TSTP Solution File: ITP339_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n027.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 : Thu Aug 31 04:11:48 EDT 2023
% Result : Theorem 34.32s 5.37s
% Output : Proof 57.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sun Aug 27 12:49:21 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 14.16/2.72 Prover 4: Preprocessing ...
% 14.16/2.73 Prover 0: Preprocessing ...
% 14.16/2.73 Prover 2: Preprocessing ...
% 14.16/2.73 Prover 5: Preprocessing ...
% 14.84/2.74 Prover 1: Preprocessing ...
% 14.84/2.80 Prover 6: Preprocessing ...
% 14.84/2.81 Prover 3: Preprocessing ...
% 32.73/5.16 Prover 6: Proving ...
% 32.73/5.16 Prover 3: Warning: ignoring some quantifiers
% 32.73/5.18 Prover 1: Warning: ignoring some quantifiers
% 33.23/5.21 Prover 3: Constructing countermodel ...
% 33.85/5.28 Prover 1: Constructing countermodel ...
% 34.32/5.36 Prover 6: proved (4725ms)
% 34.32/5.36
% 34.32/5.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.32/5.37
% 34.32/5.39 Prover 3: stopped
% 34.32/5.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 34.32/5.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 35.55/5.53 Prover 4: Warning: ignoring some quantifiers
% 36.02/5.60 Prover 0: Proving ...
% 36.02/5.60 Prover 0: stopped
% 36.02/5.63 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 36.77/5.73 Prover 4: Constructing countermodel ...
% 39.95/6.12 Prover 5: Proving ...
% 39.95/6.12 Prover 5: stopped
% 39.95/6.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 41.52/6.39 Prover 7: Preprocessing ...
% 42.99/6.52 Prover 8: Preprocessing ...
% 42.99/6.57 Prover 10: Preprocessing ...
% 44.58/6.78 Prover 2: Proving ...
% 44.58/6.78 Prover 2: stopped
% 44.58/6.79 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 46.29/6.93 Prover 11: Preprocessing ...
% 49.56/7.44 Prover 13: Preprocessing ...
% 51.58/7.71 Prover 8: Warning: ignoring some quantifiers
% 52.82/7.81 Prover 1: Found proof (size 540)
% 52.82/7.81 Prover 1: proved (7187ms)
% 52.82/7.82 Prover 8: Constructing countermodel ...
% 52.82/7.82 Prover 4: stopped
% 52.82/7.83 Prover 10: Warning: ignoring some quantifiers
% 52.82/7.84 Prover 8: stopped
% 53.64/7.93 Prover 10: Constructing countermodel ...
% 53.87/7.95 Prover 10: stopped
% 53.87/7.97 Prover 7: Warning: ignoring some quantifiers
% 53.87/7.97 Prover 13: stopped
% 54.39/8.04 Prover 11: Warning: ignoring some quantifiers
% 54.39/8.05 Prover 7: Constructing countermodel ...
% 54.39/8.07 Prover 7: stopped
% 54.69/8.11 Prover 11: Constructing countermodel ...
% 54.69/8.14 Prover 11: stopped
% 54.69/8.14
% 54.69/8.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.69/8.14
% 56.28/8.54 % SZS output start Proof for theBenchmark
% 56.28/8.55 Assumptions after simplification:
% 56.28/8.55 ---------------------------------
% 56.28/8.55
% 56.28/8.55 (axiom1)
% 56.60/8.57 Nat_int_fun$(of_nat$) &
% 56.60/8.57 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$(gauss_Jordan_column_k_PA$)
% 56.60/8.57 & A$(one$) & Nat$(ka$) & A_b_vec_c_vec$(a$) & ? [v0: A_c_vec_c_vec$] : ?
% 56.60/8.57 [v1: Nat$] : ? [v2: Nat_a_b_vec_c_vec_prod$] : ? [v3:
% 56.60/8.57 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v4: int] : ? [v5: Nat$] :
% 56.60/8.57 ? [v6: Nat_list$] : ? [v7: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ?
% 56.60/8.57 [v8: A_c_vec_c_vec$] : ? [v9: A_iarray_iarray$] : ? [v10: Nat$] : ? [v11:
% 56.60/8.57 Nat_list$] : ? [v12: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v13:
% 56.60/8.57 Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ? [v14:
% 56.60/8.57 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v15: A_c_vec_c_vec$] :
% 56.60/8.57 (mat$(one$) = v0 & pair$a(v1, a$) = v2 & pair$(v0, v2) = v3 &
% 56.60/8.57 fun_app$b(of_nat$, ka$) = v4 & nat$($sum(v4, 2)) = v5 & nat$($sum(v4, 1)) =
% 56.60/8.57 v10 & nat$(0) = v1 & upt$(v1, v10) = v11 & upt$(v1, v5) = v6 &
% 56.60/8.57 foldl$(gauss_Jordan_column_k_PA$, v3, v11) = v12 &
% 56.60/8.57 foldl$(gauss_Jordan_column_k_PA$, v3, v6) = v7 &
% 56.60/8.57 fun_app$a(gauss_Jordan_column_k_PA$, v12) = v13 & fun_app$(v13, v10) = v14 &
% 56.60/8.57 fst$(v14) = v15 & fst$(v7) = v8 & matrix_to_iarray$(v15) = v9 &
% 56.60/8.57 matrix_to_iarray$(v8) = v9 &
% 56.60/8.57 Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(v13) &
% 56.60/8.57 Nat_a_b_vec_c_vec_prod$(v2) &
% 56.60/8.57 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v14) &
% 56.60/8.57 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v12) &
% 56.60/8.57 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v7) &
% 56.60/8.57 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v3) & Nat$(v10) & Nat$(v5) &
% 56.60/8.57 Nat$(v1) & Nat_list$(v11) & Nat_list$(v6) & A_iarray_iarray$(v9) &
% 56.60/8.57 A_c_vec_c_vec$(v15) & A_c_vec_c_vec$(v8) & A_c_vec_c_vec$(v0))
% 56.60/8.57
% 56.60/8.57 (axiom136)
% 56.66/8.57 Nat_int_fun$(of_nat$) &
% 56.66/8.57 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$(gauss_Jordan_column_k_PA$)
% 56.66/8.57 & A$(one$) & Nat$(ka$) & A_b_vec_c_vec$(a$) & ? [v0: Nat$] : ? [v1: int] :
% 56.66/8.57 ? [v2: int] : ? [v3: Nat$] : ? [v4: int] : ? [v5: A_c_vec_c_vec$] : ? [v6:
% 56.66/8.57 Nat$] : ? [v7: Nat_a_b_vec_c_vec_prod$] : ? [v8:
% 56.66/8.57 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v9: Nat$] : ? [v10:
% 56.66/8.57 Nat_list$] : ? [v11: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v12:
% 56.66/8.57 Nat_a_b_vec_c_vec_prod$] : ? [v13: Nat$] : ? [v14: int] : (ncols$(a$) = v0
% 56.66/8.57 & nrows$(a$) = v3 & snd$(v11) = v12 & fst$a(v12) = v13 & mat$(one$) = v5 &
% 56.66/8.57 pair$a(v6, a$) = v7 & pair$(v5, v7) = v8 & fun_app$b(of_nat$, v13) = v14 &
% 56.66/8.57 fun_app$b(of_nat$, v3) = v4 & fun_app$b(of_nat$, v0) = v1 &
% 56.66/8.57 fun_app$b(of_nat$, ka$) = v2 & nat$($sum(v2, 1)) = v9 & nat$(0) = v6 &
% 56.66/8.57 upt$(v6, v9) = v10 & foldl$(gauss_Jordan_column_k_PA$, v8, v10) = v11 &
% 56.66/8.57 Nat_a_b_vec_c_vec_prod$(v12) & Nat_a_b_vec_c_vec_prod$(v7) &
% 56.66/8.57 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v11) &
% 56.66/8.57 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v8) & Nat$(v13) & Nat$(v9) &
% 56.66/8.57 Nat$(v6) & Nat$(v3) & Nat$(v0) & Nat_list$(v10) & A_c_vec_c_vec$(v5) & ( ~
% 56.66/8.57 ($lesseq(1, $difference(v14, v4))) | ~ ($lesseq(1, $difference(v1,
% 56.66/8.57 v2)))))
% 56.66/8.57
% 56.66/8.57 (axiom148)
% 56.66/8.57 Nat_int_fun$(of_nat$) & Nat$(ka$) & A_b_vec_c_vec$(a$) & ? [v0: Nat$] : ?
% 56.66/8.57 [v1: int] : ? [v2: int] : ($lesseq(2, $difference(v1, v2)) & ncols$(a$) = v0
% 56.66/8.57 & fun_app$b(of_nat$, v0) = v1 & fun_app$b(of_nat$, ka$) = v2 & Nat$(v0))
% 56.66/8.57
% 56.66/8.57 (axiom175)
% 56.66/8.58 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1:
% 56.66/8.58 Nat_bool_fun$] : ! [v2: Nat$] : ! [v3: int] : (v3 = 0 | ~
% 56.66/8.58 (fun_app$s(v1, v2) = v3) | ~ Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v4:
% 56.66/8.58 Nat$] : ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & $lesseq(1, v5) &
% 56.66/8.58 fun_app$s(v1, v4) = v6 & fun_app$b(of_nat$, v4) = v5 & Nat$(v4) & !
% 56.66/8.58 [v7: Nat$] : ! [v8: int] : ( ~ ($lesseq(1, $difference(v5, v8))) | ~
% 56.66/8.58 (fun_app$b(of_nat$, v7) = v8) | ~ Nat$(v7) | fun_app$s(v1, v7) = 0))
% 56.66/8.58 | ? [v4: int] : ( ~ (v4 = 0) & fun_app$s(v1, v0) = v4)))
% 56.66/8.58
% 56.66/8.58 (axiom199)
% 56.66/8.58 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1:
% 56.66/8.58 Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : ! [v4: int] : (v4 = 0 |
% 56.66/8.58 ~ (fun_app$s(v2, v0) = v4) | ~ (fun_app$b(of_nat$, v1) = v3) | ~
% 56.66/8.58 Nat_bool_fun$(v2) | ~ Nat$(v1) | ? [v5: Nat$] : ? [v6: int] : ? [v7:
% 56.66/8.58 Nat$] : ($lesseq(1, $difference(v3, v6)) & fun_app$s(v2, v7) = 0 &
% 56.66/8.58 fun_app$b(of_nat$, v5) = v6 & nat$($sum(v6, 1)) = v7 & Nat$(v7) &
% 56.66/8.58 Nat$(v5)) | ! [v5: Nat$] : ! [v6: int] : ( ~ ($lesseq(v6, v3)) | ~
% 56.66/8.58 (fun_app$b(of_nat$, v5) = v6) | ~ Nat$(v5) | ? [v7: int] : ( ~ (v7 =
% 56.66/8.58 0) & fun_app$s(v2, v5) = v7))) & ! [v1: Nat$] : ! [v2:
% 56.66/8.58 Nat_bool_fun$] : ! [v3: any] : ! [v4: int] : ( ~ (fun_app$s(v2, v0) =
% 56.66/8.58 v3) | ~ (fun_app$b(of_nat$, v1) = v4) | ~ Nat_bool_fun$(v2) | ~
% 56.66/8.58 Nat$(v1) | ? [v5: Nat$] : ? [v6: int] : ($lesseq(v6, v4) & fun_app$s(v2,
% 56.66/8.58 v5) = 0 & fun_app$b(of_nat$, v5) = v6 & Nat$(v5)) | ( ~ (v3 = 0) & !
% 56.66/8.58 [v5: Nat$] : ! [v6: int] : ! [v7: Nat$] : ( ~ ($lesseq(1,
% 56.66/8.58 $difference(v4, v6))) | ~ (fun_app$s(v2, v7) = 0) | ~
% 56.66/8.58 (fun_app$b(of_nat$, v5) = v6) | ~ (nat$($sum(v6, 1)) = v7) | ~
% 56.66/8.58 Nat$(v5)))))
% 56.66/8.58
% 56.66/8.58 (axiom2)
% 56.66/8.58 Nat_int_fun$(of_nat$) &
% 56.66/8.58 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$(gauss_Jordan_column_k_PA$)
% 56.66/8.58 & A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(a$a) & A$(one$) & Nat$(ka$) &
% 56.66/8.58 A_b_vec_c_vec$(a$) & ? [v0: A_c_vec_c_vec$] : ? [v1: Nat$] : ? [v2:
% 56.66/8.58 Nat_a_b_vec_c_vec_prod$] : ? [v3:
% 56.66/8.58 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v4: int] : ? [v5: Nat$] :
% 56.66/8.58 ? [v6: Nat_list$] : (mat$(one$) = v0 & pair$a(v1, a$) = v2 & pair$(v0, v2) =
% 56.66/8.58 v3 & fun_app$b(of_nat$, ka$) = v4 & nat$($sum(v4, 1)) = v5 & nat$(0) = v1 &
% 56.66/8.58 upt$(v1, v5) = v6 & foldl$(gauss_Jordan_column_k_PA$, v3, v6) = a$a &
% 56.66/8.58 Nat_a_b_vec_c_vec_prod$(v2) & A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v3)
% 56.66/8.58 & Nat$(v5) & Nat$(v1) & Nat_list$(v6) & A_c_vec_c_vec$(v0))
% 56.66/8.58
% 56.66/8.58 (axiom201)
% 56.66/8.59 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1:
% 56.66/8.59 Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] : ! [v4: any] : ( ~
% 56.66/8.59 (fun_app$s(v2, v0) = v4) | ~ (fun_app$b(of_nat$, v1) = v3) | ~
% 56.66/8.59 Nat_bool_fun$(v2) | ~ Nat$(v1) | ? [v5: Nat$] : ? [v6: int] : ? [v7:
% 56.66/8.59 int] : ( ~ (v7 = 0) & $lesseq(v6, v3) & fun_app$s(v2, v5) = v7 &
% 56.66/8.59 fun_app$b(of_nat$, v5) = v6 & Nat$(v5)) | (v4 = 0 & ! [v5: Nat$] : !
% 56.66/8.59 [v6: int] : ! [v7: Nat$] : ! [v8: int] : (v8 = 0 | ~ ($lesseq(1,
% 56.66/8.59 $difference(v3, v6))) | ~ (fun_app$s(v2, v7) = v8) | ~
% 56.66/8.59 (fun_app$b(of_nat$, v5) = v6) | ~ (nat$($sum(v6, 1)) = v7) | ~
% 56.66/8.59 Nat$(v5)))) & ! [v1: Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: int] :
% 56.66/8.59 ( ~ (fun_app$s(v2, v0) = 0) | ~ (fun_app$b(of_nat$, v1) = v3) | ~
% 56.66/8.59 Nat_bool_fun$(v2) | ~ Nat$(v1) | ? [v4: Nat$] : ? [v5: int] : ? [v6:
% 56.66/8.59 Nat$] : ? [v7: int] : ( ~ (v7 = 0) & $lesseq(1, $difference(v3, v5)) &
% 56.66/8.59 fun_app$s(v2, v6) = v7 & fun_app$b(of_nat$, v4) = v5 & nat$($sum(v5, 1))
% 56.66/8.59 = v6 & Nat$(v6) & Nat$(v4)) | ! [v4: Nat$] : ! [v5: int] : ( ~
% 56.66/8.59 ($lesseq(v5, v3)) | ~ (fun_app$b(of_nat$, v4) = v5) | ~ Nat$(v4) |
% 56.66/8.59 fun_app$s(v2, v4) = 0)))
% 56.66/8.59
% 56.66/8.59 (axiom204)
% 56.66/8.59 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1:
% 56.66/8.59 Nat_bool_fun$] : ! [v2: Nat$] : ! [v3: int] : ! [v4: int] : (v3 = 0 |
% 56.66/8.59 ~ (fun_app$s(v1, v0) = v3) | ~ (fun_app$b(of_nat$, v2) = v4) | ~
% 56.66/8.59 Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v5: Nat$] : ? [v6: int] :
% 56.66/8.59 ($lesseq(v6, v4) & fun_app$s(v1, v5) = 0 & fun_app$b(of_nat$, v5) = v6 &
% 56.66/8.59 Nat$(v5) & ! [v7: Nat$] : ! [v8: int] : ( ~ ($lesseq(1,
% 56.66/8.59 $difference(v6, v8))) | ~ (fun_app$b(of_nat$, v7) = v8) | ~
% 56.66/8.59 Nat$(v7) | ? [v9: int] : ( ~ (v9 = 0) & fun_app$s(v1, v7) = v9))) |
% 56.66/8.59 ? [v5: int] : ( ~ (v5 = 0) & fun_app$s(v1, v2) = v5)))
% 56.66/8.59
% 56.66/8.59 (axiom214)
% 56.66/8.59 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1:
% 56.66/8.59 Nat_bool_fun$] : ! [v2: Nat$] : ! [v3: int] : ! [v4: int] : (v3 = 0 |
% 56.66/8.59 ~ (fun_app$s(v1, v0) = v3) | ~ (fun_app$b(of_nat$, v2) = v4) | ~
% 56.66/8.59 Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v5: Nat$] : ? [v6: int] : ? [v7:
% 56.66/8.59 Nat$] : ($lesseq(1, $difference(v4, v6)) & fun_app$s(v1, v7) = 0 &
% 56.66/8.59 fun_app$b(of_nat$, v5) = v6 & nat$($sum(v6, 1)) = v7 & Nat$(v7) &
% 56.66/8.59 Nat$(v5) & ! [v8: Nat$] : ! [v9: int] : ( ~ ($lesseq(v9, v6)) | ~
% 56.66/8.59 (fun_app$b(of_nat$, v8) = v9) | ~ Nat$(v8) | ? [v10: int] : ( ~ (v10
% 56.66/8.59 = 0) & fun_app$s(v1, v8) = v10))) | ? [v5: int] : ( ~ (v5 = 0) &
% 56.66/8.59 fun_app$s(v1, v2) = v5)))
% 56.66/8.59
% 56.66/8.59 (axiom232)
% 56.66/8.59 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1:
% 56.66/8.59 Nat_bool_fun$] : ! [v2: Nat$] : ! [v3: int] : (v3 = 0 | ~
% 56.66/8.59 (fun_app$s(v1, v2) = v3) | ~ Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v4:
% 56.66/8.59 Nat$] : ? [v5: int] : ? [v6: Nat$] : ? [v7: int] : ( ~ (v7 = 0) &
% 56.66/8.59 fun_app$s(v1, v6) = v7 & fun_app$s(v1, v4) = 0 & fun_app$b(of_nat$, v4)
% 56.66/8.59 = v5 & nat$($sum(v5, 1)) = v6 & Nat$(v6) & Nat$(v4)) | ? [v4: int] : (
% 56.66/8.59 ~ (v4 = 0) & fun_app$s(v1, v0) = v4)))
% 56.66/8.59
% 56.66/8.59 (axiom233)
% 56.66/8.60 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1:
% 56.66/8.60 Nat_nat_bool_fun_fun$] : ! [v2: Nat$] : ! [v3: Nat$] : ! [v4:
% 56.66/8.60 Nat_bool_fun$] : ! [v5: int] : (v5 = 0 | ~ (fun_app$t(v1, v2) = v4) | ~
% 56.66/8.60 (fun_app$s(v4, v3) = v5) | ~ Nat$(v3) | ~ Nat$(v2) | ~
% 56.66/8.60 Nat_nat_bool_fun_fun$(v1) | ? [v6: Nat$] : ? [v7: Nat$] : ? [v8:
% 56.66/8.60 Nat_bool_fun$] : ? [v9: int] : ? [v10: Nat$] : ? [v11: Nat_bool_fun$]
% 56.66/8.60 : ? [v12: int] : ? [v13: Nat$] : ? [v14: int] : ( ~ (v14 = 0) &
% 56.66/8.60 fun_app$t(v1, v10) = v11 & fun_app$t(v1, v6) = v8 & fun_app$s(v11, v13)
% 56.66/8.60 = v14 & fun_app$s(v8, v7) = 0 & fun_app$b(of_nat$, v7) = v12 &
% 56.66/8.60 fun_app$b(of_nat$, v6) = v9 & nat$($sum(v12, 1)) = v13 & nat$($sum(v9,
% 56.66/8.60 1)) = v10 & Nat_bool_fun$(v11) & Nat_bool_fun$(v8) & Nat$(v13) &
% 56.66/8.60 Nat$(v10) & Nat$(v7) & Nat$(v6)) | ? [v6: Nat$] : ? [v7:
% 56.66/8.60 Nat_bool_fun$] : ? [v8: int] : ( ~ (v8 = 0) & fun_app$t(v1, v6) = v7 &
% 56.66/8.60 fun_app$s(v7, v0) = v8 & Nat_bool_fun$(v7) & Nat$(v6)) | ? [v6:
% 56.66/8.60 Nat_bool_fun$] : (fun_app$t(v1, v0) = v6 & Nat_bool_fun$(v6) & ? [v7:
% 56.66/8.60 Nat$] : ? [v8: int] : ? [v9: Nat$] : ? [v10: int] : ( ~ (v10 = 0) &
% 56.66/8.60 fun_app$s(v6, v9) = v10 & fun_app$b(of_nat$, v7) = v8 & nat$($sum(v8,
% 56.66/8.60 1)) = v9 & Nat$(v9) & Nat$(v7)))))
% 56.66/8.60
% 56.66/8.60 (axiom234)
% 56.66/8.60 Nat_int_fun$(of_nat$) & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1:
% 56.66/8.60 Nat_bool_fun$] : ! [v2: Nat$] : ( ~ (fun_app$s(v1, v2) = 0) | ~
% 56.66/8.60 Nat_bool_fun$(v1) | ~ Nat$(v2) | fun_app$s(v1, v0) = 0 | ? [v3: Nat$] :
% 56.66/8.60 ? [v4: int] : ? [v5: Nat$] : ? [v6: int] : ( ~ (v6 = 0) & fun_app$s(v1,
% 56.66/8.60 v5) = 0 & fun_app$s(v1, v3) = v6 & fun_app$b(of_nat$, v3) = v4 &
% 56.66/8.60 nat$($sum(v4, 1)) = v5 & Nat$(v5) & Nat$(v3))))
% 56.66/8.60
% 56.66/8.60 (axiom259)
% 56.66/8.60 Nat_int_fun$(of_nat$) & Nat$(ka$) & A_b_vec_c_vec$(a$) & ? [v0: Nat$] : ?
