TSTP Solution File: ITP339_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 04:18:47 EDT 2022
% Result : Theorem 0.40s 0.55s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 07:27:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.40/0.55 % SZS status Theorem
% 0.40/0.55 % SZS output start Proof
% 0.40/0.55 tff(tptp_fun__matrix_to_iarray___type, type, (
% 0.40/0.55 tptp_fun__matrix_to_iarray__: 'A_c_vec_c_vec$' > 'A_iarray_iarray$')).
% 0.40/0.55 tff(tptp_fun__fst___type, type, (
% 0.40/0.55 tptp_fun__fst__: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$')).
% 0.40/0.55 tff(tptp_fun__fun_app___type, type, (
% 0.40/0.55 tptp_fun__fun_app__: ( 'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$' * 'Nat$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$')).
% 0.40/0.55 tff(tptp_fun__nat___type, type, (
% 0.40/0.55 tptp_fun__nat__: $int > 'Nat$')).
% 0.40/0.55 tff(tptp_fun__fun_app_b__type, type, (
% 0.40/0.55 tptp_fun__fun_app_b_: ( 'Nat_int_fun$' * 'Nat$' ) > $int)).
% 0.40/0.55 tff(tptp_fun__ka___type, type, (
% 0.40/0.55 tptp_fun__ka__: 'Nat$')).
% 0.40/0.55 tff(tptp_fun__of_nat___type, type, (
% 0.40/0.55 tptp_fun__of_nat__: 'Nat_int_fun$')).
% 0.40/0.55 tff(tptp_fun__fun_app_a__type, type, (
% 0.40/0.55 tptp_fun__fun_app_a_: ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ) > 'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$')).
% 0.40/0.55 tff(tptp_fun__foldl___type, type, (
% 0.40/0.55 tptp_fun__foldl__: ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'Nat_list$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$')).
% 0.40/0.55 tff(tptp_fun__upt___type, type, (
% 0.40/0.55 tptp_fun__upt__: ( 'Nat$' * 'Nat$' ) > 'Nat_list$')).
% 0.40/0.55 tff(tptp_fun__pair___type, type, (
% 0.40/0.55 tptp_fun__pair__: ( 'A_c_vec_c_vec$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$')).
% 0.40/0.55 tff(tptp_fun__pair_a__type, type, (
% 0.40/0.55 tptp_fun__pair_a_: ( 'Nat$' * 'A_b_vec_c_vec$' ) > 'Nat_a_b_vec_c_vec_prod$')).
% 0.40/0.55 tff(tptp_fun__a___type, type, (
% 0.40/0.55 tptp_fun__a__: 'A_b_vec_c_vec$')).
% 0.40/0.55 tff(tptp_fun__mat___type, type, (
% 0.40/0.55 tptp_fun__mat__: 'A$' > 'A_c_vec_c_vec$')).
% 0.40/0.55 tff(tptp_fun__one___type, type, (
% 0.40/0.55 tptp_fun__one__: 'A$')).
% 0.40/0.55 tff(tptp_fun__gauss_Jordan_column_k_PA___type, type, (
% 0.40/0.55 tptp_fun__gauss_Jordan_column_k_PA__: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$')).
% 0.40/0.55 tff(tptp_fun__fst_k__type, type, (
% 0.40/0.55 tptp_fun__fst_k_: 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' > 'A_c_vec_c_vec$')).
% 0.40/0.55 tff(tptp_fun__gauss_Jordan_upt_k_PA___type, type, (
% 0.40/0.55 tptp_fun__gauss_Jordan_upt_k_PA__: ( 'A_b_vec_c_vec$' * 'Nat$' ) > 'A_c_vec_c_vec_a_b_vec_c_vec_prod$')).
% 0.40/0.55 tff(tptp_fun__snd_a__type, type, (
% 0.40/0.55 tptp_fun__snd_a_: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$')).
% 0.40/0.55 tff(tptp_fun__snd___type, type, (
% 0.40/0.55 tptp_fun__snd__: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$')).
% 0.40/0.55 tff(tptp_fun__fst_a__type, type, (
% 0.40/0.55 tptp_fun__fst_a_: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$')).
% 0.40/0.55 tff(1,plain,
% 0.40/0.55 ((~(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))) <=> (~(tptp_fun__matrix_to_iarray__(tptp_fun__fst_k_(tptp_fun__gauss_Jordan_upt_k_PA__(|'a$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(2,plain,
% 0.40/0.55 (tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))) = tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))),
% 0.40/0.55 inference(rewrite,[status(thm)],[])).
% 0.40/0.55 tff(3,plain,
% 0.40/0.55 (tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))) = tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[2])).
% 0.40/0.55 tff(4,plain,
% 0.40/0.55 (tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))) = tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[3])).
% 0.40/0.55 tff(5,plain,
% 0.40/0.55 (tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[4])).
% 0.40/0.55 tff(6,plain,
% 0.40/0.55 (tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[5])).
% 0.40/0.55 tff(7,plain,
% 0.40/0.55 (tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[5])).
% 0.40/0.55 tff(8,plain,
% 0.40/0.55 (tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))) = tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[7, 6])).
