 (step t71 (cl (= (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))) :rule cong :premises (t54 t70))
% 0.98/1.17 (step t72 (cl (= (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))) :rule cong :premises (t69 t71))
% 0.98/1.17 (step t73 (cl (= (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))) (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) :rule cong :premises (t72))
% 0.98/1.17 (step t74 (cl (= (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))) (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))) :rule cong :premises (t73))
% 0.98/1.17 (step t75 (cl (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) :rule cong :premises (t74))
% 0.98/1.17 (step t76 (cl (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule refl)
% 0.98/1.17 (step t77 (cl (= (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) :rule cong :premises (t75 t76))
% 0.98/1.17 (step t78 (cl (= (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))) :rule all_simplify)
% 0.98/1.17 (step t79 (cl (= (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))) :rule trans :premises (t77 t78))
% 0.98/1.17 (step t80 (cl (= (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))) :rule cong :premises (t47 t79))
% 0.98/1.17 (step t81 (cl (= (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))) :rule cong :premises (t75 t59))
% 0.98/1.17 (step t82 (cl (= (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))) :rule all_simplify)
% 0.98/1.17 (step t83 (cl (= (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))) :rule trans :premises (t81 t82))
% 0.98/1.17 (step t84 (cl (= (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))) :rule cong :premises (t50 t83))
% 0.98/1.17 (step t85 (cl (= (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))) :rule cong :premises (t80 t84))
% 0.98/1.17 (step t86 (cl (= (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))) :rule cong :premises (t68 t85))
% 0.98/1.17 (step t87 (cl (= (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))))) (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))))) :rule cong :premises (t63 t86))
% 0.98/1.17 (step t88 (cl (= (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))))) (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))))) :rule cong :premises (t87))
% 0.98/1.17 (anchor :step t89 :args ((A__questionmark_v0 |tptp.'C$'|) (:= A__questionmark_v0 A__questionmark_v0)))
% 0.98/1.17 (step t89.t1 (cl (= A__questionmark_v0 A__questionmark_v0)) :rule refl)
% 0.98/1.17 (step t89.t2 (cl (= (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)))) :rule refl)
% 0.98/1.17 (step t89.t3 (cl (and (= |tptp.'zero$k'| (|tptp.'from_nat$a'| (|tptp.'nat$'| 0))) (= |tptp.'zero$f'| (|tptp.'from_nat$'| (|tptp.'nat$'| 0))) (= |tptp.'zero$j'| (|tptp.'pair$m'| 0 0)) (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|))) (not (= |tptp.'zero$k'| (|tptp.'from_nat$a'| (|tptp.'nat$'| 0)))) (not (= |tptp.'zero$f'| (|tptp.'from_nat$'| (|tptp.'nat$'| 0)))) (not (= |tptp.'zero$j'| (|tptp.'pair$m'| 0 0))) (not (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|)))) (not (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0))) (not (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) (not (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) (not (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|))) (not (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|))) (not (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|))) (not (= |tptp.'uuf$'| |tptp.'uue$'|)) (not (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|))) (not (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|))) (not (= |tptp.'uua$'| |tptp.'uub$'|)) (not (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule and_neg)
% 0.98/1.17 (step t89.t4 (cl (= |tptp.'zero$k'| (|tptp.'from_nat$a'| (|tptp.'nat$'| 0)))) :rule symm :premises (a520))
% 0.98/1.17 (step t89.t5 (cl (= |tptp.'zero$f'| (|tptp.'from_nat$'| (|tptp.'nat$'| 0)))) :rule symm :premises (a519))
% 0.98/1.17 (step t89.t6 (cl (not (= (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 |tptp.'zero$a'|)) (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|))))) (not (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 |tptp.'zero$a'|))) (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule equiv_pos2)
% 0.98/1.17 (step t89.t7 (cl (= |tptp.'zero$i'| |tptp.'zero$i'|)) :rule refl)
% 0.98/1.17 (step t89.t8 (cl (= 0 0)) :rule refl)
% 0.98/1.17 (step t89.t9 (cl (and (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|))) (not (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0))) (not (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) (not (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) (not (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|))) (not (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|))) (not (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|))) (not (= |tptp.'uuf$'| |tptp.'uue$'|)) (not (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|))) (not (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|))) (not (= |tptp.'uua$'| |tptp.'uub$'|)) (not (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule and_neg)
% 0.98/1.17 (step t89.t10 (cl (not (= (= |tptp.'zero$h'| (|tptp.'pair$o'| |tptp.'zero$a'| 0)) (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)))) (not (= |tptp.'zero$h'| (|tptp.'pair$o'| |tptp.'zero$a'| 0))) (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0))) :rule equiv_pos2)
% 0.98/1.17 (step t89.t11 (cl (= |tptp.'zero$h'| |tptp.'zero$h'|)) :rule refl)
% 0.98/1.17 (step t89.t12 (cl (and (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|))) (not (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) (not (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) (not (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|))) (not (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|))) (not (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|))) (not (= |tptp.'uuf$'| |tptp.'uue$'|)) (not (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|))) (not (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|))) (not (= |tptp.'uua$'| |tptp.'uub$'|)) (not (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule and_neg)
% 0.98/1.17 (step t89.t13 (cl (not (= (= |tptp.'zero$g'| (|tptp.'pair$n'| |tptp.'zero$a'| |tptp.'zero$a'|)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))))) (not (= |tptp.'zero$g'| (|tptp.'pair$n'| |tptp.'zero$a'| |tptp.'zero$a'|))) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule equiv_pos2)
% 0.98/1.17 (step t89.t14 (cl (= |tptp.'zero$g'| |tptp.'zero$g'|)) :rule refl)
% 0.98/1.17 (step t89.t15 (cl (and (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|))) (not (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) (not (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|))) (not (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|))) (not (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|))) (not (= |tptp.'uuf$'| |tptp.'uue$'|)) (not (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|))) (not (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|))) (not (= |tptp.'uua$'| |tptp.'uub$'|)) (not (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule and_neg)
% 0.98/1.17 (step t89.t16 (cl (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) :rule symm :premises (a416))
% 0.98/1.17 (step t89.t17 (cl (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|))) :rule symm :premises (a415))
% 0.98/1.17 (step t89.t18 (cl (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|))) :rule symm :premises (a414))
% 0.98/1.17 (step t89.t19 (cl (= |tptp.'uuf$'| |tptp.'uue$'|)) :rule symm :premises (a330))
% 0.98/1.17 (step t89.t20 (cl (and (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule resolution :premises (t89.t15 t89.t16 t89.t17 t89.t18 a331 t89.t19 a329 a328 a327 a326))
% 0.98/1.17 (step t89.t21 (cl (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) :rule and :premises (t89.t20))
% 0.98/1.17 (step t89.t22 (cl (= (|tptp.'pair$n'| |tptp.'zero$a'| |tptp.'zero$a'|) (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule cong :premises (t89.t21 t89.t21))
% 0.98/1.17 (step t89.t23 (cl (= (= |tptp.'zero$g'| (|tptp.'pair$n'| |tptp.'zero$a'| |tptp.'zero$a'|)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))))) :rule cong :premises (t89.t14 t89.t22))