% 56.66/8.60 [v1: int] : ? [v2: int] : ? [v3: A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ?
% 56.66/8.60 [v4: A_c_vec_c_vec$] : ? [v5: A_iarray_iarray$] : ? [v6: A_iarray_iarray$] :
% 56.66/8.60 ? [v7: A_iarray_iarray_a_iarray_iarray_prod$] : ? [v8: A_iarray_iarray$] :
% 56.66/8.60 (gauss_Jordan_upt_k_iarrays_PA$(v6, ka$) = v7 & matrix_to_iarray$a(a$) = v6 &
% 56.66/8.60 ncols$(a$) = v0 & gauss_Jordan_upt_k_PA$(a$, ka$) = v3 & fst$k(v3) = v4 &
% 56.66/8.60 fst$c(v7) = v8 & fun_app$b(of_nat$, v0) = v1 & fun_app$b(of_nat$, ka$) = v2
% 56.66/8.60 & matrix_to_iarray$(v4) = v5 & Nat$(v0) &
% 56.66/8.60 A_c_vec_c_vec_a_b_vec_c_vec_prod$(v3) & A_iarray_iarray$(v8) &
% 56.66/8.60 A_iarray_iarray$(v6) & A_iarray_iarray$(v5) &
% 56.66/8.60 A_iarray_iarray_a_iarray_iarray_prod$(v7) & A_c_vec_c_vec$(v4) & (v8 = v5 |
% 56.66/8.60 ~ ($lesseq(1, $difference(v1, v2)))))
% 56.66/8.60
% 56.66/8.60 (axiom260)
% 56.66/8.60 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(b$) &
% 56.66/8.60 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(a$a) & ? [v0:
% 56.66/8.60 Nat_a_b_vec_c_vec_prod$] : ? [v1: A_b_vec_c_vec$] : ? [v2:
% 56.66/8.60 A_iarray_iarray$] : ? [v3: Nat_a_iarray_iarray_prod$] :
% 56.66/8.60 (matrix_to_iarray$a(v1) = v2 & snd$d(b$) = v3 & snd$b(v3) = v2 & snd$(a$a) =
% 56.66/8.60 v0 & snd$a(v0) = v1 & Nat_a_b_vec_c_vec_prod$(v0) &
% 56.66/8.60 Nat_a_iarray_iarray_prod$(v3) & A_b_vec_c_vec$(v1) & A_iarray_iarray$(v2))
% 56.66/8.60
% 56.66/8.60 (axiom261)
% 56.66/8.60 Nat_int_fun$(of_nat$) & Nat$(ka$) & A_b_vec_c_vec$(a$) & ? [v0: Nat$] : ?
% 56.66/8.60 [v1: int] : ? [v2: int] : ? [v3: A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ?
% 56.66/8.60 [v4: A_b_vec_c_vec$] : ? [v5: A_iarray_iarray$] : ? [v6: A_iarray_iarray$] :
% 56.66/8.60 ? [v7: A_iarray_iarray_a_iarray_iarray_prod$] : ? [v8: A_iarray_iarray$] :
% 56.66/8.60 (snd$l(v3) = v4 & gauss_Jordan_upt_k_iarrays_PA$(v6, ka$) = v7 &
% 56.66/8.60 matrix_to_iarray$a(v4) = v5 & matrix_to_iarray$a(a$) = v6 & ncols$(a$) = v0
% 56.66/8.60 & gauss_Jordan_upt_k_PA$(a$, ka$) = v3 & snd$c(v7) = v8 & fun_app$b(of_nat$,
% 56.66/8.60 v0) = v1 & fun_app$b(of_nat$, ka$) = v2 & Nat$(v0) & A_b_vec_c_vec$(v4) &
% 56.66/8.60 A_c_vec_c_vec_a_b_vec_c_vec_prod$(v3) & A_iarray_iarray$(v8) &
% 56.66/8.60 A_iarray_iarray$(v6) & A_iarray_iarray$(v5) &
% 56.66/8.60 A_iarray_iarray_a_iarray_iarray_prod$(v7) & (v8 = v5 | ~ ($lesseq(1,
% 56.66/8.60 $difference(v1, v2)))))
% 56.66/8.60
% 56.66/8.60 (axiom280)
% 56.66/8.61 Nat_int_fun$(of_nat$) &
% 56.66/8.61 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$(gauss_Jordan_column_k_PA$)
% 56.66/8.61 & A$(one$) & Nat$(ka$) &
% 56.66/8.61 A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$(gauss_Jordan_column_k_iarrays_PA$)
% 56.66/8.61 & A_b_vec_c_vec$(a$) & ? [v0: Nat$] : ? [v1: int] : ? [v2: int] : ? [v3:
% 56.66/8.61 A_c_vec_c_vec$] : ? [v4: Nat$] : ? [v5: Nat_a_b_vec_c_vec_prod$] : ? [v6:
% 56.66/8.61 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v7: Nat$] : ? [v8:
% 56.66/8.61 Nat_list$] : ? [v9: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v10:
% 56.66/8.61 Nat_a_b_vec_c_vec_prod$] : ? [v11: Nat$] : ? [v12: int] : ? [v13:
% 56.66/8.61 A_iarray_iarray$] : ? [v14: Nat$] : ? [v15: A_iarray_iarray$] : ? [v16:
% 56.66/8.61 Nat_a_iarray_iarray_prod$] : ? [v17:
% 56.66/8.61 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ? [v18:
% 56.66/8.61 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ? [v19:
% 56.66/8.61 Nat_a_iarray_iarray_prod$] : ? [v20: Nat$] : ? [v21: int] :
% 56.66/8.61 (nrows_iarray$(v13) = v14 & mat_iarray$(one$, v14) = v15 &
% 56.66/8.61 foldl$a(gauss_Jordan_column_k_iarrays_PA$, v17, v8) = v18 &
% 56.66/8.61 matrix_to_iarray$a(a$) = v13 & ncols$(a$) = v0 & snd$d(v18) = v19 &
% 56.66/8.61 pair$d(v15, v16) = v17 & fst$b(v19) = v20 & pair$b(v4, v13) = v16 & snd$(v9)
% 56.66/8.61 = v10 & fst$a(v10) = v11 & mat$(one$) = v3 & pair$a(v4, a$) = v5 & pair$(v3,
% 56.66/8.61 v5) = v6 & fun_app$b(of_nat$, v20) = v21 & fun_app$b(of_nat$, v11) = v12 &
% 56.66/8.61 fun_app$b(of_nat$, v0) = v1 & fun_app$b(of_nat$, ka$) = v2 & nat$($sum(v2,
% 56.66/8.61 1)) = v7 & nat$(0) = v4 & upt$(v4, v7) = v8 &
% 56.66/8.61 foldl$(gauss_Jordan_column_k_PA$, v6, v8) = v9 &
% 56.66/8.61 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(v18) &
% 56.66/8.61 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(v17) &
% 56.66/8.61 Nat_a_b_vec_c_vec_prod$(v10) & Nat_a_b_vec_c_vec_prod$(v5) &
% 56.66/8.61 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v9) &
% 56.66/8.61 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v6) &
% 56.66/8.61 Nat_a_iarray_iarray_prod$(v19) & Nat_a_iarray_iarray_prod$(v16) & Nat$(v20)
% 56.66/8.61 & Nat$(v14) & Nat$(v11) & Nat$(v7) & Nat$(v4) & Nat$(v0) & Nat_list$(v8) &
% 56.66/8.61 A_iarray_iarray$(v15) & A_iarray_iarray$(v13) & A_c_vec_c_vec$(v3) & (v21 =
% 56.66/8.61 v12 | ~ ($lesseq(1, $difference(v1, v2)))))
% 56.66/8.61
% 56.66/8.61 (axiom281)
% 56.86/8.61 Nat_int_fun$(of_nat$) &
% 56.86/8.61 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$(gauss_Jordan_column_k_PA$)
% 56.86/8.61 & A$(one$) & Nat$(ka$) &
% 56.86/8.61 A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$(gauss_Jordan_column_k_iarrays_PA$)
% 56.86/8.61 & A_b_vec_c_vec$(a$) & ? [v0: A_c_vec_c_vec$] : ? [v1: Nat$] : ? [v2:
% 56.86/8.61 Nat_a_b_vec_c_vec_prod$] : ? [v3:
% 56.86/8.61 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v4: int] : ? [v5: Nat$] :
% 56.86/8.61 ? [v6: Nat_list$] : ? [v7: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ?
% 56.86/8.61 [v8: Nat_a_b_vec_c_vec_prod$] : ? [v9: Nat$] : ? [v10: int] : ? [v11:
% 56.86/8.61 A_iarray_iarray$] : ? [v12: Nat$] : ? [v13: A_iarray_iarray$] : ? [v14:
% 56.86/8.61 Nat_a_iarray_iarray_prod$] : ? [v15:
% 56.86/8.61 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ? [v16:
% 56.86/8.61 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ? [v17:
% 56.86/8.61 Nat_a_iarray_iarray_prod$] : ? [v18: Nat$] : (nrows_iarray$(v11) = v12 &
% 56.86/8.61 mat_iarray$(one$, v12) = v13 & foldl$a(gauss_Jordan_column_k_iarrays_PA$,
% 56.86/8.61 v15, v6) = v16 & matrix_to_iarray$a(a$) = v11 & snd$d(v16) = v17 &
% 56.86/8.61 pair$d(v13, v14) = v15 & fst$b(v17) = v18 & pair$b(v1, v11) = v14 & snd$(v7)
% 56.86/8.61 = v8 & fst$a(v8) = v9 & mat$(one$) = v0 & pair$a(v1, a$) = v2 & pair$(v0,
% 56.86/8.61 v2) = v3 & fun_app$b(of_nat$, v18) = v10 & fun_app$b(of_nat$, v9) = v10 &
% 56.86/8.61 fun_app$b(of_nat$, ka$) = v4 & nat$($sum(v4, 1)) = v5 & nat$(0) = v1 &
% 56.86/8.61 upt$(v1, v5) = v6 & foldl$(gauss_Jordan_column_k_PA$, v3, v6) = v7 &
% 56.86/8.61 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(v16) &
% 56.86/8.61 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(v15) &
% 56.86/8.61 Nat_a_b_vec_c_vec_prod$(v8) & Nat_a_b_vec_c_vec_prod$(v2) &
% 56.86/8.61 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v7) &
% 56.86/8.61 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v3) &
% 56.86/8.61 Nat_a_iarray_iarray_prod$(v17) & Nat_a_iarray_iarray_prod$(v14) & Nat$(v18)
% 56.86/8.61 & Nat$(v12) & Nat$(v9) & Nat$(v5) & Nat$(v1) & Nat_list$(v6) &
% 56.86/8.61 A_iarray_iarray$(v13) & A_iarray_iarray$(v11) & A_c_vec_c_vec$(v0))
% 56.86/8.61
% 56.86/8.61 (axiom282)
% 56.86/8.61 Nat_int_fun$(of_nat$) & A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(b$) &
% 56.86/8.61 A$(one$) & Nat$(ka$) &
% 56.86/8.61 A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$(gauss_Jordan_column_k_iarrays_PA$)
% 56.86/8.61 & A_b_vec_c_vec$(a$) & ? [v0: A_iarray_iarray$] : ? [v1: Nat$] : ? [v2:
% 56.86/8.61 A_iarray_iarray$] : ? [v3: Nat$] : ? [v4: Nat_a_iarray_iarray_prod$] : ?
% 56.86/8.61 [v5: A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ? [v6: int] : ? [v7:
% 56.86/8.61 Nat$] : ? [v8: Nat_list$] : (nrows_iarray$(v0) = v1 & mat_iarray$(one$, v1)
% 56.86/8.61 = v2 & foldl$a(gauss_Jordan_column_k_iarrays_PA$, v5, v8) = b$ &
% 56.86/8.61 matrix_to_iarray$a(a$) = v0 & pair$d(v2, v4) = v5 & pair$b(v3, v0) = v4 &
% 56.86/8.61 fun_app$b(of_nat$, ka$) = v6 & nat$($sum(v6, 1)) = v7 & nat$(0) = v3 &
% 56.86/8.61 upt$(v3, v7) = v8 & A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(v5) &
% 56.86/8.61 Nat_a_iarray_iarray_prod$(v4) & Nat$(v7) & Nat$(v3) & Nat$(v1) &
% 56.86/8.61 Nat_list$(v8) & A_iarray_iarray$(v2) & A_iarray_iarray$(v0))
% 56.86/8.61
% 56.86/8.61 (axiom285)
% 56.86/8.62 Nat_int_fun$(of_nat$) & A$(one$) &
% 56.86/8.62 A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$(gauss_Jordan_column_k_iarrays_PA$)
% 56.86/8.62 & ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: A_iarray_iarray$] : !
% 56.86/8.62 [v2: Nat$] : ! [v3: Nat$] : ! [v4: A_iarray_iarray$] : ! [v5:
% 56.86/8.62 Nat_a_iarray_iarray_prod$] : ! [v6:
% 56.86/8.62 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v7: int] : ! [v8:
% 56.86/8.62 Nat$] : ! [v9: Nat_list$] : ! [v10:
% 56.86/8.62 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v11:
% 56.86/8.62 A_iarray_iarray$] : ! [v12: Nat_a_iarray_iarray_prod$] : ! [v13:
% 56.86/8.62 A_iarray_iarray$] : ! [v14: A_iarray_iarray_a_iarray_iarray_prod$] : ( ~
% 56.86/8.62 (nrows_iarray$(v1) = v3) | ~ (mat_iarray$(one$, v3) = v4) | ~
% 56.86/8.62 (foldl$a(gauss_Jordan_column_k_iarrays_PA$, v6, v9) = v10) | ~
% 56.86/8.62 (fst$d(v10) = v11) | ~ (snd$d(v10) = v12) | ~ (pair$d(v4, v5) = v6) | ~
% 56.86/8.62 (pair$c(v11, v13) = v14) | ~ (snd$b(v12) = v13) | ~ (pair$b(v0, v1) =
% 56.86/8.62 v5) | ~ (fun_app$b(of_nat$, v2) = v7) | ~ (nat$($sum(v7, 1)) = v8) |
% 56.86/8.62 ~ (upt$(v0, v8) = v9) | ~ Nat$(v2) | ~ A_iarray_iarray$(v1) |
% 56.86/8.62 (gauss_Jordan_upt_k_iarrays_PA$(v1, v2) = v14 &
% 56.86/8.62 A_iarray_iarray_a_iarray_iarray_prod$(v14))))
% 56.86/8.62
% 56.86/8.62 (axiom29)
% 56.86/8.62 Nat_int_fun$(of_nat$) &
% 56.86/8.62 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$(gauss_Jordan_column_k_PA$)
% 56.86/8.62 & A$(one$) & Nat$(ka$) & A_b_vec_c_vec$(a$) & ? [v0: int] : ? [v1: Nat$] :
% 56.86/8.62 ? [v2: A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ? [v3: A_c_vec_c_vec$] : ? [v4:
% 56.86/8.62 A_iarray_iarray$] : ? [v5: A_c_vec_c_vec$] : ? [v6: Nat$] : ? [v7:
% 56.86/8.62 Nat_a_b_vec_c_vec_prod$] : ? [v8:
% 56.86/8.62 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v9: Nat$] : ? [v10:
% 56.86/8.62 Nat_list$] : ? [v11: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v12:
% 56.86/8.62 A_c_vec_c_vec$] : (gauss_Jordan_upt_k_PA$(a$, v1) = v2 & fst$k(v2) = v3 &
% 56.86/8.62 mat$(one$) = v5 & pair$a(v6, a$) = v7 & pair$(v5, v7) = v8 &
% 56.86/8.62 fun_app$b(of_nat$, ka$) = v0 & nat$($sum(v0, 2)) = v9 & nat$($sum(v0, 1)) =
% 56.86/8.62 v1 & nat$(0) = v6 & upt$(v6, v9) = v10 & foldl$(gauss_Jordan_column_k_PA$,
% 56.86/8.62 v8, v10) = v11 & fst$(v11) = v12 & matrix_to_iarray$(v12) = v4 &
% 56.86/8.62 matrix_to_iarray$(v3) = v4 & Nat_a_b_vec_c_vec_prod$(v7) &
% 56.86/8.62 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v11) &
% 56.86/8.62 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v8) & Nat$(v9) & Nat$(v6) &
% 56.86/8.62 Nat$(v1) & Nat_list$(v10) & A_c_vec_c_vec_a_b_vec_c_vec_prod$(v2) &
% 56.86/8.62 A_iarray_iarray$(v4) & A_c_vec_c_vec$(v12) & A_c_vec_c_vec$(v5) &
% 56.86/8.62 A_c_vec_c_vec$(v3))
% 56.86/8.62
% 56.86/8.62 (axiom3)
% 56.86/8.62 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(a$a) & ? [v0: A_c_vec_c_vec$] : ?