% 0.40/0.55 tff(9,plain,
% 0.40/0.55 (tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[4])).
% 0.40/0.55 tff(10,plain,
% 0.40/0.55 (tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))))) = tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[9, 8])).
% 0.40/0.55 tff(11,plain,
% 0.40/0.55 (tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))) = tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[10])).
% 0.40/0.55 tff(12,plain,
% 0.40/0.55 (tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))) = tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))),
% 0.40/0.55 inference(monotonicity,[status(thm)],[11, 2])).
% 0.40/0.55 tff(13,plain,
% 0.40/0.55 (tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))) = tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[12])).
% 0.40/0.56 tff(14,plain,
% 0.40/0.56 (tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[13])).
% 0.40/0.56 tff(15,plain,
% 0.40/0.56 (tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[4])).
% 0.40/0.56 tff(16,plain,
% 0.40/0.56 (tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))) = tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[15, 2])).
% 0.40/0.56 tff(17,plain,
% 0.40/0.56 (tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))) = tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[16])).
% 0.40/0.56 tff(18,plain,
% 0.40/0.56 (tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[17])).
% 0.40/0.56 tff(19,plain,
% 0.40/0.56 ((tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) <=> (tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[18, 14])).
% 0.40/0.56 tff(20,plain,
% 0.40/0.56 ((~(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))) <=> (~(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[19])).
% 0.40/0.56 tff(21,plain,
% 0.40/0.56 ((~(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))) <=> (~(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(22,plain,
% 0.40/0.56 ((~(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1)))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))))))), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))))) <=> (~(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(23,axiom,(~(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1)))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))))))), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture0')).
% 0.40/0.56 tff(24,plain,
% 0.40/0.56 (~(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.40/0.56 tff(25,plain,
% 0.40/0.56 (~(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.40/0.56 tff(26,plain,
% 0.40/0.56 (~(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__pair_a_(tptp_fun__fst_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))), tptp_fun__snd_a_(tptp_fun__snd__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.40/0.56 tff(27,plain,
% 0.40/0.56 (~(tptp_fun__matrix_to_iarray__(tptp_fun__fst_k_(tptp_fun__gauss_Jordan_upt_k_PA__(|'a$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[26, 1])).
% 0.40/0.56 tff(28,plain,
% 0.40/0.56 ((tptp_fun__matrix_to_iarray__(tptp_fun__fst_k_(tptp_fun__gauss_Jordan_upt_k_PA__(|'a$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) <=> $false),
% 0.40/0.56 inference(iff_false,[status(thm)],[27])).
% 0.40/0.56 tff(29,plain,
% 0.40/0.56 ((tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) <=> (tptp_fun__matrix_to_iarray__(tptp_fun__fst_k_(tptp_fun__gauss_Jordan_upt_k_PA__(|'a$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(30,plain,
% 0.40/0.56 (tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))) = tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(31,plain,
% 0.40/0.56 (tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))) = tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[30])).
% 0.40/0.56 tff(32,plain,
% 0.40/0.56 (tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))) = tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[31])).
% 0.40/0.56 tff(33,plain,
% 0.40/0.56 (tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[32])).
% 0.40/0.56 tff(34,plain,
% 0.40/0.56 (tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[33])).
% 0.40/0.56 tff(35,plain,
% 0.40/0.56 ((tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) <=> (tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[34, 18])).
% 0.40/0.56 tff(36,plain,
% 0.40/0.56 ((tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) <=> (tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(37,plain,
% 0.40/0.56 ((tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1), 1)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1)))))) <=> (tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(38,axiom,(tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1), 1)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1))))), tptp_fun__nat__($sum(tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|), 1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom1')).
% 0.40/0.56 tff(39,plain,
% 0.40/0.56 (tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.40/0.56 tff(40,plain,
% 0.40/0.56 (tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.40/0.60 tff(41,plain,
% 0.40/0.60 (tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(2, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.40/0.60 tff(42,plain,
% 0.40/0.60 (tptp_fun__matrix_to_iarray__(tptp_fun__fst_k_(tptp_fun__gauss_Jordan_upt_k_PA__(|'a$'|, tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))) = tptp_fun__matrix_to_iarray__(tptp_fun__fst__(tptp_fun__fun_app__(tptp_fun__fun_app_a_(|'gauss_Jordan_column_k_PA$'|, tptp_fun__foldl__(|'gauss_Jordan_column_k_PA$'|, tptp_fun__pair__(tptp_fun__mat__(|'one$'|), tptp_fun__pair_a_(tptp_fun__nat__(0), |'a$'|)), tptp_fun__upt__(tptp_fun__nat__(0), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|)))))), tptp_fun__nat__($sum(1, tptp_fun__fun_app_b_(|'of_nat$'|, |'ka$'|))))))),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[41, 29])).
% 0.40/0.60 tff(43,plain,
% 0.40/0.60 ($false),
% 0.40/0.60 inference(modus_ponens,[status(thm)],[42, 28])).
% 0.40/0.60 % SZS output end Proof
%------------------------------------------------------------------------------