% 0.98/1.17 (step t89.t24 (cl (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule resolution :premises (t89.t13 t89.t23 a487))
% 0.98/1.17 (step t89.t25 (cl (and (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule resolution :premises (t89.t12 t89.t24 t89.t16 t89.t17 t89.t18 a331 t89.t19 a329 a328 a327 a326))
% 0.98/1.17 (step t89.t26 (cl (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) :rule and :premises (t89.t25))
% 0.98/1.17 (step t89.t27 (cl (= 0 0)) :rule refl)
% 0.98/1.17 (step t89.t28 (cl (= (|tptp.'pair$o'| |tptp.'zero$a'| 0) (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0))) :rule cong :premises (t89.t26 t89.t27))
% 0.98/1.17 (step t89.t29 (cl (= (= |tptp.'zero$h'| (|tptp.'pair$o'| |tptp.'zero$a'| 0)) (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)))) :rule cong :premises (t89.t11 t89.t28))
% 0.98/1.17 (step t89.t30 (cl (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0))) :rule resolution :premises (t89.t10 t89.t29 a488))
% 0.98/1.17 (step t89.t31 (cl (and (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule resolution :premises (t89.t9 t89.t30 t89.t24 t89.t16 t89.t17 t89.t18 a331 t89.t19 a329 a328 a327 a326))
% 0.98/1.17 (step t89.t32 (cl (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) :rule and :premises (t89.t31))
% 0.98/1.17 (step t89.t33 (cl (= (|tptp.'pair$p'| 0 |tptp.'zero$a'|) (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule cong :premises (t89.t8 t89.t32))
% 0.98/1.17 (step t89.t34 (cl (= (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 |tptp.'zero$a'|)) (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|))))) :rule cong :premises (t89.t7 t89.t33))
% 0.98/1.17 (step t89.t35 (cl (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule resolution :premises (t89.t6 t89.t34 a489))
% 0.98/1.17 (step t89.t36 (cl (and (= |tptp.'zero$k'| (|tptp.'from_nat$a'| (|tptp.'nat$'| 0))) (= |tptp.'zero$f'| (|tptp.'from_nat$'| (|tptp.'nat$'| 0))) (= |tptp.'zero$j'| (|tptp.'pair$m'| 0 0)) (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule resolution :premises (t89.t3 t89.t4 t89.t5 a490 t89.t35 t89.t30 t89.t24 t89.t16 t89.t17 t89.t18 a331 t89.t19 a329 a328 a327 a326))
% 0.98/1.17 (step t89.t37 (cl (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) :rule and :premises (t89.t36))
% 0.98/1.17 (step t89.t38 (cl (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)))) :rule refl)
% 0.98/1.17 (step t89.t39 (cl (= (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) :rule cong :premises (t89.t37 t89.t38))
% 0.98/1.17 (step t89.t40 (cl (= (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)))) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)))))) :rule cong :premises (t89.t2 t89.t39))
% 0.98/1.17 (step t89 (cl (= (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))))) :rule bind)
% 0.98/1.17 (step t90 (cl (= (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule refl)
% 0.98/1.17 (step t91 (cl (= (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule cong :premises (t89 t90))
% 0.98/1.17 (step t92 (cl (= (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))))) :rule refl)
% 0.98/1.17 (step t93 (cl (= (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))))) :rule cong :premises (t91 t92))
% 0.98/1.17 (anchor :step t94 :args ((A__questionmark_v0 |tptp.'C$'|) (:= A__questionmark_v0 A__questionmark_v0)))
% 0.98/1.17 (step t94.t1 (cl (= A__questionmark_v0 A__questionmark_v0)) :rule refl)
% 0.98/1.17 (step t94.t2 (cl (= (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)))) :rule refl)
% 0.98/1.17 (step t94.t3 (cl (and (= |tptp.'zero$k'| (|tptp.'from_nat$a'| (|tptp.'nat$'| 0))) (= |tptp.'zero$f'| (|tptp.'from_nat$'| (|tptp.'nat$'| 0))) (= |tptp.'zero$j'| (|tptp.'pair$m'| 0 0)) (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|))) (not (= |tptp.'zero$k'| (|tptp.'from_nat$a'| (|tptp.'nat$'| 0)))) (not (= |tptp.'zero$f'| (|tptp.'from_nat$'| (|tptp.'nat$'| 0)))) (not (= |tptp.'zero$j'| (|tptp.'pair$m'| 0 0))) (not (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|)))) (not (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0))) (not (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) (not (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) (not (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|))) (not (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|))) (not (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|))) (not (= |tptp.'uuf$'| |tptp.'uue$'|)) (not (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|))) (not (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|))) (not (= |tptp.'uua$'| |tptp.'uub$'|)) (not (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule and_neg)
% 0.98/1.17 (step t94.t4 (cl (= |tptp.'zero$k'| (|tptp.'from_nat$a'| (|tptp.'nat$'| 0)))) :rule symm :premises (a520))
% 0.98/1.17 (step t94.t5 (cl (= |tptp.'zero$f'| (|tptp.'from_nat$'| (|tptp.'nat$'| 0)))) :rule symm :premises (a519))
% 0.98/1.17 (step t94.t6 (cl (not (= (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 |tptp.'zero$a'|)) (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|))))) (not (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 |tptp.'zero$a'|))) (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule equiv_pos2)
% 0.98/1.17 (step t94.t7 (cl (= |tptp.'zero$i'| |tptp.'zero$i'|)) :rule refl)
% 0.98/1.17 (step t94.t8 (cl (= 0 0)) :rule refl)
% 0.98/1.17 (step t94.t9 (cl (and (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|))) (not (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0))) (not (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) (not (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) (not (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|))) (not (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|))) (not (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|))) (not (= |tptp.'uuf$'| |tptp.'uue$'|)) (not (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|))) (not (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|))) (not (= |tptp.'uua$'| |tptp.'uub$'|)) (not (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule and_neg)
% 0.98/1.17 (step t94.t10 (cl (not (= (= |tptp.'zero$h'| (|tptp.'pair$o'| |tptp.'zero$a'| 0)) (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)))) (not (= |tptp.'zero$h'| (|tptp.'pair$o'| |tptp.'zero$a'| 0))) (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0))) :rule equiv_pos2)
% 0.98/1.17 (step t94.t11 (cl (= |tptp.'zero$h'| |tptp.'zero$h'|)) :rule refl)
% 0.98/1.17 (step t94.t12 (cl (and (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|))) (not (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) (not (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) (not (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|))) (not (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|))) (not (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|))) (not (= |tptp.'uuf$'| |tptp.'uue$'|)) (not (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|))) (not (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|))) (not (= |tptp.'uua$'| |tptp.'uub$'|)) (not (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule and_neg)
% 0.98/1.17 (step t94.t13 (cl (not (= (= |tptp.'zero$g'| (|tptp.'pair$n'| |tptp.'zero$a'| |tptp.'zero$a'|)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))))) (not (= |tptp.'zero$g'| (|tptp.'pair$n'| |tptp.'zero$a'| |tptp.'zero$a'|))) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule equiv_pos2)
% 0.98/1.17 (step t94.t14 (cl (= |tptp.'zero$g'| |tptp.'zero$g'|)) :rule refl)
% 0.98/1.17 (step t94.t15 (cl (and (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|))) (not (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) (not (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|))) (not (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|))) (not (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|))) (not (= |tptp.'uuf$'| |tptp.'uue$'|)) (not (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|))) (not (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|))) (not (= |tptp.'uua$'| |tptp.'uub$'|)) (not (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule and_neg)
% 0.98/1.17 (step t94.t16 (cl (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) :rule symm :premises (a416))
% 0.98/1.17 (step t94.t17 (cl (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|))) :rule symm :premises (a415))