% 56.86/8.62 [v1: Nat_a_b_vec_c_vec_prod$] : ? [v2: Nat$] : ? [v3: A_b_vec_c_vec$] : ?
% 56.86/8.62 [v4: Nat_a_b_vec_c_vec_prod$] : (snd$(a$a) = v1 & fst$a(v1) = v2 & snd$a(v1) =
% 56.86/8.62 v3 & pair$a(v2, v3) = v4 & pair$(v0, v4) = a$a & fst$(a$a) = v0 &
% 56.86/8.62 Nat_a_b_vec_c_vec_prod$(v4) & Nat_a_b_vec_c_vec_prod$(v1) & Nat$(v2) &
% 56.86/8.62 A_b_vec_c_vec$(v3) & A_c_vec_c_vec$(v0))
% 56.86/8.62
% 56.86/8.62 (axiom30)
% 56.86/8.62 Nat_int_fun$(of_nat$) &
% 56.86/8.62 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$(gauss_Jordan_column_k_PA$)
% 56.86/8.62 & A$(one$) & Nat$(ka$) & A_b_vec_c_vec$(a$) & ? [v0: int] : ? [v1: Nat$] :
% 56.86/8.62 ? [v2: A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ? [v3: A_c_vec_c_vec$] : ? [v4:
% 56.86/8.62 A_iarray_iarray$] : ? [v5: A_c_vec_c_vec$] : ? [v6: Nat$] : ? [v7:
% 56.86/8.62 Nat_a_b_vec_c_vec_prod$] : ? [v8:
% 56.86/8.62 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v9: Nat_list$] : ? [v10:
% 56.86/8.62 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v11:
% 56.86/8.62 Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ? [v12:
% 56.86/8.62 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v13: A_c_vec_c_vec$] :
% 56.86/8.62 (gauss_Jordan_upt_k_PA$(a$, v1) = v2 & fst$k(v2) = v3 & mat$(one$) = v5 &
% 56.86/8.62 pair$a(v6, a$) = v7 & pair$(v5, v7) = v8 & fun_app$b(of_nat$, ka$) = v0 &
% 56.86/8.62 nat$($sum(v0, 1)) = v1 & nat$(0) = v6 & upt$(v6, v1) = v9 &
% 56.86/8.62 foldl$(gauss_Jordan_column_k_PA$, v8, v9) = v10 &
% 56.86/8.62 fun_app$a(gauss_Jordan_column_k_PA$, v10) = v11 & fun_app$(v11, v1) = v12 &
% 56.86/8.62 fst$(v12) = v13 & matrix_to_iarray$(v13) = v4 & matrix_to_iarray$(v3) = v4 &
% 56.86/8.62 Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(v11) &
% 56.86/8.62 Nat_a_b_vec_c_vec_prod$(v7) &
% 56.86/8.62 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v12) &
% 56.86/8.62 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v10) &
% 56.86/8.62 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v8) & Nat$(v6) & Nat$(v1) &
% 56.86/8.62 Nat_list$(v9) & A_c_vec_c_vec_a_b_vec_c_vec_prod$(v2) & A_iarray_iarray$(v4)
% 56.86/8.62 & A_c_vec_c_vec$(v13) & A_c_vec_c_vec$(v5) & A_c_vec_c_vec$(v3))
% 56.86/8.62
% 56.86/8.62 (axiom31)
% 56.86/8.63 Nat_int_fun$(of_nat$) &
% 56.86/8.63 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$(gauss_Jordan_column_k_PA$)
% 56.86/8.63 & A$(one$) & Nat$(ka$) & A_b_vec_c_vec$(a$) & ? [v0: Nat$] : ? [v1: int] :
% 56.86/8.63 ? [v2: A_c_vec_c_vec$] : ? [v3: Nat$] : ? [v4: Nat_a_b_vec_c_vec_prod$] : ?
% 56.86/8.63 [v5: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v6: int] : ? [v7:
% 56.86/8.63 Nat$] : ? [v8: Nat_list$] : ? [v9:
% 56.86/8.63 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v10:
% 56.86/8.63 Nat_a_b_vec_c_vec_prod$] : ? [v11: Nat$] : ? [v12: int] : ($lesseq(v12,
% 56.86/8.63 v1) & nrows$(a$) = v0 & snd$(v9) = v10 & fst$a(v10) = v11 & mat$(one$) =
% 56.86/8.63 v2 & pair$a(v3, a$) = v4 & pair$(v2, v4) = v5 & fun_app$b(of_nat$, v11) =
% 56.86/8.63 v12 & fun_app$b(of_nat$, v0) = v1 & fun_app$b(of_nat$, ka$) = v6 &
% 56.86/8.63 nat$($sum(v6, 1)) = v7 & nat$(0) = v3 & upt$(v3, v7) = v8 &
% 56.86/8.63 foldl$(gauss_Jordan_column_k_PA$, v5, v8) = v9 &
% 56.86/8.63 Nat_a_b_vec_c_vec_prod$(v10) & Nat_a_b_vec_c_vec_prod$(v4) &
% 56.86/8.63 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v9) &
% 56.86/8.63 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v5) & Nat$(v11) & Nat$(v7) &
% 56.86/8.63 Nat$(v3) & Nat$(v0) & Nat_list$(v8) & A_c_vec_c_vec$(v2))
% 56.86/8.63
% 56.86/8.63 (axiom378)
% 56.86/8.63 Nat_int_fun$(of_nat$) &
% 56.86/8.63 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$(gauss_Jordan_column_k_PA$)
% 56.86/8.63 & A$(one$) & ? [v0: A_c_vec_c_vec$] : ? [v1: Nat$] : (mat$(one$) = v0 &
% 56.86/8.63 nat$(0) = v1 & Nat$(v1) & A_c_vec_c_vec$(v0) & ! [v2: A_b_vec_c_vec$] : !
% 56.86/8.63 [v3: Nat$] : ! [v4: Nat_a_b_vec_c_vec_prod$] : ! [v5:
% 56.86/8.63 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v6: int] : ! [v7: Nat$]
% 56.86/8.63 : ! [v8: Nat_list$] : ! [v9: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] :
% 56.86/8.63 ! [v10: A_c_vec_c_vec$] : ! [v11: Nat_a_b_vec_c_vec_prod$] : ! [v12:
% 56.86/8.63 A_b_vec_c_vec$] : ! [v13: A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ( ~
% 56.86/8.63 (pair$l(v10, v12) = v13) | ~ (snd$(v9) = v11) | ~ (snd$a(v11) = v12) |
% 56.86/8.63 ~ (pair$a(v1, v2) = v4) | ~ (pair$(v0, v4) = v5) | ~ (fun_app$b(of_nat$,
% 56.86/8.63 v3) = v6) | ~ (nat$($sum(v6, 1)) = v7) | ~ (upt$(v1, v7) = v8) | ~
% 56.86/8.63 (foldl$(gauss_Jordan_column_k_PA$, v5, v8) = v9) | ~ (fst$(v9) = v10) |
% 56.86/8.63 ~ Nat$(v3) | ~ A_b_vec_c_vec$(v2) | (gauss_Jordan_upt_k_PA$(v2, v3) = v13
% 56.86/8.63 & A_c_vec_c_vec_a_b_vec_c_vec_prod$(v13))))
% 56.86/8.63
% 56.86/8.63 (axiom60)
% 56.86/8.63 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(b$) &
% 56.86/8.63 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(a$a) & ? [v0: A_c_vec_c_vec$] : ?
% 56.86/8.63 [v1: A_iarray_iarray$] : (fst$d(b$) = v1 & fst$(a$a) = v0 &
% 56.86/8.63 matrix_to_iarray$(v0) = v1 & A_iarray_iarray$(v1) & A_c_vec_c_vec$(v0))
% 56.86/8.63
% 56.86/8.63 (axiom61)
% 56.86/8.63 Nat_int_fun$(of_nat$) & A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(b$) &
% 56.86/8.63 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(a$a) & ? [v0:
% 56.86/8.63 Nat_a_b_vec_c_vec_prod$] : ? [v1: Nat$] : ? [v2: int] : ? [v3:
% 56.86/8.63 Nat_a_iarray_iarray_prod$] : ? [v4: Nat$] : (snd$d(b$) = v3 & fst$b(v3) =
% 56.86/8.63 v4 & snd$(a$a) = v0 & fst$a(v0) = v1 & fun_app$b(of_nat$, v4) = v2 &
% 56.86/8.63 fun_app$b(of_nat$, v1) = v2 & Nat_a_b_vec_c_vec_prod$(v0) &
% 56.86/8.63 Nat_a_iarray_iarray_prod$(v3) & Nat$(v4) & Nat$(v1))
% 56.86/8.63
% 56.86/8.63 (conjecture0)
% 56.86/8.63 Nat_int_fun$(of_nat$) &
% 56.86/8.63 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$(gauss_Jordan_column_k_PA$)
% 56.86/8.63 & A$(one$) & Nat$(ka$) & A_b_vec_c_vec$(a$) & ? [v0: A_c_vec_c_vec$] : ?
% 56.86/8.63 [v1: Nat$] : ? [v2: Nat_a_b_vec_c_vec_prod$] : ? [v3:
% 56.86/8.63 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v4: int] : ? [v5: Nat$] :
% 56.86/8.63 ? [v6: Nat_list$] : ? [v7: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ?
% 56.86/8.63 [v8: Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ? [v9:
% 56.86/8.63 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v10: A_c_vec_c_vec$] : ?
% 56.86/8.63 [v11: A_iarray_iarray$] : ? [v12: A_c_vec_c_vec$] : ? [v13:
% 56.86/8.63 Nat_a_b_vec_c_vec_prod$] : ? [v14: Nat$] : ? [v15: A_b_vec_c_vec$] : ?
% 56.86/8.63 [v16: Nat_a_b_vec_c_vec_prod$] : ? [v17:
% 56.86/8.63 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v18:
% 56.86/8.63 Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ? [v19:
% 56.86/8.63 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v20: A_c_vec_c_vec$] : ?
% 56.86/8.63 [v21: A_iarray_iarray$] : ( ~ (v21 = v11) & snd$(v7) = v13 & fst$a(v13) = v14
% 56.86/8.63 & snd$a(v13) = v15 & mat$(one$) = v0 & pair$a(v14, v15) = v16 & pair$a(v1,
% 56.86/8.63 a$) = v2 & pair$(v12, v16) = v17 & pair$(v0, v2) = v3 & fun_app$b(of_nat$,
% 56.86/8.63 ka$) = v4 & nat$($sum(v4, 1)) = v5 & nat$(0) = v1 & upt$(v1, v5) = v6 &
% 56.86/8.63 foldl$(gauss_Jordan_column_k_PA$, v3, v6) = v7 &
% 56.86/8.63 fun_app$a(gauss_Jordan_column_k_PA$, v17) = v18 &
% 56.86/8.63 fun_app$a(gauss_Jordan_column_k_PA$, v7) = v8 & fun_app$(v18, v5) = v19 &
% 56.86/8.63 fun_app$(v8, v5) = v9 & fst$(v19) = v20 & fst$(v9) = v10 & fst$(v7) = v12 &
% 56.86/8.63 matrix_to_iarray$(v20) = v21 & matrix_to_iarray$(v10) = v11 &
% 56.86/8.63 Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(v18) &
% 56.86/8.63 Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(v8) &
% 56.86/8.63 Nat_a_b_vec_c_vec_prod$(v16) & Nat_a_b_vec_c_vec_prod$(v13) &
% 56.86/8.63 Nat_a_b_vec_c_vec_prod$(v2) &
% 56.86/8.64 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v19) &
% 56.86/8.64 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v17) &
% 56.86/8.64 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v9) &
% 56.86/8.64 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v7) &
% 56.86/8.64 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v3) & Nat$(v14) & Nat$(v5) &
% 56.86/8.64 Nat$(v1) & A_b_vec_c_vec$(v15) & Nat_list$(v6) & A_iarray_iarray$(v21) &
% 56.86/8.64 A_iarray_iarray$(v11) & A_c_vec_c_vec$(v20) & A_c_vec_c_vec$(v12) &
% 56.86/8.64 A_c_vec_c_vec$(v10) & A_c_vec_c_vec$(v0))
% 56.86/8.64
% 56.86/8.64 (function-axioms)
% 56.98/8.66 ! [v0: A_iarray_iarray_a_iarray_iarray_prod$] : ! [v1:
% 56.98/8.66 A_iarray_iarray_a_iarray_iarray_prod$] : ! [v2: Nat$] : ! [v3: Nat$] : !
% 56.98/8.66 [v4: A_iarray_iarray_a_iarray_iarray_prod$] : (v1 = v0 | ~
% 56.98/8.66 (gauss_Jordan_in_ij_iarrays_PA$(v4, v3, v2) = v1) | ~
% 56.98/8.66 (gauss_Jordan_in_ij_iarrays_PA$(v4, v3, v2) = v0)) & ! [v0:
% 56.98/8.66 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v1:
% 56.98/8.66 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v2: Nat_list$] : !
% 56.98/8.66 [v3: A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v4:
% 56.98/8.66 A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$]
% 56.98/8.66 : (v1 = v0 | ~ (foldl$a(v4, v3, v2) = v1) | ~ (foldl$a(v4, v3, v2) = v0)) &
% 56.98/8.66 ! [v0: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v1:
% 56.98/8.66 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v2: Nat_list$] : ! [v3:
% 56.98/8.66 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v4:
% 56.98/8.66 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$]
% 56.98/8.66 : (v1 = v0 | ~ (foldl$(v4, v3, v2) = v1) | ~ (foldl$(v4, v3, v2) = v0)) & !
% 56.98/8.66 [v0: A_iarray_iarray_a_iarray_iarray_prod$] : ! [v1:
% 56.98/8.66 A_iarray_iarray_a_iarray_iarray_prod$] : ! [v2:
% 56.98/8.66 A_iarray_iarray_a_iarray_iarray_prod$] : ! [v3:
% 56.98/8.66 A_iarray_iarray_a_iarray_iarray_prod$] : (v1 = v0 | ~ (plus$l(v3, v2) = v1)
% 56.98/8.66 | ~ (plus$l(v3, v2) = v0)) & ! [v0: Nat_nat_prod$] : ! [v1:
% 56.98/8.66 Nat_nat_prod$] : ! [v2: Nat_nat_prod$] : ! [v3: Nat_nat_prod$] : (v1 = v0
% 56.98/8.66 | ~ (plus$k(v3, v2) = v1) | ~ (plus$k(v3, v2) = v0)) & ! [v0:
% 56.98/8.66 Nat_int_prod$] : ! [v1: Nat_int_prod$] : ! [v2: Nat_int_prod$] : ! [v3:
% 56.98/8.66 Nat_int_prod$] : (v1 = v0 | ~ (plus$j(v3, v2) = v1) | ~ (plus$j(v3, v2) =
% 56.98/8.66 v0)) & ! [v0: A_b_vec_c_vec$] : ! [v1: A_b_vec_c_vec$] : ! [v2:
% 56.98/8.66 A_b_vec_c_vec$] : ! [v3: A_b_vec_c_vec$] : (v1 = v0 | ~ (plus$i(v3, v2) =
% 56.98/8.66 v1) | ~ (plus$i(v3, v2) = v0)) & ! [v0: Int_nat_prod$] : ! [v1:
% 56.98/8.66 Int_nat_prod$] : ! [v2: Int_nat_prod$] : ! [v3: Int_nat_prod$] : (v1 = v0
% 56.98/8.66 | ~ (plus$h(v3, v2) = v1) | ~ (plus$h(v3, v2) = v0)) & ! [v0:
% 56.98/8.66 Int_int_prod$] : ! [v1: Int_int_prod$] : ! [v2: Int_int_prod$] : ! [v3:
% 56.98/8.66 Int_int_prod$] : (v1 = v0 | ~ (plus$g(v3, v2) = v1) | ~ (plus$g(v3, v2) =
% 56.98/8.66 v0)) & ! [v0: A_iarray_iarray$] : ! [v1: A_iarray_iarray$] : ! [v2:
% 56.98/8.66 A_iarray_iarray$] : ! [v3: A_iarray_iarray$] : (v1 = v0 | ~ (plus$e(v3,
% 56.98/8.66 v2) = v1) | ~ (plus$e(v3, v2) = v0)) & ! [v0:
% 56.98/8.66 Nat_a_iarray_iarray_prod$] : ! [v1: Nat_a_iarray_iarray_prod$] : ! [v2:
% 56.98/8.66 Nat_a_iarray_iarray_prod$] : ! [v3: Nat_a_iarray_iarray_prod$] : (v1 = v0 |
% 56.98/8.66 ~ (plus$f(v3, v2) = v1) | ~ (plus$f(v3, v2) = v0)) & ! [v0:
% 56.98/8.66 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v1:
% 56.98/8.66 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v2:
% 56.98/8.66 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v3:
% 56.98/8.66 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : (v1 = v0 | ~ (plus$d(v3,
% 56.98/8.66 v2) = v1) | ~ (plus$d(v3, v2) = v0)) & ! [v0: A_c_vec_c_vec$] : !
% 56.98/8.66 [v1: A_c_vec_c_vec$] : ! [v2: A_c_vec_c_vec$] : ! [v3: A_c_vec_c_vec$] : (v1
% 56.98/8.66 = v0 | ~ (plus$b(v3, v2) = v1) | ~ (plus$b(v3, v2) = v0)) & ! [v0:
% 56.98/8.66 Nat_a_b_vec_c_vec_prod$] : ! [v1: Nat_a_b_vec_c_vec_prod$] : ! [v2:
% 56.98/8.66 Nat_a_b_vec_c_vec_prod$] : ! [v3: Nat_a_b_vec_c_vec_prod$] : (v1 = v0 | ~
% 56.98/8.66 (plus$c(v3, v2) = v1) | ~ (plus$c(v3, v2) = v0)) & ! [v0:
% 56.98/8.66 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v1:
% 56.98/8.66 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v2:
% 56.98/8.66 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v3:
% 56.98/8.66 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : (v1 = v0 | ~ (plus$a(v3, v2)
% 56.98/8.66 = v1) | ~ (plus$a(v3, v2) = v0)) & ! [v0: A_iarray$] : ! [v1:
% 56.98/8.66 A_iarray$] : ! [v2: A_iarray_iarray$] : ! [v3: Nat$] : (v1 = v0 | ~
% 56.98/8.66 (column_iarray$(v3, v2) = v1) | ~ (column_iarray$(v3, v2) = v0)) & ! [v0:
% 56.98/8.66 A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ! [v1:
% 56.98/8.66 A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ! [v2: A_b_vec_c_vec$] : ! [v3:
% 56.98/8.66 A_c_vec_c_vec$] : (v1 = v0 | ~ (pair$l(v3, v2) = v1) | ~ (pair$l(v3, v2) =
% 56.98/8.66 v0)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: Int_int_fun$]
% 56.98/8.66 : (v1 = v0 | ~ (fun_app$z(v3, v2) = v1) | ~ (fun_app$z(v3, v2) = v0)) & !