% 0.98/1.17 (step t94.t18 (cl (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|))) :rule symm :premises (a414))
% 0.98/1.17 (step t94.t19 (cl (= |tptp.'uuf$'| |tptp.'uue$'|)) :rule symm :premises (a330))
% 0.98/1.17 (step t94.t20 (cl (and (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule resolution :premises (t94.t15 t94.t16 t94.t17 t94.t18 a331 t94.t19 a329 a328 a327 a326))
% 0.98/1.17 (step t94.t21 (cl (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) :rule and :premises (t94.t20))
% 0.98/1.17 (step t94.t22 (cl (= (|tptp.'pair$n'| |tptp.'zero$a'| |tptp.'zero$a'|) (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule cong :premises (t94.t21 t94.t21))
% 0.98/1.17 (step t94.t23 (cl (= (= |tptp.'zero$g'| (|tptp.'pair$n'| |tptp.'zero$a'| |tptp.'zero$a'|)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))))) :rule cong :premises (t94.t14 t94.t22))
% 0.98/1.17 (step t94.t24 (cl (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule resolution :premises (t94.t13 t94.t23 a487))
% 0.98/1.17 (step t94.t25 (cl (and (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule resolution :premises (t94.t12 t94.t24 t94.t16 t94.t17 t94.t18 a331 t94.t19 a329 a328 a327 a326))
% 0.98/1.17 (step t94.t26 (cl (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) :rule and :premises (t94.t25))
% 0.98/1.17 (step t94.t27 (cl (= 0 0)) :rule refl)
% 0.98/1.17 (step t94.t28 (cl (= (|tptp.'pair$o'| |tptp.'zero$a'| 0) (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0))) :rule cong :premises (t94.t26 t94.t27))
% 0.98/1.17 (step t94.t29 (cl (= (= |tptp.'zero$h'| (|tptp.'pair$o'| |tptp.'zero$a'| 0)) (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)))) :rule cong :premises (t94.t11 t94.t28))
% 0.98/1.17 (step t94.t30 (cl (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0))) :rule resolution :premises (t94.t10 t94.t29 a488))
% 0.98/1.17 (step t94.t31 (cl (and (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule resolution :premises (t94.t9 t94.t30 t94.t24 t94.t16 t94.t17 t94.t18 a331 t94.t19 a329 a328 a327 a326))
% 0.98/1.17 (step t94.t32 (cl (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) :rule and :premises (t94.t31))
% 0.98/1.17 (step t94.t33 (cl (= (|tptp.'pair$p'| 0 |tptp.'zero$a'|) (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule cong :premises (t94.t8 t94.t32))
% 0.98/1.17 (step t94.t34 (cl (= (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 |tptp.'zero$a'|)) (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|))))) :rule cong :premises (t94.t7 t94.t33))
% 0.98/1.17 (step t94.t35 (cl (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule resolution :premises (t94.t6 t94.t34 a489))
% 0.98/1.17 (step t94.t36 (cl (and (= |tptp.'zero$k'| (|tptp.'from_nat$a'| (|tptp.'nat$'| 0))) (= |tptp.'zero$f'| (|tptp.'from_nat$'| (|tptp.'nat$'| 0))) (= |tptp.'zero$j'| (|tptp.'pair$m'| 0 0)) (= |tptp.'zero$i'| (|tptp.'pair$p'| 0 (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$h'| (|tptp.'pair$o'| (|tptp.'fst$'| |tptp.'zero$b'|) 0)) (= |tptp.'zero$g'| (|tptp.'pair$n'| (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fst$'| |tptp.'zero$b'|))) (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|)) (= |tptp.'zero$e'| (|tptp.'snd$a'| |tptp.'zero$d'|)) (= |tptp.'zero$c'| (|tptp.'snd$b'| |tptp.'zero$b'|)) (= |tptp.'uug$'| (|tptp.'times$b'| |tptp.'one$a'|)) (= |tptp.'uuf$'| |tptp.'uue$'|) (= |tptp.'uud$'| (|tptp.'times$'| |tptp.'one$'|)) (= |tptp.'uuc$'| (|tptp.'times$b'| |tptp.'zero$'|)) (= |tptp.'uua$'| |tptp.'uub$'|) (= |tptp.'uu$'| (|tptp.'times$'| |tptp.'zero$a'|)))) :rule resolution :premises (t94.t3 t94.t4 t94.t5 a490 t94.t35 t94.t30 t94.t24 t94.t16 t94.t17 t94.t18 a331 t94.t19 a329 a328 a327 a326))
% 0.98/1.17 (step t94.t37 (cl (= |tptp.'zero$a'| (|tptp.'fst$'| |tptp.'zero$b'|))) :rule and :premises (t94.t36))
% 0.98/1.17 (step t94.t38 (cl (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)))) :rule refl)
% 0.98/1.17 (step t94.t39 (cl (= (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) :rule cong :premises (t94.t37 t94.t38))
% 0.98/1.17 (step t94.t40 (cl (= (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)))) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)))))) :rule cong :premises (t94.t2 t94.t39))
% 0.98/1.17 (step t94 (cl (= (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))))) :rule bind)
% 0.98/1.17 (step t95 (cl (= (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule cong :premises (t94 t90))
% 0.98/1.17 (step t96 (cl (= (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))))) :rule cong :premises (t95))
% 0.98/1.17 (step t97 (cl (= (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))) :rule refl)
% 0.98/1.17 (step t98 (cl (= (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))) :rule cong :premises (t96 t97))
% 0.98/1.17 (step t99 (cl (= (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))) (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))))) :rule cong :premises (t93 t98))
% 0.98/1.17 (step t100 (cl (= (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))) (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))))) :rule cong :premises (t99))
% 0.98/1.17 (anchor :step t101 :args ((A__questionmark_v0 |tptp.'C$'|) (:= A__questionmark_v0 A__questionmark_v0)))
% 0.98/1.17 (step t101.t1 (cl (= A__questionmark_v0 A__questionmark_v0)) :rule refl)
% 0.98/1.17 (step t101.t2 (cl (= (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)))) :rule refl)
% 0.98/1.17 (step t101.t3 (cl (= (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule all_simplify)
% 0.98/1.17 (step t101.t4 (cl (= (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)))) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|))))) :rule cong :premises (t101.t2 t101.t3))
% 0.98/1.17 (step t101 (cl (= (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))))) :rule bind)
% 0.98/1.17 (step t102 (cl (= (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule cong :premises (t101 t45))
% 0.98/1.17 (step t103 (cl (= (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))))) :rule refl)
% 0.98/1.17 (step t104 (cl (= (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))))) :rule cong :premises (t102 t103))
% 0.98/1.17 (anchor :step t105 :args ((A__questionmark_v0 |tptp.'C$'|) (:= A__questionmark_v0 A__questionmark_v0)))
% 0.98/1.17 (step t105.t1 (cl (= A__questionmark_v0 A__questionmark_v0)) :rule refl)
% 0.98/1.17 (step t105.t2 (cl (= (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)))) :rule refl)
% 0.98/1.17 (step t105.t3 (cl (= (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) :rule all_simplify)
% 0.98/1.17 (step t105.t4 (cl (= (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)))) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|))))) :rule cong :premises (t105.t2 t105.t3))
% 0.98/1.17 (step t105 (cl (= (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))))) :rule bind)
% 0.98/1.17 (step t106 (cl (= (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule cong :premises (t105 t45))
% 0.98/1.17 (step t107 (cl (= (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))))) :rule cong :premises (t106))
% 0.98/1.17 (step t108 (cl (= (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))) :rule refl)
% 0.98/1.17 (step t109 (cl (= (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))) :rule cong :premises (t107 t108))
% 0.98/1.17 (step t110 (cl (= (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))) (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))))) :rule cong :premises (t104 t109))
% 0.98/1.17 (step t111 (cl (= (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fst$'| |tptp.'zero$b'|) (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))) (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))))) :rule cong :premises (t110))
% 0.98/1.17 (step t112 (cl (= (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= |tptp.'zero$a'| (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))) (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))))) :rule trans :premises (t100 t111))
% 0.98/1.17 (step t113 (cl (= (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (=> (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) |tptp.'zero$a'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ (|tptp.'of_nat$'| |tptp.'i$'|) 1)) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))))) (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))))) :rule trans :premises (t88 t112))