% 56.98/8.66 [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: int] : ! [v3:
% 56.98/8.66 Int_int_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$y(v3, v2) = v1) | ~
% 56.98/8.66 (fun_app$y(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 56.98/8.66 MultipleValueBool] : ! [v2: int] : ! [v3: Int_bool_fun$] : (v1 = v0 | ~
% 56.98/8.66 (fun_app$x(v3, v2) = v1) | ~ (fun_app$x(v3, v2) = v0)) & ! [v0:
% 56.98/8.66 A_iarray_iarray$] : ! [v1: A_iarray_iarray$] : ! [v2: Nat$] : ! [v3: A$]
% 56.98/8.66 : (v1 = v0 | ~ (mat_iarray$(v3, v2) = v1) | ~ (mat_iarray$(v3, v2) = v0)) &
% 56.98/8.66 ! [v0: A_iarray_iarray_a_iarray_iarray_prod$] : ! [v1:
% 56.98/8.66 A_iarray_iarray_a_iarray_iarray_prod$] : ! [v2: Nat$] : ! [v3:
% 56.98/8.66 A_iarray_iarray$] : (v1 = v0 | ~ (gauss_Jordan_upt_k_iarrays_PA$(v3, v2) =
% 56.98/8.66 v1) | ~ (gauss_Jordan_upt_k_iarrays_PA$(v3, v2) = v0)) & ! [v0:
% 56.98/8.66 Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$] : ! [v1:
% 56.98/8.66 Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$] : ! [v2:
% 56.98/8.66 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v3:
% 56.98/8.66 A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$]
% 56.98/8.66 : (v1 = v0 | ~ (fun_app$w(v3, v2) = v1) | ~ (fun_app$w(v3, v2) = v0)) & !
% 56.98/8.66 [v0: A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v1:
% 56.98/8.66 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v2: Nat$] : ! [v3:
% 56.98/8.66 Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$] : (v1 = v0 | ~
% 56.98/8.66 (fun_app$v(v3, v2) = v1) | ~ (fun_app$v(v3, v2) = v0)) & ! [v0:
% 56.98/8.66 Nat_a_c_vec_c_vec_prod$] : ! [v1: Nat_a_c_vec_c_vec_prod$] : ! [v2:
% 56.98/8.66 A_c_vec_c_vec$] : ! [v3: Nat$] : (v1 = v0 | ~ (pair$k(v3, v2) = v1) | ~
% 56.98/8.66 (pair$k(v3, v2) = v0)) & ! [v0: A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$]
% 56.98/8.66 : ! [v1: A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$] : ! [v2:
% 56.98/8.67 Nat_a_c_vec_c_vec_prod$] : ! [v3: A_c_vec_c_vec$] : (v1 = v0 | ~
% 56.98/8.67 (pair$j(v3, v2) = v1) | ~ (pair$j(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$] : ! [v1:
% 56.98/8.67 A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$] : ! [v2: Nat$] : ! [v3:
% 56.98/8.67 A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$] : (v1 = v0 | ~
% 56.98/8.67 (gauss_Jordan_column_k_PA$a(v3, v2) = v1) | ~
% 56.98/8.67 (gauss_Jordan_column_k_PA$a(v3, v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] :
% 56.98/8.67 ! [v2: Nat$] : ! [v3: Nat_nat_fun$] : (v1 = v0 | ~ (fun_app$u(v3, v2) = v1)
% 56.98/8.67 | ~ (fun_app$u(v3, v2) = v0)) & ! [v0: Nat_bool_fun$] : ! [v1:
% 56.98/8.67 Nat_bool_fun$] : ! [v2: Nat$] : ! [v3: Nat_nat_bool_fun_fun$] : (v1 = v0 |
% 56.98/8.67 ~ (fun_app$t(v3, v2) = v1) | ~ (fun_app$t(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat$] : ! [v3:
% 56.98/8.67 Nat_bool_fun$] : (v1 = v0 | ~ (fun_app$s(v3, v2) = v1) | ~ (fun_app$s(v3,
% 56.98/8.67 v2) = v0)) & ! [v0: A_iarray_iarray_bool_fun$] : ! [v1:
% 56.98/8.67 A_iarray_iarray_bool_fun$] : ! [v2: Nat$] : ! [v3:
% 56.98/8.67 Nat_a_iarray_iarray_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$r(v3, v2) = v1)
% 56.98/8.67 | ~ (fun_app$r(v3, v2) = v0)) & ! [v0: A_b_vec_c_vec_bool_fun$] : ! [v1:
% 56.98/8.67 A_b_vec_c_vec_bool_fun$] : ! [v2: Nat$] : ! [v3:
% 56.98/8.67 Nat_a_b_vec_c_vec_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$q(v3, v2) = v1) |
% 56.98/8.67 ~ (fun_app$q(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 56.98/8.67 MultipleValueBool] : ! [v2: A_b_vec_c_vec$] : ! [v3:
% 56.98/8.67 A_b_vec_c_vec_bool_fun$] : (v1 = v0 | ~ (fun_app$p(v3, v2) = v1) | ~
% 56.98/8.67 (fun_app$p(v3, v2) = v0)) & ! [v0: A_iarray_iarray_bool_fun$] : ! [v1:
% 56.98/8.67 A_iarray_iarray_bool_fun$] : ! [v2: A_iarray_iarray$] : ! [v3:
% 56.98/8.67 A_iarray_iarray_a_iarray_iarray_bool_fun_fun$] : (v1 = v0 | ~
% 56.98/8.67 (fun_app$o(v3, v2) = v1) | ~ (fun_app$o(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: A_iarray_iarray$]
% 56.98/8.67 : ! [v3: A_iarray_iarray_bool_fun$] : (v1 = v0 | ~ (fun_app$n(v3, v2) = v1)
% 56.98/8.67 | ~ (fun_app$n(v3, v2) = v0)) & ! [v0: Nat_a_iarray_iarray_prod_bool_fun$]
% 56.98/8.67 : ! [v1: Nat_a_iarray_iarray_prod_bool_fun$] : ! [v2: A_iarray_iarray$] : !
% 56.98/8.67 [v3: A_iarray_iarray_nat_a_iarray_iarray_prod_bool_fun_fun$] : (v1 = v0 | ~
% 56.98/8.67 (fun_app$m(v3, v2) = v1) | ~ (fun_app$m(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 Nat_a_b_vec_c_vec_prod_bool_fun$] : ! [v1:
% 56.98/8.67 Nat_a_b_vec_c_vec_prod_bool_fun$] : ! [v2: A_c_vec_c_vec$] : ! [v3:
% 56.98/8.67 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_bool_fun_fun$] : (v1 = v0 | ~
% 56.98/8.67 (fun_app$l(v3, v2) = v1) | ~ (fun_app$l(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 56.98/8.67 Nat_a_iarray_iarray_prod$] : ! [v3: Nat_a_iarray_iarray_prod_bool_fun$] :
% 56.98/8.67 (v1 = v0 | ~ (fun_app$k(v3, v2) = v1) | ~ (fun_app$k(v3, v2) = v0)) & !
% 56.98/8.67 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 56.98/8.67 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v3:
% 56.98/8.67 A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$] : (v1 = v0 | ~
% 56.98/8.67 (fun_app$j(v3, v2) = v1) | ~ (fun_app$j(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 56.98/8.67 Nat_a_b_vec_c_vec_prod$] : ! [v3: Nat_a_b_vec_c_vec_prod_bool_fun$] : (v1 =
% 56.98/8.67 v0 | ~ (fun_app$i(v3, v2) = v1) | ~ (fun_app$i(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 56.98/8.67 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v3:
% 56.98/8.67 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$] : (v1 = v0 | ~
% 56.98/8.67 (fun_app$h(v3, v2) = v1) | ~ (fun_app$h(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Int_int_prod$] :
% 56.98/8.67 ! [v3: Int_int_prod_bool_fun$] : (v1 = v0 | ~ (fun_app$g(v3, v2) = v1) | ~
% 56.98/8.67 (fun_app$g(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 56.98/8.67 MultipleValueBool] : ! [v2: Int_nat_prod$] : ! [v3:
% 56.98/8.67 Int_nat_prod_bool_fun$] : (v1 = v0 | ~ (fun_app$f(v3, v2) = v1) | ~
% 56.98/8.67 (fun_app$f(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 56.98/8.67 MultipleValueBool] : ! [v2: Nat_int_prod$] : ! [v3:
% 56.98/8.67 Nat_int_prod_bool_fun$] : (v1 = v0 | ~ (fun_app$e(v3, v2) = v1) | ~
% 56.98/8.67 (fun_app$e(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 56.98/8.67 MultipleValueBool] : ! [v2: Nat_nat_prod$] : ! [v3:
% 56.98/8.67 Nat_nat_prod_bool_fun$] : (v1 = v0 | ~ (fun_app$d(v3, v2) = v1) | ~
% 56.98/8.67 (fun_app$d(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 56.98/8.67 MultipleValueBool] : ! [v2: Nat_a_iarray_prod$] : ! [v3:
% 56.98/8.67 Nat_a_iarray_prod_bool_fun$] : (v1 = v0 | ~ (fun_app$c(v3, v2) = v1) | ~
% 56.98/8.67 (fun_app$c(v3, v2) = v0)) & ! [v0: A_c_vec_c_vec_a_b_vec_c_vec_prod$] : !
% 56.98/8.67 [v1: A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ! [v2: Nat$] : ! [v3:
% 56.98/8.67 A_b_vec_c_vec$] : (v1 = v0 | ~ (gauss_Jordan_upt_k_PA$(v3, v2) = v1) | ~
% 56.98/8.67 (gauss_Jordan_upt_k_PA$(v3, v2) = v0)) & ! [v0: Nat_a_iarray_prod$] : !
% 56.98/8.67 [v1: Nat_a_iarray_prod$] : ! [v2: A_iarray$] : ! [v3: Nat$] : (v1 = v0 | ~
% 56.98/8.67 (pair$i(v3, v2) = v1) | ~ (pair$i(v3, v2) = v0)) & ! [v0: Int_int_prod$] :
% 56.98/8.67 ! [v1: Int_int_prod$] : ! [v2: int] : ! [v3: int] : (v1 = v0 | ~
% 56.98/8.67 (pair$h(v3, v2) = v1) | ~ (pair$h(v3, v2) = v0)) & ! [v0: Int_nat_prod$] :
% 56.98/8.67 ! [v1: Int_nat_prod$] : ! [v2: Nat$] : ! [v3: int] : (v1 = v0 | ~
% 56.98/8.67 (pair$g(v3, v2) = v1) | ~ (pair$g(v3, v2) = v0)) & ! [v0: Nat_int_prod$] :
% 56.98/8.67 ! [v1: Nat_int_prod$] : ! [v2: int] : ! [v3: Nat$] : (v1 = v0 | ~
% 56.98/8.67 (pair$f(v3, v2) = v1) | ~ (pair$f(v3, v2) = v0)) & ! [v0: Nat_nat_prod$] :
% 56.98/8.67 ! [v1: Nat_nat_prod$] : ! [v2: Nat$] : ! [v3: Nat$] : (v1 = v0 | ~
% 56.98/8.67 (pair$e(v3, v2) = v1) | ~ (pair$e(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v1:
% 56.98/8.67 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v2:
% 56.98/8.67 Nat_a_iarray_iarray_prod$] : ! [v3: A_iarray_iarray$] : (v1 = v0 | ~
% 56.98/8.67 (pair$d(v3, v2) = v1) | ~ (pair$d(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 A_iarray_iarray_a_iarray_iarray_prod$] : ! [v1:
% 56.98/8.67 A_iarray_iarray_a_iarray_iarray_prod$] : ! [v2: A_iarray_iarray$] : ! [v3:
% 56.98/8.67 A_iarray_iarray$] : (v1 = v0 | ~ (pair$c(v3, v2) = v1) | ~ (pair$c(v3, v2)
% 56.98/8.67 = v0)) & ! [v0: Nat_a_iarray_iarray_prod$] : ! [v1:
% 56.98/8.67 Nat_a_iarray_iarray_prod$] : ! [v2: A_iarray_iarray$] : ! [v3: Nat$] : (v1
% 56.98/8.67 = v0 | ~ (pair$b(v3, v2) = v1) | ~ (pair$b(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 Nat_a_b_vec_c_vec_prod$] : ! [v1: Nat_a_b_vec_c_vec_prod$] : ! [v2:
% 56.98/8.67 A_b_vec_c_vec$] : ! [v3: Nat$] : (v1 = v0 | ~ (pair$a(v3, v2) = v1) | ~
% 56.98/8.67 (pair$a(v3, v2) = v0)) & ! [v0: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$]
% 56.98/8.67 : ! [v1: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v2:
% 56.98/8.67 Nat_a_b_vec_c_vec_prod$] : ! [v3: A_c_vec_c_vec$] : (v1 = v0 | ~
% 56.98/8.67 (pair$(v3, v2) = v1) | ~ (pair$(v3, v2) = v0)) & ! [v0: int] : ! [v1:
% 56.98/8.67 int] : ! [v2: Nat$] : ! [v3: Nat_int_fun$] : (v1 = v0 | ~ (fun_app$b(v3,
% 56.98/8.67 v2) = v1) | ~ (fun_app$b(v3, v2) = v0)) & ! [v0: Nat_list$] : ! [v1:
% 56.98/8.67 Nat_list$] : ! [v2: Nat$] : ! [v3: Nat$] : (v1 = v0 | ~ (upt$(v3, v2) =
% 56.98/8.67 v1) | ~ (upt$(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ! [v1:
% 56.98/8.67 Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ! [v2:
% 56.98/8.67 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v3:
% 56.98/8.67 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$]
% 56.98/8.67 : (v1 = v0 | ~ (fun_app$a(v3, v2) = v1) | ~ (fun_app$a(v3, v2) = v0)) & !
% 56.98/8.67 [v0: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v1:
% 56.98/8.67 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v2: Nat$] : ! [v3:
% 56.98/8.67 Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : (v1 = v0 | ~
% 56.98/8.67 (fun_app$(v3, v2) = v1) | ~ (fun_app$(v3, v2) = v0)) & ! [v0:
% 56.98/8.67 Nat_nat_fun$] : ! [v1: Nat_nat_fun$] : ! [v2: Nat$] : (v1 = v0 | ~
% 56.98/8.67 (plus$(v2) = v1) | ~ (plus$(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : !
% 56.98/8.67 [v2: A_iarray_iarray$] : (v1 = v0 | ~ (nrows_iarray$(v2) = v1) | ~
% 56.98/8.67 (nrows_iarray$(v2) = v0)) & ! [v0: A_b_vec_c_vec$] : ! [v1:
% 56.98/8.67 A_b_vec_c_vec$] : ! [v2: A_c_vec_c_vec_a_b_vec_c_vec_prod$] : (v1 = v0 | ~
% 56.98/8.67 (snd$l(v2) = v1) | ~ (snd$l(v2) = v0)) & ! [v0: A_c_vec_c_vec$] : ! [v1:
% 56.98/8.67 A_c_vec_c_vec$] : ! [v2: A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$] : (v1
% 56.98/8.67 = v0 | ~ (fst$l(v2) = v1) | ~ (fst$l(v2) = v0)) & ! [v0:
% 56.98/8.67 A_iarray_iarray$] : ! [v1: A_iarray_iarray$] : ! [v2: A_b_vec_c_vec$] :
% 56.98/8.67 (v1 = v0 | ~ (matrix_to_iarray$a(v2) = v1) | ~ (matrix_to_iarray$a(v2) =
% 56.98/8.67 v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: A_c_vec_c_vec$] : (v1 = v0
% 56.98/8.67 | ~ (nrows$a(v2) = v1) | ~ (nrows$a(v2) = v0)) & ! [v0: Nat$] : ! [v1:
% 56.98/8.67 Nat$] : ! [v2: A_c_vec_c_vec$] : (v1 = v0 | ~ (ncols$a(v2) = v1) | ~
% 56.98/8.67 (ncols$a(v2) = v0)) & ! [v0: Nat_a_c_vec_c_vec_prod$] : ! [v1:
% 56.98/8.67 Nat_a_c_vec_c_vec_prod$] : ! [v2:
% 56.98/8.67 A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$] : (v1 = v0 | ~ (snd$k(v2) = v1)
% 56.98/8.67 | ~ (snd$k(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 56.98/8.67 A_b_vec_c_vec$] : (v1 = v0 | ~ (ncols$(v2) = v1) | ~ (ncols$(v2) = v0)) &
% 56.98/8.67 ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: A_b_vec_c_vec$] : (v1 = v0 | ~
% 56.98/8.67 (nrows$(v2) = v1) | ~ (nrows$(v2) = v0)) & ! [v0: A_c_vec_c_vec$] : !
% 56.98/8.67 [v1: A_c_vec_c_vec$] : ! [v2: A_c_vec_c_vec_a_b_vec_c_vec_prod$] : (v1 = v0 |
% 56.98/8.67 ~ (fst$k(v2) = v1) | ~ (fst$k(v2) = v0)) & ! [v0: A_c_vec_c_vec$] : !
% 56.98/8.67 [v1: A_c_vec_c_vec$] : ! [v2: Nat_a_c_vec_c_vec_prod$] : (v1 = v0 | ~
% 56.98/8.67 (snd$j(v2) = v1) | ~ (snd$j(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : !
% 56.98/8.67 [v2: Nat_a_c_vec_c_vec_prod$] : (v1 = v0 | ~ (fst$j(v2) = v1) | ~ (fst$j(v2)
% 56.98/8.67 = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_a_iarray_prod$] : (v1
% 56.98/8.67 = v0 | ~ (fst$i(v2) = v1) | ~ (fst$i(v2) = v0)) & ! [v0: A_iarray$] : !
% 56.98/8.67 [v1: A_iarray$] : ! [v2: Nat_a_iarray_prod$] : (v1 = v0 | ~ (snd$i(v2) = v1)
% 56.98/8.67 | ~ (snd$i(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 56.98/8.67 Int_int_prod$] : (v1 = v0 | ~ (fst$h(v2) = v1) | ~ (fst$h(v2) = v0)) & !
% 56.98/8.67 [v0: int] : ! [v1: int] : ! [v2: Int_int_prod$] : (v1 = v0 | ~ (snd$h(v2) =
% 56.98/8.67 v1) | ~ (snd$h(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 56.98/8.67 Int_nat_prod$] : (v1 = v0 | ~ (fst$g(v2) = v1) | ~ (fst$g(v2) = v0)) & !
% 56.98/8.67 [v0: Nat$] : ! [v1: Nat$] : ! [v2: Int_nat_prod$] : (v1 = v0 | ~ (snd$g(v2)
% 56.98/8.67 = v1) | ~ (snd$g(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 56.98/8.67 Nat_int_prod$] : (v1 = v0 | ~ (fst$f(v2) = v1) | ~ (fst$f(v2) = v0)) & !
% 56.98/8.67 [v0: int] : ! [v1: int] : ! [v2: Nat_int_prod$] : (v1 = v0 | ~ (snd$f(v2) =
% 56.98/8.67 v1) | ~ (snd$f(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 56.98/8.67 Nat_nat_prod$] : (v1 = v0 | ~ (fst$e(v2) = v1) | ~ (fst$e(v2) = v0)) & !
% 56.98/8.67 [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_nat_prod$] : (v1 = v0 | ~ (snd$e(v2)
% 56.98/8.67 = v1) | ~ (snd$e(v2) = v0)) & ! [v0: A_iarray_iarray$] : ! [v1:
% 56.98/8.67 A_iarray_iarray$] : ! [v2: A_iarray_iarray_nat_a_iarray_iarray_prod_prod$]
% 56.98/8.67 : (v1 = v0 | ~ (fst$d(v2) = v1) | ~ (fst$d(v2) = v0)) & ! [v0:
% 56.98/8.67 Nat_a_iarray_iarray_prod$] : ! [v1: Nat_a_iarray_iarray_prod$] : ! [v2:
% 56.98/8.67 A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : (v1 = v0 | ~ (snd$d(v2) =
% 56.98/8.67 v1) | ~ (snd$d(v2) = v0)) & ! [v0: A_iarray_iarray$] : ! [v1:
% 56.98/8.67 A_iarray_iarray$] : ! [v2: A_iarray_iarray_a_iarray_iarray_prod$] : (v1 =
% 56.98/8.67 v0 | ~ (fst$c(v2) = v1) | ~ (fst$c(v2) = v0)) & ! [v0: A_iarray_iarray$]
% 56.98/8.67 : ! [v1: A_iarray_iarray$] : ! [v2: A_iarray_iarray_a_iarray_iarray_prod$] :
% 56.98/8.67 (v1 = v0 | ~ (snd$c(v2) = v1) | ~ (snd$c(v2) = v0)) & ! [v0: Nat$] : !
% 56.98/8.67 [v1: Nat$] : ! [v2: Nat_a_iarray_iarray_prod$] : (v1 = v0 | ~ (fst$b(v2) =
% 56.98/8.67 v1) | ~ (fst$b(v2) = v0)) & ! [v0: A_iarray_iarray$] : ! [v1:
% 56.98/8.67 A_iarray_iarray$] : ! [v2: Nat_a_iarray_iarray_prod$] : (v1 = v0 | ~
% 56.98/8.67 (snd$b(v2) = v1) | ~ (snd$b(v2) = v0)) & ! [v0: Nat_a_b_vec_c_vec_prod$] :
% 56.98/8.67 ! [v1: Nat_a_b_vec_c_vec_prod$] : ! [v2:
% 56.98/8.67 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : (v1 = v0 | ~ (snd$(v2) = v1)
% 56.98/8.67 | ~ (snd$(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 56.98/8.67 Nat_a_b_vec_c_vec_prod$] : (v1 = v0 | ~ (fst$a(v2) = v1) | ~ (fst$a(v2) =
% 56.98/8.67 v0)) & ! [v0: A_b_vec_c_vec$] : ! [v1: A_b_vec_c_vec$] : ! [v2:
% 56.98/8.67 Nat_a_b_vec_c_vec_prod$] : (v1 = v0 | ~ (snd$a(v2) = v1) | ~ (snd$a(v2) =
% 56.98/8.67 v0)) & ! [v0: A_c_vec_c_vec$] : ! [v1: A_c_vec_c_vec$] : ! [v2: A$] :
% 56.98/8.67 (v1 = v0 | ~ (mat$(v2) = v1) | ~ (mat$(v2) = v0)) & ! [v0: Nat$] : ! [v1:
% 56.98/8.67 Nat$] : ! [v2: int] : (v1 = v0 | ~ (nat$(v2) = v1) | ~ (nat$(v2) = v0)) &
% 56.98/8.67 ! [v0: A_c_vec_c_vec$] : ! [v1: A_c_vec_c_vec$] : ! [v2:
% 56.98/8.67 A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : (v1 = v0 | ~ (fst$(v2) = v1)
% 56.98/8.67 | ~ (fst$(v2) = v0)) & ! [v0: A_iarray_iarray$] : ! [v1:
% 56.98/8.67 A_iarray_iarray$] : ! [v2: A_c_vec_c_vec$] : (v1 = v0 | ~
% 56.98/8.67 (matrix_to_iarray$(v2) = v1) | ~ (matrix_to_iarray$(v2) = v0))
% 56.98/8.67
% 56.98/8.67 Further assumptions not needed in the proof:
% 56.98/8.67 --------------------------------------------
% 56.98/8.67 axiom10, axiom100, axiom101, axiom102, axiom103, axiom104, axiom105, axiom106,
% 56.98/8.67 axiom107, axiom108, axiom109, axiom11, axiom110, axiom111, axiom112, axiom113,
% 56.98/8.67 axiom114, axiom115, axiom116, axiom117, axiom118, axiom119, axiom12, axiom120,
% 56.98/8.67 axiom121, axiom122, axiom123, axiom124, axiom125, axiom126, axiom127, axiom128,
% 56.98/8.67 axiom129, axiom13, axiom130, axiom131, axiom132, axiom133, axiom134, axiom135,
% 56.98/8.67 axiom137, axiom138, axiom139, axiom14, axiom140, axiom141, axiom142, axiom143,
% 56.98/8.67 axiom144, axiom145, axiom146, axiom147, axiom149, axiom15, axiom150, axiom151,
% 56.98/8.67 axiom152, axiom153, axiom154, axiom155, axiom156, axiom157, axiom158, axiom159,
% 56.98/8.67 axiom16, axiom160, axiom161, axiom162, axiom163, axiom164, axiom165, axiom166,
% 56.98/8.67 axiom167, axiom168, axiom169, axiom17, axiom170, axiom171, axiom172, axiom173,
% 56.98/8.67 axiom174, axiom176, axiom177, axiom178, axiom179, axiom18, axiom180, axiom181,
% 56.98/8.67 axiom182, axiom183, axiom184, axiom185, axiom186, axiom187, axiom188, axiom189,
% 56.98/8.67 axiom19, axiom190, axiom191, axiom192, axiom193, axiom194, axiom195, axiom196,
% 56.98/8.67 axiom197, axiom198, axiom20, axiom200, axiom202, axiom203, axiom205, axiom206,
% 56.98/8.67 axiom207, axiom208, axiom209, axiom21, axiom210, axiom211, axiom212, axiom213,
% 56.98/8.67 axiom215, axiom216, axiom217, axiom218, axiom219, axiom22, axiom220, axiom221,
% 56.98/8.67 axiom222, axiom223, axiom224, axiom225, axiom226, axiom227, axiom228, axiom229,
% 56.98/8.67 axiom23, axiom230, axiom231, axiom235, axiom236, axiom237, axiom238, axiom239,
% 56.98/8.67 axiom24, axiom240, axiom241, axiom242, axiom243, axiom244, axiom245, axiom246,
% 56.98/8.67 axiom247, axiom248, axiom249, axiom25, axiom250, axiom251, axiom252, axiom253,
% 56.98/8.67 axiom254, axiom255, axiom256, axiom257, axiom258, axiom26, axiom262, axiom263,
% 56.98/8.67 axiom264, axiom265, axiom266, axiom267, axiom268, axiom269, axiom27, axiom270,
% 56.98/8.67 axiom271, axiom272, axiom273, axiom274, axiom275, axiom276, axiom277, axiom278,
% 56.98/8.67 axiom279, axiom28, axiom283, axiom284, axiom286, axiom287, axiom288, axiom289,
% 56.98/8.67 axiom290, axiom291, axiom292, axiom293, axiom294, axiom295, axiom296, axiom297,
% 56.98/8.67 axiom298, axiom299, axiom300, axiom301, axiom302, axiom303, axiom304, axiom305,
% 56.98/8.67 axiom306, axiom307, axiom308, axiom309, axiom310, axiom311, axiom312, axiom313,
% 56.98/8.67 axiom314, axiom315, axiom316, axiom317, axiom318, axiom319, axiom32, axiom320,
% 56.98/8.67 axiom321, axiom322, axiom323, axiom324, axiom325, axiom326, axiom327, axiom328,
% 56.98/8.67 axiom329, axiom33, axiom330, axiom331, axiom332, axiom333, axiom334, axiom335,
% 56.98/8.67 axiom336, axiom337, axiom338, axiom339, axiom34, axiom340, axiom341, axiom342,
% 56.98/8.67 axiom343, axiom344, axiom345, axiom346, axiom347, axiom348, axiom349, axiom35,
% 56.98/8.67 axiom350, axiom351, axiom352, axiom353, axiom354, axiom355, axiom356, axiom357,
% 56.98/8.67 axiom358, axiom359, axiom36, axiom360, axiom361, axiom362, axiom363, axiom364,
% 56.98/8.67 axiom365, axiom366, axiom367, axiom368, axiom369, axiom37, axiom370, axiom371,
% 56.98/8.67 axiom372, axiom373, axiom374, axiom375, axiom376, axiom377, axiom379, axiom38,
% 56.98/8.67 axiom380, axiom381, axiom382, axiom383, axiom384, axiom385, axiom386, axiom387,
% 56.98/8.67 axiom388, axiom389, axiom39, axiom390, axiom391, axiom392, axiom393, axiom394,
% 56.98/8.67 axiom395, axiom396, axiom397, axiom398, axiom399, axiom4, axiom40, axiom400,
% 56.98/8.67 axiom401, axiom402, axiom403, axiom404, axiom405, axiom406, axiom407, axiom408,
% 56.98/8.67 axiom409, axiom41, axiom410, axiom411, axiom412, axiom413, axiom414, axiom415,
% 56.98/8.67 axiom416, axiom417, axiom418, axiom419, axiom42, axiom420, axiom421, axiom422,
% 56.98/8.67 axiom423, axiom424, axiom425, axiom426, axiom427, axiom428, axiom429, axiom43,
% 56.98/8.67 axiom430, axiom431, axiom432, axiom433, axiom434, axiom435, axiom436, axiom437,
% 56.98/8.67 axiom438, axiom439, axiom44, axiom440, axiom441, axiom442, axiom443, axiom444,
% 56.98/8.67 axiom445, axiom446, axiom447, axiom448, axiom449, axiom45, axiom450, axiom451,
% 56.98/8.67 axiom452, axiom453, axiom454, axiom455, axiom456, axiom457, axiom458, axiom459,
% 56.98/8.67 axiom46, axiom460, axiom461, axiom462, axiom463, axiom464, axiom465, axiom466,
% 56.98/8.67 axiom467, axiom468, axiom469, axiom47, axiom470, axiom471, axiom472, axiom473,
% 56.98/8.67 axiom474, axiom475, axiom476, axiom477, axiom478, axiom479, axiom48, axiom480,
% 56.98/8.67 axiom481, axiom482, axiom483, axiom484, axiom485, axiom486, axiom487, axiom488,
% 56.98/8.67 axiom489, axiom49, axiom490, axiom491, axiom492, axiom493, axiom494, axiom495,
% 56.98/8.67 axiom496, axiom497, axiom498, axiom499, axiom5, axiom50, axiom500, axiom501,
% 56.98/8.67 axiom502, axiom503, axiom504, axiom505, axiom506, axiom507, axiom508, axiom509,
% 56.98/8.67 axiom51, axiom510, axiom511, axiom512, axiom513, axiom514, axiom515, axiom516,
% 56.98/8.67 axiom517, axiom518, axiom519, axiom52, axiom520, axiom521, axiom522, axiom523,
% 56.98/8.67 axiom524, axiom525, axiom526, axiom527, axiom528, axiom529, axiom53, axiom530,
% 56.98/8.67 axiom531, axiom532, axiom533, axiom534, axiom535, axiom536, axiom537, axiom538,
% 56.98/8.67 axiom539, axiom54, axiom540, axiom541, axiom542, axiom543, axiom544, axiom545,
% 56.98/8.67 axiom546, axiom547, axiom548, axiom549, axiom55, axiom550, axiom551, axiom552,
% 56.98/8.67 axiom553, axiom554, axiom555, axiom556, axiom557, axiom558, axiom559, axiom56,
% 56.98/8.67 axiom560, axiom561, axiom562, axiom563, axiom564, axiom565, axiom566, axiom567,
% 56.98/8.67 axiom568, axiom569, axiom57, axiom570, axiom571, axiom572, axiom573, axiom574,
% 56.98/8.67 axiom575, axiom576, axiom577, axiom578, axiom579, axiom58, axiom580, axiom581,
% 56.98/8.67 axiom582, axiom583, axiom584, axiom585, axiom586, axiom587, axiom588, axiom589,
% 56.98/8.67 axiom59, axiom590, axiom591, axiom592, axiom593, axiom594, axiom595, axiom596,
% 56.98/8.67 axiom597, axiom598, axiom599, axiom6, axiom600, axiom601, axiom602, axiom603,
% 56.98/8.67 axiom604, axiom605, axiom606, axiom607, axiom608, axiom609, axiom610, axiom611,
% 56.98/8.67 axiom612, axiom613, axiom614, axiom615, axiom616, axiom617, axiom618, axiom619,
% 56.98/8.67 axiom62, axiom620, axiom621, axiom622, axiom623, axiom624, axiom625, axiom626,
% 56.98/8.67 axiom627, axiom628, axiom629, axiom63, axiom630, axiom631, axiom64, axiom65,
% 56.98/8.67 axiom66, axiom67, axiom68, axiom69, axiom7, axiom70, axiom71, axiom72, axiom73,
% 56.98/8.67 axiom74, axiom75, axiom76, axiom77, axiom78, axiom79, axiom8, axiom80, axiom81,
% 56.98/8.67 axiom82, axiom83, axiom84, axiom85, axiom86, axiom87, axiom88, axiom89, axiom9,
% 56.98/8.67 axiom90, axiom91, axiom92, axiom93, axiom94, axiom95, axiom96, axiom97, axiom98,
% 56.98/8.67 axiom99, formula_633, formula_634
% 56.98/8.67
% 56.98/8.67 Those formulas are unsatisfiable:
% 56.98/8.67 ---------------------------------
% 56.98/8.67
% 56.98/8.67 Begin of proof
% 56.98/8.67 |
% 56.98/8.67 | ALPHA: (axiom1) implies:
% 56.98/8.68 | (1) ? [v0: A_c_vec_c_vec$] : ? [v1: Nat$] : ? [v2:
% 56.98/8.68 | Nat_a_b_vec_c_vec_prod$] : ? [v3:
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v4: int] : ? [v5:
% 56.98/8.68 | Nat$] : ? [v6: Nat_list$] : ? [v7:
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v8: A_c_vec_c_vec$]
% 56.98/8.68 | : ? [v9: A_iarray_iarray$] : ? [v10: Nat$] : ? [v11: Nat_list$] : ?
% 56.98/8.68 | [v12: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v13:
% 56.98/8.68 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ? [v14:
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v15:
% 56.98/8.68 | A_c_vec_c_vec$] : (mat$(one$) = v0 & pair$a(v1, a$) = v2 & pair$(v0,
% 56.98/8.68 | v2) = v3 & fun_app$b(of_nat$, ka$) = v4 & nat$($sum(v4, 2)) = v5 &
% 56.98/8.68 | nat$($sum(v4, 1)) = v10 & nat$(0) = v1 & upt$(v1, v10) = v11 &
% 56.98/8.68 | upt$(v1, v5) = v6 & foldl$(gauss_Jordan_column_k_PA$, v3, v11) = v12
% 56.98/8.68 | & foldl$(gauss_Jordan_column_k_PA$, v3, v6) = v7 &
% 56.98/8.68 | fun_app$a(gauss_Jordan_column_k_PA$, v12) = v13 & fun_app$(v13, v10)
% 56.98/8.68 | = v14 & fst$(v14) = v15 & fst$(v7) = v8 & matrix_to_iarray$(v15) = v9
% 56.98/8.68 | & matrix_to_iarray$(v8) = v9 &
% 56.98/8.68 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(v13) &
% 56.98/8.68 | Nat_a_b_vec_c_vec_prod$(v2) &
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v14) &
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v12) &
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v7) &
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v3) & Nat$(v10) & Nat$(v5)
% 56.98/8.68 | & Nat$(v1) & Nat_list$(v11) & Nat_list$(v6) & A_iarray_iarray$(v9) &
% 56.98/8.68 | A_c_vec_c_vec$(v15) & A_c_vec_c_vec$(v8) & A_c_vec_c_vec$(v0))
% 56.98/8.68 |
% 56.98/8.68 | ALPHA: (axiom2) implies:
% 56.98/8.68 | (2) ? [v0: A_c_vec_c_vec$] : ? [v1: Nat$] : ? [v2:
% 56.98/8.68 | Nat_a_b_vec_c_vec_prod$] : ? [v3:
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v4: int] : ? [v5:
% 56.98/8.68 | Nat$] : ? [v6: Nat_list$] : (mat$(one$) = v0 & pair$a(v1, a$) = v2 &
% 56.98/8.68 | pair$(v0, v2) = v3 & fun_app$b(of_nat$, ka$) = v4 & nat$($sum(v4, 1))
% 56.98/8.68 | = v5 & nat$(0) = v1 & upt$(v1, v5) = v6 &
% 56.98/8.68 | foldl$(gauss_Jordan_column_k_PA$, v3, v6) = a$a &
% 56.98/8.68 | Nat_a_b_vec_c_vec_prod$(v2) &
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v3) & Nat$(v5) & Nat$(v1)
% 56.98/8.68 | & Nat_list$(v6) & A_c_vec_c_vec$(v0))
% 56.98/8.68 |
% 56.98/8.68 | ALPHA: (axiom3) implies:
% 56.98/8.68 | (3) ? [v0: A_c_vec_c_vec$] : ? [v1: Nat_a_b_vec_c_vec_prod$] : ? [v2:
% 56.98/8.68 | Nat$] : ? [v3: A_b_vec_c_vec$] : ? [v4: Nat_a_b_vec_c_vec_prod$] :
% 56.98/8.68 | (snd$(a$a) = v1 & fst$a(v1) = v2 & snd$a(v1) = v3 & pair$a(v2, v3) = v4
% 56.98/8.68 | & pair$(v0, v4) = a$a & fst$(a$a) = v0 & Nat_a_b_vec_c_vec_prod$(v4)
% 56.98/8.68 | & Nat_a_b_vec_c_vec_prod$(v1) & Nat$(v2) & A_b_vec_c_vec$(v3) &
% 56.98/8.68 | A_c_vec_c_vec$(v0))
% 56.98/8.68 |
% 56.98/8.68 | ALPHA: (axiom29) implies:
% 56.98/8.68 | (4) ? [v0: int] : ? [v1: Nat$] : ? [v2:
% 56.98/8.68 | A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ? [v3: A_c_vec_c_vec$] : ?