% 0.98/1.17 (step t114 (cl (not (and (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))))) :rule resolution :premises (t41 t113 a8))
% 0.98/1.17 (step t115 (cl (not (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))))) (not (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))))) :rule not_and :premises (t114))
% 0.98/1.17 (step t116 (cl (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))))) (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule implies_neg1)
% 0.98/1.17 (step t117 (cl (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))) :rule reordering :premises (t116))
% 0.98/1.17 (step t118 (cl (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule or_neg)
% 0.98/1.17 (step t119 (cl (not (= (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (or (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) (not (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (or (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule equiv_pos2)
% 0.98/1.17 (step t120 (cl (= (= (= (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) true) (= (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))) :rule equiv_simplify)
% 0.98/1.17 (step t121 (cl (not (= (= (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) true)) (= (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule equiv1 :premises (t120))
% 0.98/1.17 (step t122 (cl (= (= (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (= (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))))) :rule all_simplify)
% 0.98/1.17 (step t123 (cl (= (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule refl)
% 0.98/1.17 (step t124 (cl (= (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule all_simplify)
% 0.98/1.17 (step t125 (cl (= (= (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))) (= (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))) :rule cong :premises (t123 t124))
% 0.98/1.17 (step t126 (cl (= (= (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) true)) :rule all_simplify)
% 0.98/1.17 (step t127 (cl (= (= (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))) true)) :rule trans :premises (t125 t126))
% 0.98/1.17 (step t128 (cl (= (= (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) true)) :rule trans :premises (t122 t127))
% 0.98/1.17 (step t129 (cl (= (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule resolution :premises (t121 t128))
% 0.98/1.17 (step t130 (cl (= (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)))) :rule refl)
% 0.98/1.17 (step t131 (cl (= (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule refl)
% 0.98/1.17 (step t132 (cl (= (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (or (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule cong :premises (t129 t130 t131))
% 0.98/1.17 (step t133 (cl (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule and_neg)
% 0.98/1.17 (step t134 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t135)
% 0.98/1.17 (assume t135.a0 (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))
% 0.98/1.17 (assume t135.a1 (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))
% 0.98/1.17 (step t135.t1 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t135.t2)
% 0.98/1.17 (assume t135.t2.a0 (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))
% 0.98/1.17 (assume t135.t2.a1 (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))
% 0.98/1.17 (step t135.t2.t1 (cl (not (= (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule equiv_pos2)
% 0.98/1.17 (step t135.t2.t2 (cl (= (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule all_simplify)
% 0.98/1.17 (step t135.t2.t3 (cl (or (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (not (<= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))))) :rule la_disequality)
% 0.98/1.17 (step t135.t2.t4 (cl (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (not (<= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))))) :rule or :premises (t135.t2.t3))
% 0.98/1.17 (step t135.t2.t5 (cl (not (= (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule equiv_pos2)
% 0.98/1.17 (step t135.t2.t6 (cl (= (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))))) :rule comp_simplify)
% 0.98/1.17 (step t135.t2.t7 (cl (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule resolution :premises (t135.t2.t5 t135.t2.t6 t135.t2.a1))
% 0.98/1.17 (step t135.t2.t8 (cl (not (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (<= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule la_generic :args (1 1))
% 0.98/1.17 (step t135.t2.t9 (cl (not (= (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) :rule equiv_pos2)
% 0.98/1.17 (step t135.t2.t10 (cl (= (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))) :rule all_simplify)
% 0.98/1.17 (step t135.t2.t11 (cl (= (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule symm :premises (t135.t2.t10))
% 0.98/1.17 (step t135.t2.t12 (cl (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) :rule resolution :premises (t135.t2.t9 t135.t2.t11 t135.t2.a0))
% 0.98/1.17 (step t135.t2.t13 (cl (<= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule resolution :premises (t135.t2.t8 t135.t2.t12))
% 0.98/1.17 (step t135.t2.t14 (cl (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule resolution :premises (t135.t2.t4 t135.t2.t7 t135.t2.t13))
% 0.98/1.17 (step t135.t2.t15 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule resolution :premises (t135.t2.t1 t135.t2.t2 t135.t2.t14))
% 0.98/1.17 (step t135.t2 (cl (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule subproof :discharge (t135.t2.a0 t135.t2.a1))
% 0.98/1.17 (step t135.t3 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule and_pos)
% 0.98/1.17 (step t135.t4 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule and_pos)
% 0.98/1.17 (step t135.t5 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)))) :rule resolution :premises (t135.t2 t135.t3 t135.t4))
% 0.98/1.17 (step t135.t6 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule reordering :premises (t135.t5))
% 0.98/1.17 (step t135.t7 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule contraction :premises (t135.t6))
% 0.98/1.17 (step t135.t8 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule resolution :premises (t135.t1 t135.t7))
% 0.98/1.17 (step t135.t9 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule implies_neg2)
% 0.98/1.17 (step t135.t10 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule resolution :premises (t135.t8 t135.t9))
% 0.98/1.17 (step t135.t11 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule contraction :premises (t135.t10))
% 0.98/1.17 (step t135.t12 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule implies :premises (t135.t11))
% 0.98/1.17 (step t135.t13 (cl (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule and_neg)
% 0.98/1.17 (step t135.t14 (cl (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule resolution :premises (t135.t13 t135.a0 t135.a1))
% 0.98/1.17 (step t135.t15 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule resolution :premises (t135.t12 t135.t14))
% 0.98/1.17 (step t135 (cl (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule subproof :discharge (t135.a0 t135.a1))
% 0.98/1.17 (step t136 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule and_pos)
% 0.98/1.17 (step t137 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule and_pos)
% 0.98/1.17 (step t138 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)))) :rule resolution :premises (t135 t136 t137))
% 0.98/1.17 (step t139 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule reordering :premises (t138))
% 0.98/1.17 (step t140 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule contraction :premises (t139))
% 0.98/1.17 (step t141 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule resolution :premises (t134 t140))
% 0.98/1.17 (step t142 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule implies_neg2)
% 0.98/1.17 (step t143 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule resolution :premises (t141 t142))
% 0.98/1.17 (step t144 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule contraction :premises (t143))
% 0.98/1.17 (step t145 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule implies :premises (t144))