% 56.98/8.68 | [v4: A_iarray_iarray$] : ? [v5: A_c_vec_c_vec$] : ? [v6: Nat$] : ?
% 56.98/8.68 | [v7: Nat_a_b_vec_c_vec_prod$] : ? [v8:
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v9: Nat$] : ?
% 56.98/8.68 | [v10: Nat_list$] : ? [v11: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$]
% 56.98/8.68 | : ? [v12: A_c_vec_c_vec$] : (gauss_Jordan_upt_k_PA$(a$, v1) = v2 &
% 56.98/8.68 | fst$k(v2) = v3 & mat$(one$) = v5 & pair$a(v6, a$) = v7 & pair$(v5,
% 56.98/8.68 | v7) = v8 & fun_app$b(of_nat$, ka$) = v0 & nat$($sum(v0, 2)) = v9 &
% 56.98/8.68 | nat$($sum(v0, 1)) = v1 & nat$(0) = v6 & upt$(v6, v9) = v10 &
% 56.98/8.68 | foldl$(gauss_Jordan_column_k_PA$, v8, v10) = v11 & fst$(v11) = v12 &
% 56.98/8.68 | matrix_to_iarray$(v12) = v4 & matrix_to_iarray$(v3) = v4 &
% 56.98/8.68 | Nat_a_b_vec_c_vec_prod$(v7) &
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v11) &
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v8) & Nat$(v9) & Nat$(v6)
% 56.98/8.68 | & Nat$(v1) & Nat_list$(v10) & A_c_vec_c_vec_a_b_vec_c_vec_prod$(v2) &
% 56.98/8.68 | A_iarray_iarray$(v4) & A_c_vec_c_vec$(v12) & A_c_vec_c_vec$(v5) &
% 56.98/8.68 | A_c_vec_c_vec$(v3))
% 56.98/8.68 |
% 56.98/8.68 | ALPHA: (axiom30) implies:
% 56.98/8.68 | (5) ? [v0: int] : ? [v1: Nat$] : ? [v2:
% 56.98/8.68 | A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ? [v3: A_c_vec_c_vec$] : ?
% 56.98/8.68 | [v4: A_iarray_iarray$] : ? [v5: A_c_vec_c_vec$] : ? [v6: Nat$] : ?
% 56.98/8.68 | [v7: Nat_a_b_vec_c_vec_prod$] : ? [v8:
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v9: Nat_list$] : ?
% 56.98/8.68 | [v10: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v11:
% 56.98/8.68 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ? [v12:
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v13:
% 56.98/8.68 | A_c_vec_c_vec$] : (gauss_Jordan_upt_k_PA$(a$, v1) = v2 & fst$k(v2) =
% 56.98/8.68 | v3 & mat$(one$) = v5 & pair$a(v6, a$) = v7 & pair$(v5, v7) = v8 &
% 56.98/8.68 | fun_app$b(of_nat$, ka$) = v0 & nat$($sum(v0, 1)) = v1 & nat$(0) = v6
% 56.98/8.68 | & upt$(v6, v1) = v9 & foldl$(gauss_Jordan_column_k_PA$, v8, v9) = v10
% 56.98/8.68 | & fun_app$a(gauss_Jordan_column_k_PA$, v10) = v11 & fun_app$(v11, v1)
% 56.98/8.68 | = v12 & fst$(v12) = v13 & matrix_to_iarray$(v13) = v4 &
% 56.98/8.68 | matrix_to_iarray$(v3) = v4 &
% 56.98/8.68 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(v11) &
% 56.98/8.68 | Nat_a_b_vec_c_vec_prod$(v7) &
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v12) &
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v10) &
% 56.98/8.68 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v8) & Nat$(v6) & Nat$(v1)
% 56.98/8.68 | & Nat_list$(v9) & A_c_vec_c_vec_a_b_vec_c_vec_prod$(v2) &
% 56.98/8.68 | A_iarray_iarray$(v4) & A_c_vec_c_vec$(v13) & A_c_vec_c_vec$(v5) &
% 56.98/8.68 | A_c_vec_c_vec$(v3))
% 56.98/8.68 |
% 56.98/8.68 | ALPHA: (axiom31) implies:
% 56.98/8.69 | (6) ? [v0: Nat$] : ? [v1: int] : ? [v2: A_c_vec_c_vec$] : ? [v3: Nat$]
% 56.98/8.69 | : ? [v4: Nat_a_b_vec_c_vec_prod$] : ? [v5:
% 56.98/8.69 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v6: int] : ? [v7:
% 56.98/8.69 | Nat$] : ? [v8: Nat_list$] : ? [v9:
% 56.98/8.69 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v10:
% 56.98/8.69 | Nat_a_b_vec_c_vec_prod$] : ? [v11: Nat$] : ? [v12: int] :
% 56.98/8.69 | ($lesseq(v12, v1) & nrows$(a$) = v0 & snd$(v9) = v10 & fst$a(v10) = v11
% 56.98/8.69 | & mat$(one$) = v2 & pair$a(v3, a$) = v4 & pair$(v2, v4) = v5 &
% 56.98/8.69 | fun_app$b(of_nat$, v11) = v12 & fun_app$b(of_nat$, v0) = v1 &
% 56.98/8.69 | fun_app$b(of_nat$, ka$) = v6 & nat$($sum(v6, 1)) = v7 & nat$(0) = v3
% 56.98/8.69 | & upt$(v3, v7) = v8 & foldl$(gauss_Jordan_column_k_PA$, v5, v8) = v9
% 56.98/8.69 | & Nat_a_b_vec_c_vec_prod$(v10) & Nat_a_b_vec_c_vec_prod$(v4) &
% 56.98/8.69 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v9) &
% 56.98/8.69 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v5) & Nat$(v11) & Nat$(v7)
% 56.98/8.69 | & Nat$(v3) & Nat$(v0) & Nat_list$(v8) & A_c_vec_c_vec$(v2))
% 56.98/8.69 |
% 56.98/8.69 | ALPHA: (axiom60) implies:
% 56.98/8.69 | (7) ? [v0: A_c_vec_c_vec$] : ? [v1: A_iarray_iarray$] : (fst$d(b$) = v1 &
% 56.98/8.69 | fst$(a$a) = v0 & matrix_to_iarray$(v0) = v1 & A_iarray_iarray$(v1) &
% 56.98/8.69 | A_c_vec_c_vec$(v0))
% 56.98/8.69 |
% 56.98/8.69 | ALPHA: (axiom61) implies:
% 56.98/8.69 | (8) ? [v0: Nat_a_b_vec_c_vec_prod$] : ? [v1: Nat$] : ? [v2: int] : ?
% 56.98/8.69 | [v3: Nat_a_iarray_iarray_prod$] : ? [v4: Nat$] : (snd$d(b$) = v3 &
% 56.98/8.69 | fst$b(v3) = v4 & snd$(a$a) = v0 & fst$a(v0) = v1 & fun_app$b(of_nat$,
% 56.98/8.69 | v4) = v2 & fun_app$b(of_nat$, v1) = v2 &
% 56.98/8.69 | Nat_a_b_vec_c_vec_prod$(v0) & Nat_a_iarray_iarray_prod$(v3) &
% 56.98/8.69 | Nat$(v4) & Nat$(v1))
% 56.98/8.69 |
% 56.98/8.69 | ALPHA: (axiom136) implies:
% 56.98/8.69 | (9) ? [v0: Nat$] : ? [v1: int] : ? [v2: int] : ? [v3: Nat$] : ? [v4:
% 56.98/8.69 | int] : ? [v5: A_c_vec_c_vec$] : ? [v6: Nat$] : ? [v7:
% 56.98/8.69 | Nat_a_b_vec_c_vec_prod$] : ? [v8:
% 56.98/8.69 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v9: Nat$] : ?
% 56.98/8.69 | [v10: Nat_list$] : ? [v11: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$]
% 56.98/8.69 | : ? [v12: Nat_a_b_vec_c_vec_prod$] : ? [v13: Nat$] : ? [v14: int] :
% 56.98/8.69 | (ncols$(a$) = v0 & nrows$(a$) = v3 & snd$(v11) = v12 & fst$a(v12) = v13
% 56.98/8.69 | & mat$(one$) = v5 & pair$a(v6, a$) = v7 & pair$(v5, v7) = v8 &
% 56.98/8.69 | fun_app$b(of_nat$, v13) = v14 & fun_app$b(of_nat$, v3) = v4 &
% 56.98/8.69 | fun_app$b(of_nat$, v0) = v1 & fun_app$b(of_nat$, ka$) = v2 &
% 56.98/8.69 | nat$($sum(v2, 1)) = v9 & nat$(0) = v6 & upt$(v6, v9) = v10 &
% 56.98/8.69 | foldl$(gauss_Jordan_column_k_PA$, v8, v10) = v11 &
% 56.98/8.69 | Nat_a_b_vec_c_vec_prod$(v12) & Nat_a_b_vec_c_vec_prod$(v7) &
% 56.98/8.69 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v11) &
% 56.98/8.69 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v8) & Nat$(v13) & Nat$(v9)
% 56.98/8.69 | & Nat$(v6) & Nat$(v3) & Nat$(v0) & Nat_list$(v10) &
% 56.98/8.69 | A_c_vec_c_vec$(v5) & ( ~ ($lesseq(1, $difference(v14, v4))) | ~
% 56.98/8.69 | ($lesseq(1, $difference(v1, v2)))))
% 56.98/8.69 |
% 56.98/8.69 | ALPHA: (axiom148) implies:
% 56.98/8.69 | (10) ? [v0: Nat$] : ? [v1: int] : ? [v2: int] : ($lesseq(2,
% 56.98/8.69 | $difference(v1, v2)) & ncols$(a$) = v0 & fun_app$b(of_nat$, v0) =
% 56.98/8.69 | v1 & fun_app$b(of_nat$, ka$) = v2 & Nat$(v0))
% 56.98/8.69 |
% 56.98/8.69 | ALPHA: (axiom175) implies:
% 56.98/8.69 | (11) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_bool_fun$] : !
% 56.98/8.69 | [v2: Nat$] : ! [v3: int] : (v3 = 0 | ~ (fun_app$s(v1, v2) = v3) |
% 56.98/8.69 | ~ Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v4: Nat$] : ? [v5: int] :
% 56.98/8.69 | ? [v6: int] : ( ~ (v6 = 0) & $lesseq(1, v5) & fun_app$s(v1, v4) =
% 56.98/8.69 | v6 & fun_app$b(of_nat$, v4) = v5 & Nat$(v4) & ! [v7: Nat$] : !
% 56.98/8.69 | [v8: int] : ( ~ ($lesseq(1, $difference(v5, v8))) | ~
% 56.98/8.69 | (fun_app$b(of_nat$, v7) = v8) | ~ Nat$(v7) | fun_app$s(v1,
% 56.98/8.69 | v7) = 0)) | ? [v4: int] : ( ~ (v4 = 0) & fun_app$s(v1, v0)
% 56.98/8.69 | = v4)))
% 56.98/8.69 |
% 56.98/8.69 | ALPHA: (axiom199) implies:
% 56.98/8.69 | (12) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat$] : ! [v2:
% 56.98/8.69 | Nat_bool_fun$] : ! [v3: int] : ! [v4: int] : (v4 = 0 | ~
% 56.98/8.69 | (fun_app$s(v2, v0) = v4) | ~ (fun_app$b(of_nat$, v1) = v3) | ~
% 56.98/8.69 | Nat_bool_fun$(v2) | ~ Nat$(v1) | ? [v5: Nat$] : ? [v6: int] :
% 56.98/8.69 | ? [v7: Nat$] : ($lesseq(1, $difference(v3, v6)) & fun_app$s(v2,
% 56.98/8.69 | v7) = 0 & fun_app$b(of_nat$, v5) = v6 & nat$($sum(v6, 1)) = v7
% 56.98/8.69 | & Nat$(v7) & Nat$(v5)) | ! [v5: Nat$] : ! [v6: int] : ( ~
% 56.98/8.69 | ($lesseq(v6, v3)) | ~ (fun_app$b(of_nat$, v5) = v6) | ~
% 56.98/8.69 | Nat$(v5) | ? [v7: int] : ( ~ (v7 = 0) & fun_app$s(v2, v5) =
% 56.98/8.69 | v7))) & ! [v1: Nat$] : ! [v2: Nat_bool_fun$] : ! [v3: any]
% 56.98/8.69 | : ! [v4: int] : ( ~ (fun_app$s(v2, v0) = v3) | ~
% 56.98/8.69 | (fun_app$b(of_nat$, v1) = v4) | ~ Nat_bool_fun$(v2) | ~ Nat$(v1)
% 56.98/8.69 | | ? [v5: Nat$] : ? [v6: int] : ($lesseq(v6, v4) & fun_app$s(v2,
% 56.98/8.69 | v5) = 0 & fun_app$b(of_nat$, v5) = v6 & Nat$(v5)) | ( ~ (v3 =
% 56.98/8.69 | 0) & ! [v5: Nat$] : ! [v6: int] : ! [v7: Nat$] : ( ~
% 56.98/8.69 | ($lesseq(1, $difference(v4, v6))) | ~ (fun_app$s(v2, v7) = 0)
% 56.98/8.69 | | ~ (fun_app$b(of_nat$, v5) = v6) | ~ (nat$($sum(v6, 1)) =
% 56.98/8.69 | v7) | ~ Nat$(v5)))))
% 56.98/8.69 |
% 56.98/8.69 | ALPHA: (axiom201) implies:
% 56.98/8.70 | (13) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat$] : ! [v2:
% 56.98/8.70 | Nat_bool_fun$] : ! [v3: int] : ! [v4: any] : ( ~ (fun_app$s(v2,
% 56.98/8.70 | v0) = v4) | ~ (fun_app$b(of_nat$, v1) = v3) | ~
% 56.98/8.70 | Nat_bool_fun$(v2) | ~ Nat$(v1) | ? [v5: Nat$] : ? [v6: int] :
% 56.98/8.70 | ? [v7: int] : ( ~ (v7 = 0) & $lesseq(v6, v3) & fun_app$s(v2, v5) =
% 56.98/8.70 | v7 & fun_app$b(of_nat$, v5) = v6 & Nat$(v5)) | (v4 = 0 & ! [v5:
% 56.98/8.70 | Nat$] : ! [v6: int] : ! [v7: Nat$] : ! [v8: int] : (v8 = 0
% 56.98/8.70 | | ~ ($lesseq(1, $difference(v3, v6))) | ~ (fun_app$s(v2, v7)
% 56.98/8.70 | = v8) | ~ (fun_app$b(of_nat$, v5) = v6) | ~ (nat$($sum(v6,
% 56.98/8.70 | 1)) = v7) | ~ Nat$(v5)))) & ! [v1: Nat$] : ! [v2:
% 56.98/8.70 | Nat_bool_fun$] : ! [v3: int] : ( ~ (fun_app$s(v2, v0) = 0) | ~
% 56.98/8.70 | (fun_app$b(of_nat$, v1) = v3) | ~ Nat_bool_fun$(v2) | ~ Nat$(v1)
% 56.98/8.70 | | ? [v4: Nat$] : ? [v5: int] : ? [v6: Nat$] : ? [v7: int] : (
% 56.98/8.70 | ~ (v7 = 0) & $lesseq(1, $difference(v3, v5)) & fun_app$s(v2, v6)
% 56.98/8.70 | = v7 & fun_app$b(of_nat$, v4) = v5 & nat$($sum(v5, 1)) = v6 &
% 56.98/8.70 | Nat$(v6) & Nat$(v4)) | ! [v4: Nat$] : ! [v5: int] : ( ~
% 56.98/8.70 | ($lesseq(v5, v3)) | ~ (fun_app$b(of_nat$, v4) = v5) | ~
% 56.98/8.70 | Nat$(v4) | fun_app$s(v2, v4) = 0)))
% 56.98/8.70 |
% 56.98/8.70 | ALPHA: (axiom204) implies:
% 56.98/8.70 | (14) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_bool_fun$] : !
% 56.98/8.70 | [v2: Nat$] : ! [v3: int] : ! [v4: int] : (v3 = 0 | ~
% 56.98/8.70 | (fun_app$s(v1, v0) = v3) | ~ (fun_app$b(of_nat$, v2) = v4) | ~
% 56.98/8.70 | Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v5: Nat$] : ? [v6: int] :
% 56.98/8.70 | ($lesseq(v6, v4) & fun_app$s(v1, v5) = 0 & fun_app$b(of_nat$, v5)
% 56.98/8.70 | = v6 & Nat$(v5) & ! [v7: Nat$] : ! [v8: int] : ( ~ ($lesseq(1,
% 56.98/8.70 | $difference(v6, v8))) | ~ (fun_app$b(of_nat$, v7) = v8) |
% 56.98/8.70 | ~ Nat$(v7) | ? [v9: int] : ( ~ (v9 = 0) & fun_app$s(v1, v7)
% 56.98/8.70 | = v9))) | ? [v5: int] : ( ~ (v5 = 0) & fun_app$s(v1, v2) =
% 56.98/8.70 | v5)))
% 56.98/8.70 |
% 56.98/8.70 | ALPHA: (axiom214) implies:
% 56.98/8.70 | (15) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_bool_fun$] : !
% 56.98/8.70 | [v2: Nat$] : ! [v3: int] : ! [v4: int] : (v3 = 0 | ~
% 56.98/8.70 | (fun_app$s(v1, v0) = v3) | ~ (fun_app$b(of_nat$, v2) = v4) | ~
% 56.98/8.70 | Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v5: Nat$] : ? [v6: int] :
% 56.98/8.70 | ? [v7: Nat$] : ($lesseq(1, $difference(v4, v6)) & fun_app$s(v1,
% 56.98/8.70 | v7) = 0 & fun_app$b(of_nat$, v5) = v6 & nat$($sum(v6, 1)) = v7
% 56.98/8.70 | & Nat$(v7) & Nat$(v5) & ! [v8: Nat$] : ! [v9: int] : ( ~
% 56.98/8.70 | ($lesseq(v9, v6)) | ~ (fun_app$b(of_nat$, v8) = v9) | ~
% 56.98/8.70 | Nat$(v8) | ? [v10: int] : ( ~ (v10 = 0) & fun_app$s(v1, v8) =
% 56.98/8.70 | v10))) | ? [v5: int] : ( ~ (v5 = 0) & fun_app$s(v1, v2) =
% 56.98/8.70 | v5)))
% 56.98/8.70 |
% 56.98/8.70 | ALPHA: (axiom232) implies:
% 56.98/8.70 | (16) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_bool_fun$] : !
% 56.98/8.70 | [v2: Nat$] : ! [v3: int] : (v3 = 0 | ~ (fun_app$s(v1, v2) = v3) |
% 56.98/8.70 | ~ Nat_bool_fun$(v1) | ~ Nat$(v2) | ? [v4: Nat$] : ? [v5: int] :
% 56.98/8.70 | ? [v6: Nat$] : ? [v7: int] : ( ~ (v7 = 0) & fun_app$s(v1, v6) =
% 56.98/8.70 | v7 & fun_app$s(v1, v4) = 0 & fun_app$b(of_nat$, v4) = v5 &
% 56.98/8.70 | nat$($sum(v5, 1)) = v6 & Nat$(v6) & Nat$(v4)) | ? [v4: int] : (
% 56.98/8.70 | ~ (v4 = 0) & fun_app$s(v1, v0) = v4)))
% 56.98/8.70 |
% 56.98/8.70 | ALPHA: (axiom233) implies:
% 56.98/8.70 | (17) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1:
% 56.98/8.70 | Nat_nat_bool_fun_fun$] : ! [v2: Nat$] : ! [v3: Nat$] : ! [v4:
% 56.98/8.70 | Nat_bool_fun$] : ! [v5: int] : (v5 = 0 | ~ (fun_app$t(v1, v2) =
% 56.98/8.70 | v4) | ~ (fun_app$s(v4, v3) = v5) | ~ Nat$(v3) | ~ Nat$(v2) |
% 56.98/8.70 | ~ Nat_nat_bool_fun_fun$(v1) | ? [v6: Nat$] : ? [v7: Nat$] : ?
% 56.98/8.70 | [v8: Nat_bool_fun$] : ? [v9: int] : ? [v10: Nat$] : ? [v11:
% 56.98/8.70 | Nat_bool_fun$] : ? [v12: int] : ? [v13: Nat$] : ? [v14: int]
% 56.98/8.70 | : ( ~ (v14 = 0) & fun_app$t(v1, v10) = v11 & fun_app$t(v1, v6) =
% 56.98/8.70 | v8 & fun_app$s(v11, v13) = v14 & fun_app$s(v8, v7) = 0 &
% 56.98/8.70 | fun_app$b(of_nat$, v7) = v12 & fun_app$b(of_nat$, v6) = v9 &
% 56.98/8.70 | nat$($sum(v12, 1)) = v13 & nat$($sum(v9, 1)) = v10 &
% 56.98/8.70 | Nat_bool_fun$(v11) & Nat_bool_fun$(v8) & Nat$(v13) & Nat$(v10) &
% 56.98/8.70 | Nat$(v7) & Nat$(v6)) | ? [v6: Nat$] : ? [v7: Nat_bool_fun$] :
% 56.98/8.70 | ? [v8: int] : ( ~ (v8 = 0) & fun_app$t(v1, v6) = v7 &
% 56.98/8.70 | fun_app$s(v7, v0) = v8 & Nat_bool_fun$(v7) & Nat$(v6)) | ? [v6:
% 56.98/8.70 | Nat_bool_fun$] : (fun_app$t(v1, v0) = v6 & Nat_bool_fun$(v6) &
% 56.98/8.70 | ? [v7: Nat$] : ? [v8: int] : ? [v9: Nat$] : ? [v10: int] : (
% 56.98/8.70 | ~ (v10 = 0) & fun_app$s(v6, v9) = v10 & fun_app$b(of_nat$, v7)
% 56.98/8.70 | = v8 & nat$($sum(v8, 1)) = v9 & Nat$(v9) & Nat$(v7)))))
% 56.98/8.70 |
% 56.98/8.70 | ALPHA: (axiom234) implies:
% 56.98/8.70 | (18) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: Nat_bool_fun$] : !
% 56.98/8.70 | [v2: Nat$] : ( ~ (fun_app$s(v1, v2) = 0) | ~ Nat_bool_fun$(v1) | ~
% 56.98/8.70 | Nat$(v2) | fun_app$s(v1, v0) = 0 | ? [v3: Nat$] : ? [v4: int] :
% 56.98/8.70 | ? [v5: Nat$] : ? [v6: int] : ( ~ (v6 = 0) & fun_app$s(v1, v5) = 0
% 56.98/8.70 | & fun_app$s(v1, v3) = v6 & fun_app$b(of_nat$, v3) = v4 &
% 56.98/8.70 | nat$($sum(v4, 1)) = v5 & Nat$(v5) & Nat$(v3))))
% 56.98/8.70 |
% 56.98/8.70 | ALPHA: (axiom259) implies:
% 56.98/8.71 | (19) ? [v0: Nat$] : ? [v1: int] : ? [v2: int] : ? [v3:
% 56.98/8.71 | A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ? [v4: A_c_vec_c_vec$] : ?
% 56.98/8.71 | [v5: A_iarray_iarray$] : ? [v6: A_iarray_iarray$] : ? [v7:
% 56.98/8.71 | A_iarray_iarray_a_iarray_iarray_prod$] : ? [v8: A_iarray_iarray$] :
% 56.98/8.71 | (gauss_Jordan_upt_k_iarrays_PA$(v6, ka$) = v7 & matrix_to_iarray$a(a$)
% 56.98/8.71 | = v6 & ncols$(a$) = v0 & gauss_Jordan_upt_k_PA$(a$, ka$) = v3 &
% 56.98/8.71 | fst$k(v3) = v4 & fst$c(v7) = v8 & fun_app$b(of_nat$, v0) = v1 &
% 56.98/8.71 | fun_app$b(of_nat$, ka$) = v2 & matrix_to_iarray$(v4) = v5 & Nat$(v0)
% 56.98/8.71 | & A_c_vec_c_vec_a_b_vec_c_vec_prod$(v3) & A_iarray_iarray$(v8) &
% 56.98/8.71 | A_iarray_iarray$(v6) & A_iarray_iarray$(v5) &
% 56.98/8.71 | A_iarray_iarray_a_iarray_iarray_prod$(v7) & A_c_vec_c_vec$(v4) & (v8
% 56.98/8.71 | = v5 | ~ ($lesseq(1, $difference(v1, v2)))))
% 56.98/8.71 |
% 56.98/8.71 | ALPHA: (axiom260) implies:
% 56.98/8.71 | (20) ? [v0: Nat_a_b_vec_c_vec_prod$] : ? [v1: A_b_vec_c_vec$] : ? [v2:
% 56.98/8.71 | A_iarray_iarray$] : ? [v3: Nat_a_iarray_iarray_prod$] :
% 56.98/8.71 | (matrix_to_iarray$a(v1) = v2 & snd$d(b$) = v3 & snd$b(v3) = v2 &
% 56.98/8.71 | snd$(a$a) = v0 & snd$a(v0) = v1 & Nat_a_b_vec_c_vec_prod$(v0) &
% 56.98/8.71 | Nat_a_iarray_iarray_prod$(v3) & A_b_vec_c_vec$(v1) &
% 56.98/8.71 | A_iarray_iarray$(v2))
% 56.98/8.71 |
% 56.98/8.71 | ALPHA: (axiom261) implies:
% 56.98/8.71 | (21) ? [v0: Nat$] : ? [v1: int] : ? [v2: int] : ? [v3:
% 56.98/8.71 | A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ? [v4: A_b_vec_c_vec$] : ?
% 56.98/8.71 | [v5: A_iarray_iarray$] : ? [v6: A_iarray_iarray$] : ? [v7:
% 56.98/8.71 | A_iarray_iarray_a_iarray_iarray_prod$] : ? [v8: A_iarray_iarray$] :
% 56.98/8.71 | (snd$l(v3) = v4 & gauss_Jordan_upt_k_iarrays_PA$(v6, ka$) = v7 &
% 56.98/8.71 | matrix_to_iarray$a(v4) = v5 & matrix_to_iarray$a(a$) = v6 &
% 56.98/8.71 | ncols$(a$) = v0 & gauss_Jordan_upt_k_PA$(a$, ka$) = v3 & snd$c(v7) =
% 56.98/8.71 | v8 & fun_app$b(of_nat$, v0) = v1 & fun_app$b(of_nat$, ka$) = v2 &
% 56.98/8.71 | Nat$(v0) & A_b_vec_c_vec$(v4) &
% 56.98/8.71 | A_c_vec_c_vec_a_b_vec_c_vec_prod$(v3) & A_iarray_iarray$(v8) &
% 56.98/8.71 | A_iarray_iarray$(v6) & A_iarray_iarray$(v5) &
% 56.98/8.71 | A_iarray_iarray_a_iarray_iarray_prod$(v7) & (v8 = v5 | ~
% 56.98/8.71 | ($lesseq(1, $difference(v1, v2)))))
% 56.98/8.71 |
% 56.98/8.71 | ALPHA: (axiom280) implies:
% 56.98/8.71 | (22) ? [v0: Nat$] : ? [v1: int] : ? [v2: int] : ? [v3: A_c_vec_c_vec$]
% 56.98/8.71 | : ? [v4: Nat$] : ? [v5: Nat_a_b_vec_c_vec_prod$] : ? [v6:
% 56.98/8.71 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v7: Nat$] : ?
% 56.98/8.71 | [v8: Nat_list$] : ? [v9: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$]
% 56.98/8.71 | : ? [v10: Nat_a_b_vec_c_vec_prod$] : ? [v11: Nat$] : ? [v12: int] :
% 56.98/8.71 | ? [v13: A_iarray_iarray$] : ? [v14: Nat$] : ? [v15:
% 56.98/8.71 | A_iarray_iarray$] : ? [v16: Nat_a_iarray_iarray_prod$] : ? [v17:
% 56.98/8.71 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ? [v18:
% 56.98/8.71 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ? [v19:
% 56.98/8.71 | Nat_a_iarray_iarray_prod$] : ? [v20: Nat$] : ? [v21: int] :
% 56.98/8.71 | (nrows_iarray$(v13) = v14 & mat_iarray$(one$, v14) = v15 &
% 56.98/8.71 | foldl$a(gauss_Jordan_column_k_iarrays_PA$, v17, v8) = v18 &
% 56.98/8.71 | matrix_to_iarray$a(a$) = v13 & ncols$(a$) = v0 & snd$d(v18) = v19 &
% 56.98/8.71 | pair$d(v15, v16) = v17 & fst$b(v19) = v20 & pair$b(v4, v13) = v16 &
% 56.98/8.71 | snd$(v9) = v10 & fst$a(v10) = v11 & mat$(one$) = v3 & pair$a(v4, a$)
% 56.98/8.71 | = v5 & pair$(v3, v5) = v6 & fun_app$b(of_nat$, v20) = v21 &
% 56.98/8.71 | fun_app$b(of_nat$, v11) = v12 & fun_app$b(of_nat$, v0) = v1 &
% 56.98/8.71 | fun_app$b(of_nat$, ka$) = v2 & nat$($sum(v2, 1)) = v7 & nat$(0) = v4
% 56.98/8.71 | & upt$(v4, v7) = v8 & foldl$(gauss_Jordan_column_k_PA$, v6, v8) = v9
% 56.98/8.71 | & A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(v18) &
% 56.98/8.71 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(v17) &
% 56.98/8.71 | Nat_a_b_vec_c_vec_prod$(v10) & Nat_a_b_vec_c_vec_prod$(v5) &
% 56.98/8.71 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v9) &
% 56.98/8.71 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v6) &
% 56.98/8.71 | Nat_a_iarray_iarray_prod$(v19) & Nat_a_iarray_iarray_prod$(v16) &
% 56.98/8.71 | Nat$(v20) & Nat$(v14) & Nat$(v11) & Nat$(v7) & Nat$(v4) & Nat$(v0) &
% 56.98/8.71 | Nat_list$(v8) & A_iarray_iarray$(v15) & A_iarray_iarray$(v13) &
% 56.98/8.71 | A_c_vec_c_vec$(v3) & (v21 = v12 | ~ ($lesseq(1, $difference(v1,
% 56.98/8.71 | v2)))))
% 56.98/8.71 |
% 56.98/8.71 | ALPHA: (axiom281) implies:
% 56.98/8.71 | (23) ? [v0: A_c_vec_c_vec$] : ? [v1: Nat$] : ? [v2:
% 56.98/8.71 | Nat_a_b_vec_c_vec_prod$] : ? [v3:
% 56.98/8.71 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v4: int] : ? [v5:
% 56.98/8.71 | Nat$] : ? [v6: Nat_list$] : ? [v7:
% 56.98/8.71 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v8:
% 56.98/8.71 | Nat_a_b_vec_c_vec_prod$] : ? [v9: Nat$] : ? [v10: int] : ? [v11:
% 56.98/8.71 | A_iarray_iarray$] : ? [v12: Nat$] : ? [v13: A_iarray_iarray$] : ?
% 56.98/8.71 | [v14: Nat_a_iarray_iarray_prod$] : ? [v15:
% 56.98/8.71 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ? [v16:
% 56.98/8.71 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ? [v17:
% 56.98/8.71 | Nat_a_iarray_iarray_prod$] : ? [v18: Nat$] : (nrows_iarray$(v11) =
% 56.98/8.71 | v12 & mat_iarray$(one$, v12) = v13 &
% 56.98/8.71 | foldl$a(gauss_Jordan_column_k_iarrays_PA$, v15, v6) = v16 &
% 56.98/8.71 | matrix_to_iarray$a(a$) = v11 & snd$d(v16) = v17 & pair$d(v13, v14) =
% 56.98/8.71 | v15 & fst$b(v17) = v18 & pair$b(v1, v11) = v14 & snd$(v7) = v8 &
% 56.98/8.71 | fst$a(v8) = v9 & mat$(one$) = v0 & pair$a(v1, a$) = v2 & pair$(v0,
% 56.98/8.71 | v2) = v3 & fun_app$b(of_nat$, v18) = v10 & fun_app$b(of_nat$, v9)
% 56.98/8.71 | = v10 & fun_app$b(of_nat$, ka$) = v4 & nat$($sum(v4, 1)) = v5 &
% 56.98/8.71 | nat$(0) = v1 & upt$(v1, v5) = v6 & foldl$(gauss_Jordan_column_k_PA$,
% 56.98/8.71 | v3, v6) = v7 & A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(v16)
% 56.98/8.71 | & A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(v15) &
% 56.98/8.71 | Nat_a_b_vec_c_vec_prod$(v8) & Nat_a_b_vec_c_vec_prod$(v2) &
% 56.98/8.71 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v7) &
% 56.98/8.71 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v3) &
% 56.98/8.71 | Nat_a_iarray_iarray_prod$(v17) & Nat_a_iarray_iarray_prod$(v14) &
% 56.98/8.71 | Nat$(v18) & Nat$(v12) & Nat$(v9) & Nat$(v5) & Nat$(v1) &
% 56.98/8.71 | Nat_list$(v6) & A_iarray_iarray$(v13) & A_iarray_iarray$(v11) &
% 56.98/8.71 | A_c_vec_c_vec$(v0))
% 56.98/8.71 |
% 56.98/8.71 | ALPHA: (axiom282) implies:
% 56.98/8.71 | (24) ? [v0: A_iarray_iarray$] : ? [v1: Nat$] : ? [v2: A_iarray_iarray$]
% 56.98/8.71 | : ? [v3: Nat$] : ? [v4: Nat_a_iarray_iarray_prod$] : ? [v5:
% 56.98/8.71 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ? [v6: int] : ?
% 56.98/8.71 | [v7: Nat$] : ? [v8: Nat_list$] : (nrows_iarray$(v0) = v1 &
% 56.98/8.71 | mat_iarray$(one$, v1) = v2 &
% 56.98/8.71 | foldl$a(gauss_Jordan_column_k_iarrays_PA$, v5, v8) = b$ &
% 56.98/8.71 | matrix_to_iarray$a(a$) = v0 & pair$d(v2, v4) = v5 & pair$b(v3, v0) =
% 56.98/8.71 | v4 & fun_app$b(of_nat$, ka$) = v6 & nat$($sum(v6, 1)) = v7 & nat$(0)
% 56.98/8.71 | = v3 & upt$(v3, v7) = v8 &
% 56.98/8.71 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(v5) &
% 56.98/8.71 | Nat_a_iarray_iarray_prod$(v4) & Nat$(v7) & Nat$(v3) & Nat$(v1) &
% 56.98/8.71 | Nat_list$(v8) & A_iarray_iarray$(v2) & A_iarray_iarray$(v0))
% 56.98/8.71 |
% 56.98/8.71 | ALPHA: (axiom285) implies:
% 56.98/8.72 | (25) ? [v0: Nat$] : (nat$(0) = v0 & Nat$(v0) & ! [v1: A_iarray_iarray$] :
% 56.98/8.72 | ! [v2: Nat$] : ! [v3: Nat$] : ! [v4: A_iarray_iarray$] : ! [v5:
% 56.98/8.72 | Nat_a_iarray_iarray_prod$] : ! [v6:
% 56.98/8.72 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v7: int] :
% 56.98/8.72 | ! [v8: Nat$] : ! [v9: Nat_list$] : ! [v10:
% 56.98/8.72 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v11:
% 56.98/8.72 | A_iarray_iarray$] : ! [v12: Nat_a_iarray_iarray_prod$] : ! [v13:
% 56.98/8.72 | A_iarray_iarray$] : ! [v14:
% 56.98/8.72 | A_iarray_iarray_a_iarray_iarray_prod$] : ( ~ (nrows_iarray$(v1) =
% 56.98/8.72 | v3) | ~ (mat_iarray$(one$, v3) = v4) | ~
% 56.98/8.72 | (foldl$a(gauss_Jordan_column_k_iarrays_PA$, v6, v9) = v10) | ~
% 56.98/8.72 | (fst$d(v10) = v11) | ~ (snd$d(v10) = v12) | ~ (pair$d(v4, v5) =
% 56.98/8.72 | v6) | ~ (pair$c(v11, v13) = v14) | ~ (snd$b(v12) = v13) | ~
% 56.98/8.72 | (pair$b(v0, v1) = v5) | ~ (fun_app$b(of_nat$, v2) = v7) | ~
% 56.98/8.72 | (nat$($sum(v7, 1)) = v8) | ~ (upt$(v0, v8) = v9) | ~ Nat$(v2) |
% 56.98/8.72 | ~ A_iarray_iarray$(v1) | (gauss_Jordan_upt_k_iarrays_PA$(v1, v2) =
% 56.98/8.72 | v14 & A_iarray_iarray_a_iarray_iarray_prod$(v14))))
% 56.98/8.72 |
% 56.98/8.72 | ALPHA: (axiom378) implies:
% 56.98/8.72 | (26) ? [v0: A_c_vec_c_vec$] : ? [v1: Nat$] : (mat$(one$) = v0 & nat$(0) =
% 56.98/8.72 | v1 & Nat$(v1) & A_c_vec_c_vec$(v0) & ! [v2: A_b_vec_c_vec$] : !
% 56.98/8.72 | [v3: Nat$] : ! [v4: Nat_a_b_vec_c_vec_prod$] : ! [v5:
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v6: int] : !