% 0.98/1.17 (step t146 (cl (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule resolution :premises (t133 t145))
% 0.98/1.17 (step t147 (cl (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))))) :rule or_neg)
% 0.98/1.17 (step t148 (cl (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)))) :rule or_neg)
% 0.98/1.17 (step t149 (cl (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule or_neg)
% 0.98/1.17 (step t150 (cl (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule resolution :premises (t146 t147 t148 t149))
% 0.98/1.17 (step t151 (cl (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule contraction :premises (t150))
% 0.98/1.17 (step t152 (cl (or (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule resolution :premises (t119 t132 t151))
% 0.98/1.17 (step t153 (cl (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule or :premises (t152))
% 0.98/1.17 (step t154 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule reordering :premises (t153))
% 0.98/1.17 (step t155 (cl (not (= (<= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))) (not (<= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule equiv_pos2)
% 0.98/1.17 (step t156 (cl (= (<= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))) :rule all_simplify)
% 0.98/1.17 (step t157 (cl (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule resolution :premises (t155 t156 a9))
% 0.98/1.17 (step t158 (cl (not (= (not (< (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (not (not (< (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule equiv_pos2)
% 0.98/1.17 (step t159 (cl (= (< (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (not (>= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule all_simplify)
% 0.98/1.17 (step t160 (cl (= (>= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule all_simplify)
% 0.98/1.17 (step t161 (cl (= (not (>= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)))) :rule cong :premises (t160))
% 0.98/1.17 (step t162 (cl (= (< (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)))) :rule trans :premises (t159 t161))
% 0.98/1.17 (step t163 (cl (= (not (< (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))))) :rule cong :premises (t162))
% 0.98/1.17 (step t164 (cl (= (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule all_simplify)
% 0.98/1.17 (step t165 (cl (= (not (< (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule trans :premises (t163 t164))
% 0.98/1.17 (step t166 (cl (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule resolution :premises (t158 t165 a10))
% 0.98/1.17 (step t167 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule resolution :premises (t154 t157 t166))
% 0.98/1.17 (step t168 (cl (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule resolution :premises (t118 t167))
% 0.98/1.17 (step t169 (cl (=> (not (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|)))) |tptp.'n$'|) (|tptp.'pair$a'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$b'| (|tptp.'gauss_Jordan_in_ij_det_P$'| |tptp.'a$'| (|tptp.'from_nat$'| |tptp.'i$'|) (|tptp.'from_nat$a'| |tptp.'k$'|))))))))))))) :rule resolution :premises (t117 t168))
% 0.98/1.17 (step t170 (cl (not (=> (or (forall ((A__questionmark_v0 |tptp.'C$'|)) (or (not (|tptp.'less_eq$'| (|tptp.'from_nat$'| |tptp.'i$'|) A__questionmark_v0)) (= (|tptp.'fun_app$c'| (|tptp.'vec_nth$'| (|tptp.'fun_app$d'| (|tptp.'vec_nth$a'| |tptp.'a$'|) A__questionmark_v0)) (|tptp.'from_nat$a'| |tptp.'k$'|)) (|tptp.'fst$'| |tptp.'zero$b'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))))))) :rule resolution :premises (t115 t169))
% 0.98/1.17 (step t171 (cl (not (and (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))))) :rule resolution :premises (t40 t170))
% 0.98/1.17 (step t172 (cl (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|)))))))) (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule implies_neg1)
% 0.98/1.17 (step t173 (cl (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))) :rule reordering :premises (t172))
% 0.98/1.17 (step t174 (cl (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (not (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule or_neg)
% 0.98/1.17 (step t175 (cl (not (= (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (or (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (not (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (or (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule equiv_pos2)
% 0.98/1.17 (step t176 (cl (= (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule refl)
% 0.98/1.17 (step t177 (cl (= (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule refl)
% 0.98/1.17 (step t178 (cl (= (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (or (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule cong :premises (t129 t130 t176 t177))
% 0.98/1.17 (step t179 (cl (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule and_neg)
% 0.98/1.17 (step t180 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t181)
% 0.98/1.17 (assume t181.a0 (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))
% 0.98/1.17 (assume t181.a1 (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))
% 0.98/1.17 (assume t181.a2 (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))
% 0.98/1.17 (step t181.t1 (cl (=> (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t181.t2)
% 0.98/1.17 (assume t181.t2.a0 (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))
% 0.98/1.17 (assume t181.t2.a1 (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))
% 0.98/1.17 (step t181.t2.t1 (cl (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| |tptp.'i$'|))) :rule symm :premises (t181.t2.a1))
% 0.98/1.17 (step t181.t2.t2 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule symm :premises (t181.t2.t1))
% 0.98/1.17 (step t181.t2.t3 (cl (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule symm :premises (t181.t2.a0))
% 0.98/1.17 (step t181.t2.t4 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule trans :premises (t181.t2.t2 t181.t2.t3))
% 0.98/1.17 (step t181.t2 (cl (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule subproof :discharge (t181.t2.a0 t181.t2.a1))
% 0.98/1.17 (step t181.t3 (cl (not (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule and_pos)
% 0.98/1.17 (step t181.t4 (cl (not (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule and_pos)
% 0.98/1.17 (step t181.t5 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (not (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule resolution :premises (t181.t2 t181.t3 t181.t4))
% 0.98/1.17 (step t181.t6 (cl (not (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule reordering :premises (t181.t5))
% 0.98/1.17 (step t181.t7 (cl (not (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule contraction :premises (t181.t6))
% 0.98/1.17 (step t181.t8 (cl (=> (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule resolution :premises (t181.t1 t181.t7))
% 0.98/1.17 (step t181.t9 (cl (=> (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (not (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule implies_neg2)
% 0.98/1.17 (step t181.t10 (cl (=> (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (=> (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule resolution :premises (t181.t8 t181.t9))
% 0.98/1.17 (step t181.t11 (cl (=> (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule contraction :premises (t181.t10))
% 0.98/1.17 (step t181.t12 (cl (not (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule implies :premises (t181.t11))
% 0.98/1.17 (step t181.t13 (cl (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule and_neg)
% 0.98/1.17 (step t181.t14 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t181.t15)
% 0.98/1.17 (assume t181.t15.a0 (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))
% 0.98/1.17 (assume t181.t15.a1 (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))
% 0.98/1.17 (step t181.t15.t1 (cl (not (= (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule equiv_pos2)
% 0.98/1.17 (step t181.t15.t2 (cl (= (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule all_simplify)
% 0.98/1.17 (step t181.t15.t3 (cl (or (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (not (<= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))))) :rule la_disequality)
% 0.98/1.17 (step t181.t15.t4 (cl (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (not (<= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))))) :rule or :premises (t181.t15.t3))
% 0.98/1.17 (step t181.t15.t5 (cl (not (= (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule equiv_pos2)
% 0.98/1.17 (step t181.t15.t6 (cl (= (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))))) :rule comp_simplify)
% 0.98/1.17 (step t181.t15.t7 (cl (<= 0 (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule resolution :premises (t181.t15.t5 t181.t15.t6 t181.t15.a1))
% 0.98/1.17 (step t181.t15.t8 (cl (not (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (<= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule la_generic :args (1 1))
% 0.98/1.17 (step t181.t15.t9 (cl (not (= (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) :rule equiv_pos2)
% 0.98/1.17 (step t181.t15.t10 (cl (= (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)))) :rule all_simplify)
% 0.98/1.17 (step t181.t15.t11 (cl (= (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule symm :premises (t181.t15.t10))
% 0.98/1.17 (step t181.t15.t12 (cl (< (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) :rule resolution :premises (t181.t15.t9 t181.t15.t11 t181.t15.a0))
% 0.98/1.17 (step t181.t15.t13 (cl (<= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule resolution :premises (t181.t15.t8 t181.t15.t12))
% 0.98/1.17 (step t181.t15.t14 (cl (= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule resolution :premises (t181.t15.t4 t181.t15.t7 t181.t15.t13))
% 0.98/1.17 (step t181.t15.t15 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule resolution :premises (t181.t15.t1 t181.t15.t2 t181.t15.t14))
% 0.98/1.17 (step t181.t15 (cl (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule subproof :discharge (t181.t15.a0 t181.t15.a1))
% 0.98/1.17 (step t181.t16 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule and_pos)
% 0.98/1.17 (step t181.t17 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule and_pos)
% 0.98/1.17 (step t181.t18 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)))) :rule resolution :premises (t181.t15 t181.t16 t181.t17))
% 0.98/1.17 (step t181.t19 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule reordering :premises (t181.t18))
% 0.98/1.17 (step t181.t20 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule contraction :premises (t181.t19))
% 0.98/1.17 (step t181.t21 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule resolution :premises (t181.t14 t181.t20))
% 0.98/1.17 (step t181.t22 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (not (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule implies_neg2)
% 0.98/1.17 (step t181.t23 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule resolution :premises (t181.t21 t181.t22))
% 0.98/1.17 (step t181.t24 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule contraction :premises (t181.t23))
% 0.98/1.17 (step t181.t25 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule implies :premises (t181.t24))
% 0.98/1.17 (step t181.t26 (cl (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule and_neg)
% 0.98/1.17 (step t181.t27 (cl (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0))) :rule resolution :premises (t181.t26 t181.a0 t181.a1))
% 0.98/1.17 (step t181.t28 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule resolution :premises (t181.t25 t181.t27))
% 0.98/1.17 (step t181.t29 (cl (and (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule resolution :premises (t181.t13 t181.a2 t181.t28))
% 0.98/1.17 (step t181.t30 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule resolution :premises (t181.t12 t181.t29))
% 0.98/1.17 (step t181 (cl (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule subproof :discharge (t181.a0 t181.a1 t181.a2))
% 0.98/1.17 (step t182 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) :rule and_pos)
% 0.98/1.17 (step t183 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) :rule and_pos)
% 0.98/1.17 (step t184 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule and_pos)
% 0.98/1.17 (step t185 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule resolution :premises (t181 t182 t183 t184))
% 0.98/1.17 (step t186 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule reordering :premises (t185))
% 0.98/1.17 (step t187 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule contraction :premises (t186))
% 0.98/1.17 (step t188 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule resolution :premises (t180 t187))
% 0.98/1.17 (step t189 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (not (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule implies_neg2)
% 0.98/1.17 (step t190 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule resolution :premises (t188 t189))
% 0.98/1.17 (step t191 (cl (=> (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule contraction :premises (t190))
% 0.98/1.17 (step t192 (cl (not (and (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1)) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule implies :premises (t191))
% 0.98/1.17 (step t193 (cl (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule resolution :premises (t179 t192))
% 0.98/1.17 (step t194 (cl (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (not (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))))) :rule or_neg)
% 0.98/1.17 (step t195 (cl (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)))) :rule or_neg)
% 0.98/1.17 (step t196 (cl (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (not (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule or_neg)
% 0.98/1.17 (step t197 (cl (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (not (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule or_neg)
% 0.98/1.17 (step t198 (cl (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule resolution :premises (t193 t194 t195 t196 t197))
% 0.98/1.17 (step t199 (cl (or (not (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1))) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule contraction :premises (t198))
% 0.98/1.17 (step t200 (cl (or (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule resolution :premises (t175 t178 t199))
% 0.98/1.17 (step t201 (cl (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule or :premises (t200))
% 0.98/1.17 (step t202 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 1) (not (>= (+ (|tptp.'of_nat$'| |tptp.'i$'|) (* (- 1) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) 0)) (not (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule reordering :premises (t201))
% 0.98/1.17 (step t203 (cl (not (= (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) (not (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule equiv_pos2)
% 0.98/1.17 (step t204 (cl (= (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))))) :rule refl)
% 0.98/1.17 (step t205 (cl (= (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule all_simplify)
% 0.98/1.17 (step t206 (cl (= (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))))) :rule cong :premises (t204 t205))
% 0.98/1.17 (step t207 (cl (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0)))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t208)
% 0.98/1.17 (assume t208.a0 (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))))
% 0.98/1.17 (step t208.t1 (cl (or (not (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0)))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule forall_inst :args ((:= A__questionmark_v0 |tptp.'a$'|)))
% 0.98/1.17 (step t208.t2 (cl (not (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0)))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule or :premises (t208.t1))
% 0.98/1.17 (step t208.t3 (cl (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule resolution :premises (t208.t2 t208.a0))
% 0.98/1.17 (step t208 (cl (not (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0)))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule subproof :discharge (t208.a0))
% 0.98/1.17 (step t209 (cl (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule resolution :premises (t207 t208))
% 0.98/1.17 (step t210 (cl (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (not (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule implies_neg2)
% 0.98/1.17 (step t211 (cl (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule resolution :premises (t209 t210))
% 0.98/1.17 (step t212 (cl (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule contraction :premises (t211))
% 0.98/1.17 (step t213 (cl (=> (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0))))) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|))))) :rule resolution :premises (t203 t206 t212))
% 0.98/1.17 (step t214 (cl (not (forall ((A__questionmark_v0 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'of_nat$'| (|tptp.'nrows$'| A__questionmark_v0)) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| A__questionmark_v0)))))) (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule implies :premises (t213))
% 0.98/1.17 (step t215 (cl (= (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'of_nat$'| (|tptp.'nrows$'| |tptp.'a$'|)))) :rule resolution :premises (t214 a571))
% 0.98/1.17 (step t216 (cl (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule resolution :premises (t202 t157 t166 t215))
% 0.98/1.17 (step t217 (cl (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule resolution :premises (t174 t216))
% 0.98/1.17 (step t218 (cl (=> (not (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| (|tptp.'fun_app$b'| (|tptp.'times$'| (|tptp.'fst$a'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))) |tptp.'n$'|) (|tptp.'pair$d'| (|tptp.'nat$'| (+ 1 (|tptp.'of_nat$'| |tptp.'i$'|))) (|tptp.'snd$e'| (|tptp.'gauss_Jordan_in_ij_det_P_iarrays$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) |tptp.'i$'| |tptp.'k$'|))))))))) :rule resolution :premises (t173 t217))
% 0.98/1.17 (step t219 (cl (not (=> (or (|tptp.'fun_app$e'| |tptp.'vector_all_zero_from_index$'| (|tptp.'pair$b'| |tptp.'i$'| (|tptp.'column_iarray$'| |tptp.'k$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (= (|tptp.'of_nat$'| |tptp.'i$'|) (|tptp.'of_nat$'| (|tptp.'nrows_iarray$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))))) :rule resolution :premises (t39 t171 t218))
% 0.98/1.17 (step t220 (cl (not (= (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (|tptp.'matrix_to_iarray$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))))) :rule resolution :premises (t38 t219))
% 0.98/1.17 (step t221 (cl (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (not (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule and_neg)
% 0.98/1.17 (step t222 (cl (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t223)
% 0.98/1.17 (assume t223.a0 (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))
% 0.98/1.17 (assume t223.a1 (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))
% 0.98/1.17 (step t223.t1 (cl (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t223.t2)
% 0.98/1.17 (assume t223.t2.a0 (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))
% 0.98/1.17 (assume t223.t2.a1 (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))
% 0.98/1.17 (step t223.t2.t1 (cl (= (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) :rule symm :premises (t223.t2.a1))
% 0.98/1.17 (step t223.t2.t2 (cl (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule symm :premises (t223.t2.t1))
% 0.98/1.17 (step t223.t2.t3 (cl (= (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))) :rule symm :premises (t223.t2.a0))
% 0.98/1.17 (step t223.t2.t4 (cl (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule symm :premises (t223.t2.t3))
% 0.98/1.17 (step t223.t2.t5 (cl (= (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule cong :premises (t223.t2.t4))
% 0.98/1.17 (step t223.t2.t6 (cl (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule trans :premises (t223.t2.t2 t223.t2.t5))
% 0.98/1.17 (step t223.t2 (cl (not (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule subproof :discharge (t223.t2.a0 t223.t2.a1))
% 0.98/1.17 (step t223.t3 (cl (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule and_pos)
% 0.98/1.17 (step t223.t4 (cl (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule and_pos)
% 0.98/1.17 (step t223.t5 (cl (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule resolution :premises (t223.t2 t223.t3 t223.t4))
% 0.98/1.17 (step t223.t6 (cl (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule reordering :premises (t223.t5))
% 0.98/1.17 (step t223.t7 (cl (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule contraction :premises (t223.t6))
% 0.98/1.17 (step t223.t8 (cl (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule resolution :premises (t223.t1 t223.t7))
% 0.98/1.17 (step t223.t9 (cl (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) :rule implies_neg2)
% 0.98/1.17 (step t223.t10 (cl (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) :rule resolution :premises (t223.t8 t223.t9))
% 0.98/1.17 (step t223.t11 (cl (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) :rule contraction :premises (t223.t10))
% 0.98/1.17 (step t223.t12 (cl (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule implies :premises (t223.t11))
% 0.98/1.17 (step t223.t13 (cl (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (not (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule and_neg)
% 0.98/1.17 (step t223.t14 (cl (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule resolution :premises (t223.t13 t223.a0 t223.a1))
% 0.98/1.17 (step t223.t15 (cl (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule resolution :premises (t223.t12 t223.t14))
% 0.98/1.17 (step t223 (cl (not (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule subproof :discharge (t223.a0 t223.a1))
% 0.98/1.17 (step t224 (cl (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule and_pos)
% 0.98/1.17 (step t225 (cl (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule and_pos)
% 0.98/1.17 (step t226 (cl (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule resolution :premises (t223 t224 t225))
% 0.98/1.17 (step t227 (cl (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule reordering :premises (t226))
% 0.98/1.17 (step t228 (cl (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule contraction :premises (t227))
% 0.98/1.17 (step t229 (cl (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule resolution :premises (t222 t228))
% 0.98/1.17 (step t230 (cl (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) :rule implies_neg2)
% 0.98/1.17 (step t231 (cl (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) :rule resolution :premises (t229 t230))
% 0.98/1.17 (step t232 (cl (=> (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))))) :rule contraction :premises (t231))
% 0.98/1.17 (step t233 (cl (not (and (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule implies :premises (t232))
% 0.98/1.17 (step t234 (cl (not (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule resolution :premises (t221 t233))
% 0.98/1.17 (step t235 (cl (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule reordering :premises (t234))
% 0.98/1.17 (step t236 (cl (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t237)
% 0.98/1.17 (assume t237.a0 (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (step t237.t1 (cl (or (not (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule forall_inst :args ((:= A__questionmark_v0 |tptp.'n$'|) (:= A__questionmark_v1 (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))
% 0.98/1.17 (step t237.t2 (cl (not (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule or :premises (t237.t1))
% 0.98/1.17 (step t237.t3 (cl (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule resolution :premises (t237.t2 t237.a0))
% 0.98/1.17 (step t237 (cl (not (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule subproof :discharge (t237.a0))
% 0.98/1.17 (step t238 (cl (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule resolution :premises (t236 t237))
% 0.98/1.17 (step t239 (cl (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (not (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule implies_neg2)
% 0.98/1.17 (step t240 (cl (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule resolution :premises (t238 t239))
% 0.98/1.17 (step t241 (cl (=> (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule contraction :premises (t240))
% 0.98/1.17 (step t242 (cl (not (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule implies :premises (t241))
% 0.98/1.17 (step t243 (cl (not (= (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)))))) (not (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1))))) :rule equiv_pos2)
% 0.98/1.17 (anchor :step t244 :args ((A__questionmark_v0 |tptp.'A$'|) (:= A__questionmark_v0 A__questionmark_v0) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|) (:= A__questionmark_v1 A__questionmark_v1)))
% 0.98/1.17 (step t244.t1 (cl (= A__questionmark_v0 A__questionmark_v0)) :rule refl)
% 0.98/1.17 (step t244.t2 (cl (= A__questionmark_v1 A__questionmark_v1)) :rule refl)
% 0.98/1.17 (step t244.t3 (cl (= (= (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1))))) :rule all_simplify)
% 0.98/1.17 (step t244 (cl (= (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1)))))) :rule bind)
% 0.98/1.17 (step t245 (cl (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_iarray_iarray_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$d'| (|tptp.'pair$c'| A__questionmark_v0 A__questionmark_v1))))) :rule resolution :premises (t243 t244 a276))
% 0.98/1.17 (step t246 (cl (= (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)) (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule resolution :premises (t242 t245))
% 0.98/1.17 (step t247 (cl (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t248)
% 0.98/1.17 (assume t248.a0 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (step t248.t1 (cl (or (not (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule forall_inst :args ((:= A__questionmark_v0 |tptp.'i$'|) (:= A__questionmark_v1 (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))
% 0.98/1.17 (step t248.t2 (cl (not (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule or :premises (t248.t1))
% 0.98/1.17 (step t248.t3 (cl (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule resolution :premises (t248.t2 t248.a0))
% 0.98/1.17 (step t248 (cl (not (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule subproof :discharge (t248.a0))
% 0.98/1.17 (step t249 (cl (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule resolution :premises (t247 t248))
% 0.98/1.17 (step t250 (cl (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (not (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule implies_neg2)
% 0.98/1.17 (step t251 (cl (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule resolution :premises (t249 t250))
% 0.98/1.17 (step t252 (cl (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|)))))) :rule contraction :premises (t251))
% 0.98/1.17 (step t253 (cl (not (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1))))) (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule implies :premises (t252))
% 0.98/1.17 (step t254 (cl (not (= (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)))))) (not (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1))))) :rule equiv_pos2)
% 0.98/1.17 (anchor :step t255 :args ((A__questionmark_v0 |tptp.'Nat$'|) (:= A__questionmark_v0 A__questionmark_v0) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|) (:= A__questionmark_v1 A__questionmark_v1)))
% 0.98/1.17 (step t255.t1 (cl (= A__questionmark_v0 A__questionmark_v0)) :rule refl)
% 0.98/1.17 (step t255.t2 (cl (= A__questionmark_v1 A__questionmark_v1)) :rule refl)
% 0.98/1.17 (step t255.t3 (cl (= (= (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1))))) :rule all_simplify)
% 0.98/1.17 (step t255 (cl (= (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1)))))) :rule bind)
% 0.98/1.17 (step t256 (cl (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_iarray_iarray$'|)) (= A__questionmark_v1 (|tptp.'snd$c'| (|tptp.'pair$d'| A__questionmark_v0 A__questionmark_v1))))) :rule resolution :premises (t254 t255 a273))
% 0.98/1.17 (step t257 (cl (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))) :rule resolution :premises (t253 t256))
% 0.98/1.17 (step t258 (cl (= (|tptp.'matrix_to_iarray$'| |tptp.'a$'|) (|tptp.'snd$c'| (|tptp.'snd$d'| (|tptp.'pair$c'| |tptp.'n$'| (|tptp.'pair$d'| |tptp.'i$'| (|tptp.'matrix_to_iarray$'| |tptp.'a$'|))))))) :rule resolution :premises (t235 t246 t257))
% 0.98/1.17 (step t259 (cl (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))))) :rule resolution :premises (t37 t220 t258))
% 0.98/1.17 (step t260 (cl (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1))))) :rule implies_neg1)
% 0.98/1.17 (anchor :step t261)
% 0.98/1.17 (assume t261.a0 (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)))))
% 0.98/1.17 (step t261.t1 (cl (or (not (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule forall_inst :args ((:= A__questionmark_v0 |tptp.'i$'|) (:= A__questionmark_v1 |tptp.'a$'|)))
% 0.98/1.17 (step t261.t2 (cl (not (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) :rule or :premises (t261.t1))
% 0.98/1.17 (step t261.t3 (cl (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) :rule resolution :premises (t261.t2 t261.a0))
% 0.98/1.17 (step t261 (cl (not (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) :rule subproof :discharge (t261.a0))
% 0.98/1.17 (step t262 (cl (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) :rule resolution :premises (t260 t261))
% 0.98/1.17 (step t263 (cl (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (not (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule implies_neg2)
% 0.98/1.17 (step t264 (cl (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule resolution :premises (t262 t263))
% 0.98/1.17 (step t265 (cl (=> (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|))))) :rule contraction :premises (t264))
% 0.98/1.17 (step t266 (cl (not (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1))))) (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) :rule implies :premises (t265))
% 0.98/1.17 (step t267 (cl (not (= (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)))))) (not (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1))))) :rule equiv_pos2)
% 0.98/1.17 (anchor :step t268 :args ((A__questionmark_v0 |tptp.'Nat$'|) (:= A__questionmark_v0 A__questionmark_v0) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|) (:= A__questionmark_v1 A__questionmark_v1)))
% 0.98/1.17 (step t268.t1 (cl (= A__questionmark_v0 A__questionmark_v0)) :rule refl)
% 0.98/1.17 (step t268.t2 (cl (= A__questionmark_v1 A__questionmark_v1)) :rule refl)
% 0.98/1.17 (step t268.t3 (cl (= (= (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1))))) :rule all_simplify)
% 0.98/1.17 (step t268 (cl (= (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)) (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1)))))) :rule bind)
% 0.98/1.17 (step t269 (cl (forall ((A__questionmark_v0 |tptp.'Nat$'|) (A__questionmark_v1 |tptp.'A_b_vec_c_vec$'|)) (= A__questionmark_v1 (|tptp.'snd$'| (|tptp.'pair$a'| A__questionmark_v0 A__questionmark_v1))))) :rule resolution :premises (t267 t268 a271))
% 0.98/1.17 (step t270 (cl (= |tptp.'a$'| (|tptp.'snd$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))) :rule resolution :premises (t266 t269))
% 0.98/1.17 (step t271 (cl (not (= (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|) (|tptp.'snd$a'| (|tptp.'pair$'| |tptp.'n$'| (|tptp.'pair$a'| |tptp.'i$'| |tptp.'a$'|)))))) :rule resolution :premises (t22 t259 t270))
% 0.98/1.17 (step t272 (cl (not (= (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)))))) (not (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1))) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1))))) :rule equiv_pos2)
% 0.98/1.18 (anchor :step t273 :args ((A__questionmark_v0 |tptp.'A$'|) (:= A__questionmark_v0 A__questionmark_v0) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|) (:= A__questionmark_v1 A__questionmark_v1)))
% 0.98/1.18 (step t273.t1 (cl (= A__questionmark_v0 A__questionmark_v0)) :rule refl)
% 0.98/1.18 (step t273.t2 (cl (= A__questionmark_v1 A__questionmark_v1)) :rule refl)
% 0.98/1.18 (step t273.t3 (cl (= (= (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1))))) :rule all_simplify)
% 0.98/1.18 (step t273 (cl (= (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)) A__questionmark_v1)) (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1)))))) :rule bind)
% 0.98/1.18 (step t274 (cl (forall ((A__questionmark_v0 |tptp.'A$'|) (A__questionmark_v1 |tptp.'Nat_a_b_vec_c_vec_prod$'|)) (= A__questionmark_v1 (|tptp.'snd$a'| (|tptp.'pair$'| A__questionmark_v0 A__questionmark_v1))))) :rule resolution :premises (t272 t273 a275))
% 0.98/1.18 (step t275 (cl) :rule resolution :premises (t7 t271 t274))
% 0.98/1.18
% 0.98/1.18 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.P7bCphahst/cvc5---1.0.5_22502.smt2
% 0.98/1.18 % cvc5---1.0.5 exiting
% 0.98/1.18 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------