% 56.98/8.72 | [v7: Nat$] : ! [v8: Nat_list$] : ! [v9:
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v10:
% 56.98/8.72 | A_c_vec_c_vec$] : ! [v11: Nat_a_b_vec_c_vec_prod$] : ! [v12:
% 56.98/8.72 | A_b_vec_c_vec$] : ! [v13: A_c_vec_c_vec_a_b_vec_c_vec_prod$] : (
% 56.98/8.72 | ~ (pair$l(v10, v12) = v13) | ~ (snd$(v9) = v11) | ~ (snd$a(v11)
% 56.98/8.72 | = v12) | ~ (pair$a(v1, v2) = v4) | ~ (pair$(v0, v4) = v5) | ~
% 56.98/8.72 | (fun_app$b(of_nat$, v3) = v6) | ~ (nat$($sum(v6, 1)) = v7) | ~
% 56.98/8.72 | (upt$(v1, v7) = v8) | ~ (foldl$(gauss_Jordan_column_k_PA$, v5,
% 56.98/8.72 | v8) = v9) | ~ (fst$(v9) = v10) | ~ Nat$(v3) | ~
% 56.98/8.72 | A_b_vec_c_vec$(v2) | (gauss_Jordan_upt_k_PA$(v2, v3) = v13 &
% 56.98/8.72 | A_c_vec_c_vec_a_b_vec_c_vec_prod$(v13))))
% 56.98/8.72 |
% 56.98/8.72 | ALPHA: (conjecture0) implies:
% 56.98/8.72 | (27) ? [v0: A_c_vec_c_vec$] : ? [v1: Nat$] : ? [v2:
% 56.98/8.72 | Nat_a_b_vec_c_vec_prod$] : ? [v3:
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v4: int] : ? [v5:
% 56.98/8.72 | Nat$] : ? [v6: Nat_list$] : ? [v7:
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v8:
% 56.98/8.72 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ? [v9:
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v10:
% 56.98/8.72 | A_c_vec_c_vec$] : ? [v11: A_iarray_iarray$] : ? [v12:
% 56.98/8.72 | A_c_vec_c_vec$] : ? [v13: Nat_a_b_vec_c_vec_prod$] : ? [v14: Nat$]
% 56.98/8.72 | : ? [v15: A_b_vec_c_vec$] : ? [v16: Nat_a_b_vec_c_vec_prod$] : ?
% 56.98/8.72 | [v17: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v18:
% 56.98/8.72 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ? [v19:
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ? [v20:
% 56.98/8.72 | A_c_vec_c_vec$] : ? [v21: A_iarray_iarray$] : ( ~ (v21 = v11) &
% 56.98/8.72 | snd$(v7) = v13 & fst$a(v13) = v14 & snd$a(v13) = v15 & mat$(one$) =
% 56.98/8.72 | v0 & pair$a(v14, v15) = v16 & pair$a(v1, a$) = v2 & pair$(v12, v16)
% 56.98/8.72 | = v17 & pair$(v0, v2) = v3 & fun_app$b(of_nat$, ka$) = v4 &
% 56.98/8.72 | nat$($sum(v4, 1)) = v5 & nat$(0) = v1 & upt$(v1, v5) = v6 &
% 56.98/8.72 | foldl$(gauss_Jordan_column_k_PA$, v3, v6) = v7 &
% 56.98/8.72 | fun_app$a(gauss_Jordan_column_k_PA$, v17) = v18 &
% 56.98/8.72 | fun_app$a(gauss_Jordan_column_k_PA$, v7) = v8 & fun_app$(v18, v5) =
% 56.98/8.72 | v19 & fun_app$(v8, v5) = v9 & fst$(v19) = v20 & fst$(v9) = v10 &
% 56.98/8.72 | fst$(v7) = v12 & matrix_to_iarray$(v20) = v21 &
% 56.98/8.72 | matrix_to_iarray$(v10) = v11 &
% 56.98/8.72 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(v18) &
% 56.98/8.72 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(v8) &
% 56.98/8.72 | Nat_a_b_vec_c_vec_prod$(v16) & Nat_a_b_vec_c_vec_prod$(v13) &
% 56.98/8.72 | Nat_a_b_vec_c_vec_prod$(v2) &
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v19) &
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v17) &
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v9) &
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v7) &
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(v3) & Nat$(v14) &
% 56.98/8.72 | Nat$(v5) & Nat$(v1) & A_b_vec_c_vec$(v15) & Nat_list$(v6) &
% 56.98/8.72 | A_iarray_iarray$(v21) & A_iarray_iarray$(v11) & A_c_vec_c_vec$(v20)
% 56.98/8.72 | & A_c_vec_c_vec$(v12) & A_c_vec_c_vec$(v10) & A_c_vec_c_vec$(v0))
% 56.98/8.72 |
% 56.98/8.72 | ALPHA: (function-axioms) implies:
% 56.98/8.72 | (28) ! [v0: A_iarray_iarray$] : ! [v1: A_iarray_iarray$] : ! [v2:
% 56.98/8.72 | A_c_vec_c_vec$] : (v1 = v0 | ~ (matrix_to_iarray$(v2) = v1) | ~
% 56.98/8.72 | (matrix_to_iarray$(v2) = v0))
% 56.98/8.72 | (29) ! [v0: A_c_vec_c_vec$] : ! [v1: A_c_vec_c_vec$] : ! [v2:
% 56.98/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : (v1 = v0 | ~
% 56.98/8.72 | (fst$(v2) = v1) | ~ (fst$(v2) = v0))
% 56.98/8.72 | (30) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : (v1 = v0 | ~ (nat$(v2)
% 56.98/8.72 | = v1) | ~ (nat$(v2) = v0))
% 56.98/8.72 | (31) ! [v0: A_c_vec_c_vec$] : ! [v1: A_c_vec_c_vec$] : ! [v2: A$] : (v1
% 56.98/8.72 | = v0 | ~ (mat$(v2) = v1) | ~ (mat$(v2) = v0))
% 56.98/8.72 | (32) ! [v0: A_b_vec_c_vec$] : ! [v1: A_b_vec_c_vec$] : ! [v2:
% 56.98/8.72 | Nat_a_b_vec_c_vec_prod$] : (v1 = v0 | ~ (snd$a(v2) = v1) | ~
% 56.98/8.72 | (snd$a(v2) = v0))
% 56.98/8.72 | (33) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Nat_a_b_vec_c_vec_prod$] : (v1
% 56.98/8.72 | = v0 | ~ (fst$a(v2) = v1) | ~ (fst$a(v2) = v0))
% 56.98/8.72 | (34) ! [v0: Nat_a_b_vec_c_vec_prod$] : ! [v1: Nat_a_b_vec_c_vec_prod$] :
% 56.98/8.72 | ! [v2: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : (v1 = v0 | ~
% 56.98/8.72 | (snd$(v2) = v1) | ~ (snd$(v2) = v0))
% 57.39/8.72 | (35) ! [v0: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v1:
% 57.39/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v2: Nat$] : !
% 57.39/8.72 | [v3: Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : (v1 = v0 |
% 57.39/8.72 | ~ (fun_app$(v3, v2) = v1) | ~ (fun_app$(v3, v2) = v0))
% 57.39/8.72 | (36) ! [v0: Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ! [v1:
% 57.39/8.72 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$] : ! [v2:
% 57.39/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v3:
% 57.39/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$]
% 57.39/8.72 | : (v1 = v0 | ~ (fun_app$a(v3, v2) = v1) | ~ (fun_app$a(v3, v2) =
% 57.39/8.72 | v0))
% 57.39/8.72 | (37) ! [v0: Nat_list$] : ! [v1: Nat_list$] : ! [v2: Nat$] : ! [v3:
% 57.39/8.72 | Nat$] : (v1 = v0 | ~ (upt$(v3, v2) = v1) | ~ (upt$(v3, v2) = v0))
% 57.39/8.72 | (38) ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : ! [v3: Nat_int_fun$] :
% 57.39/8.72 | (v1 = v0 | ~ (fun_app$b(v3, v2) = v1) | ~ (fun_app$b(v3, v2) = v0))
% 57.39/8.72 | (39) ! [v0: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v1:
% 57.39/8.72 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v2:
% 57.39/8.72 | Nat_a_b_vec_c_vec_prod$] : ! [v3: A_c_vec_c_vec$] : (v1 = v0 | ~
% 57.39/8.72 | (pair$(v3, v2) = v1) | ~ (pair$(v3, v2) = v0))
% 57.39/8.72 | (40) ! [v0: Nat_a_b_vec_c_vec_prod$] : ! [v1: Nat_a_b_vec_c_vec_prod$] :
% 57.39/8.72 | ! [v2: A_b_vec_c_vec$] : ! [v3: Nat$] : (v1 = v0 | ~ (pair$a(v3, v2)
% 57.39/8.72 | = v1) | ~ (pair$a(v3, v2) = v0))
% 57.39/8.73 | (41) ! [v0: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v1:
% 57.39/8.73 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v2: Nat_list$] :
% 57.39/8.73 | ! [v3: A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v4:
% 57.39/8.73 | 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$]
% 57.39/8.73 | : (v1 = v0 | ~ (foldl$(v4, v3, v2) = v1) | ~ (foldl$(v4, v3, v2) =
% 57.39/8.73 | v0))
% 57.39/8.73 |
% 57.39/8.73 | DELTA: instantiating (7) with fresh symbols all_410_0, all_410_1 gives:
% 57.39/8.73 | (42) fst$d(b$) = all_410_0 & fst$(a$a) = all_410_1 &
% 57.39/8.73 | matrix_to_iarray$(all_410_1) = all_410_0 & A_iarray_iarray$(all_410_0)
% 57.39/8.73 | & A_c_vec_c_vec$(all_410_1)
% 57.39/8.73 |
% 57.39/8.73 | ALPHA: (42) implies:
% 57.39/8.73 | (43) fst$(a$a) = all_410_1
% 57.39/8.73 |
% 57.39/8.73 | DELTA: instantiating (10) with fresh symbols all_412_0, all_412_1, all_412_2
% 57.39/8.73 | gives:
% 57.39/8.73 | (44) $lesseq(2, $difference(all_412_1, all_412_0)) & ncols$(a$) = all_412_2
% 57.39/8.73 | & fun_app$b(of_nat$, all_412_2) = all_412_1 & fun_app$b(of_nat$, ka$)
% 57.39/8.73 | = all_412_0 & Nat$(all_412_2)
% 57.39/8.73 |
% 57.39/8.73 | ALPHA: (44) implies:
% 57.39/8.73 | (45) fun_app$b(of_nat$, ka$) = all_412_0
% 57.39/8.73 |
% 57.39/8.73 | DELTA: instantiating (20) with fresh symbols all_488_0, all_488_1, all_488_2,
% 57.39/8.73 | all_488_3 gives:
% 57.39/8.73 | (46) matrix_to_iarray$a(all_488_2) = all_488_1 & snd$d(b$) = all_488_0 &
% 57.39/8.73 | snd$b(all_488_0) = all_488_1 & snd$(a$a) = all_488_3 &
% 57.39/8.73 | snd$a(all_488_3) = all_488_2 & Nat_a_b_vec_c_vec_prod$(all_488_3) &
% 57.39/8.73 | Nat_a_iarray_iarray_prod$(all_488_0) & A_b_vec_c_vec$(all_488_2) &
% 57.39/8.73 | A_iarray_iarray$(all_488_1)
% 57.39/8.73 |
% 57.39/8.73 | ALPHA: (46) implies:
% 57.39/8.73 | (47) snd$a(all_488_3) = all_488_2
% 57.39/8.73 | (48) snd$(a$a) = all_488_3
% 57.39/8.73 |
% 57.39/8.73 | DELTA: instantiating (8) with fresh symbols all_490_0, all_490_1, all_490_2,
% 57.39/8.73 | all_490_3, all_490_4 gives:
% 57.39/8.73 | (49) snd$d(b$) = all_490_1 & fst$b(all_490_1) = all_490_0 & snd$(a$a) =
% 57.39/8.73 | all_490_4 & fst$a(all_490_4) = all_490_3 & fun_app$b(of_nat$,
% 57.39/8.73 | all_490_0) = all_490_2 & fun_app$b(of_nat$, all_490_3) = all_490_2 &
% 57.39/8.73 | Nat_a_b_vec_c_vec_prod$(all_490_4) &
% 57.39/8.73 | Nat_a_iarray_iarray_prod$(all_490_1) & Nat$(all_490_0) &
% 57.39/8.73 | Nat$(all_490_3)
% 57.39/8.73 |
% 57.39/8.73 | ALPHA: (49) implies:
% 57.39/8.73 | (50) fst$a(all_490_4) = all_490_3
% 57.39/8.73 | (51) snd$(a$a) = all_490_4
% 57.39/8.73 |
% 57.39/8.73 | DELTA: instantiating (3) with fresh symbols all_492_0, all_492_1, all_492_2,
% 57.39/8.73 | all_492_3, all_492_4 gives:
% 57.39/8.73 | (52) snd$(a$a) = all_492_3 & fst$a(all_492_3) = all_492_2 &
% 57.39/8.73 | snd$a(all_492_3) = all_492_1 & pair$a(all_492_2, all_492_1) =
% 57.39/8.73 | all_492_0 & pair$(all_492_4, all_492_0) = a$a & fst$(a$a) = all_492_4
% 57.39/8.73 | & Nat_a_b_vec_c_vec_prod$(all_492_0) &
% 57.39/8.73 | Nat_a_b_vec_c_vec_prod$(all_492_3) & Nat$(all_492_2) &
% 57.39/8.73 | A_b_vec_c_vec$(all_492_1) & A_c_vec_c_vec$(all_492_4)
% 57.39/8.73 |
% 57.39/8.73 | ALPHA: (52) implies:
% 57.39/8.73 | (53) fst$(a$a) = all_492_4
% 57.39/8.73 | (54) pair$(all_492_4, all_492_0) = a$a
% 57.39/8.73 | (55) pair$a(all_492_2, all_492_1) = all_492_0
% 57.39/8.73 | (56) snd$a(all_492_3) = all_492_1
% 57.39/8.73 | (57) fst$a(all_492_3) = all_492_2
% 57.39/8.73 | (58) snd$(a$a) = all_492_3
% 57.39/8.73 |
% 57.39/8.73 | DELTA: instantiating (18) with fresh symbol all_504_0 gives:
% 57.39/8.73 | (59) nat$(0) = all_504_0 & Nat$(all_504_0) & ! [v0: Nat_bool_fun$] : !
% 57.39/8.73 | [v1: Nat$] : ( ~ (fun_app$s(v0, v1) = 0) | ~ Nat_bool_fun$(v0) | ~
% 57.39/8.73 | Nat$(v1) | fun_app$s(v0, all_504_0) = 0 | ? [v2: Nat$] : ? [v3:
% 57.39/8.73 | int] : ? [v4: Nat$] : ? [v5: int] : ( ~ (v5 = 0) & fun_app$s(v0,
% 57.39/8.73 | v4) = 0 & fun_app$s(v0, v2) = v5 & fun_app$b(of_nat$, v2) = v3 &
% 57.39/8.73 | nat$($sum(v3, 1)) = v4 & Nat$(v4) & Nat$(v2)))
% 57.39/8.73 |
% 57.39/8.73 | ALPHA: (59) implies:
% 57.39/8.73 | (60) nat$(0) = all_504_0
% 57.39/8.73 |
% 57.39/8.73 | DELTA: instantiating (2) with fresh symbols all_522_0, all_522_1, all_522_2,
% 57.39/8.73 | all_522_3, all_522_4, all_522_5, all_522_6 gives:
% 57.39/8.73 | (61) mat$(one$) = all_522_6 & pair$a(all_522_5, a$) = all_522_4 &
% 57.39/8.73 | pair$(all_522_6, all_522_4) = all_522_3 & fun_app$b(of_nat$, ka$) =
% 57.39/8.73 | all_522_2 & nat$($sum(all_522_2, 1)) = all_522_1 & nat$(0) = all_522_5
% 57.39/8.73 | & upt$(all_522_5, all_522_1) = all_522_0 &
% 57.39/8.73 | foldl$(gauss_Jordan_column_k_PA$, all_522_3, all_522_0) = a$a &
% 57.39/8.73 | Nat_a_b_vec_c_vec_prod$(all_522_4) &
% 57.39/8.73 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_522_3) &
% 57.39/8.73 | Nat$(all_522_1) & Nat$(all_522_5) & Nat_list$(all_522_0) &
% 57.39/8.73 | A_c_vec_c_vec$(all_522_6)
% 57.39/8.73 |
% 57.39/8.73 | ALPHA: (61) implies:
% 57.39/8.73 | (62) foldl$(gauss_Jordan_column_k_PA$, all_522_3, all_522_0) = a$a
% 57.39/8.73 | (63) upt$(all_522_5, all_522_1) = all_522_0
% 57.39/8.73 | (64) nat$(0) = all_522_5
% 57.39/8.73 | (65) nat$($sum(all_522_2, 1)) = all_522_1
% 57.39/8.73 | (66) fun_app$b(of_nat$, ka$) = all_522_2
% 57.39/8.73 | (67) pair$(all_522_6, all_522_4) = all_522_3
% 57.39/8.73 | (68) pair$a(all_522_5, a$) = all_522_4
% 57.39/8.73 | (69) mat$(one$) = all_522_6
% 57.39/8.73 |
% 57.39/8.73 | DELTA: instantiating (16) with fresh symbol all_527_0 gives:
% 57.39/8.73 | (70) nat$(0) = all_527_0 & Nat$(all_527_0) & ! [v0: Nat_bool_fun$] : !
% 57.39/8.73 | [v1: Nat$] : ! [v2: int] : (v2 = 0 | ~ (fun_app$s(v0, v1) = v2) | ~
% 57.39/8.73 | Nat_bool_fun$(v0) | ~ Nat$(v1) | ? [v3: Nat$] : ? [v4: int] : ?
% 57.39/8.73 | [v5: Nat$] : ? [v6: int] : ( ~ (v6 = 0) & fun_app$s(v0, v5) = v6 &
% 57.39/8.73 | fun_app$s(v0, v3) = 0 & fun_app$b(of_nat$, v3) = v4 &
% 57.39/8.73 | nat$($sum(v4, 1)) = v5 & Nat$(v5) & Nat$(v3)) | ? [v3: int] : ( ~
% 57.39/8.73 | (v3 = 0) & fun_app$s(v0, all_527_0) = v3))
% 57.39/8.73 |
% 57.39/8.73 | ALPHA: (70) implies:
% 57.39/8.73 | (71) nat$(0) = all_527_0
% 57.39/8.73 |
% 57.39/8.73 | DELTA: instantiating (11) with fresh symbol all_539_0 gives:
% 57.39/8.74 | (72) nat$(0) = all_539_0 & Nat$(all_539_0) & ! [v0: Nat_bool_fun$] : !
% 57.39/8.74 | [v1: Nat$] : ! [v2: int] : (v2 = 0 | ~ (fun_app$s(v0, v1) = v2) | ~
% 57.39/8.74 | Nat_bool_fun$(v0) | ~ Nat$(v1) | ? [v3: Nat$] : ? [v4: int] : ?
% 57.39/8.74 | [v5: int] : ( ~ (v5 = 0) & $lesseq(1, v4) & fun_app$s(v0, v3) = v5 &
% 57.39/8.74 | fun_app$b(of_nat$, v3) = v4 & Nat$(v3) & ! [v6: Nat$] : ! [v7:
% 57.39/8.74 | int] : ( ~ ($lesseq(1, $difference(v4, v7))) | ~
% 57.39/8.74 | (fun_app$b(of_nat$, v6) = v7) | ~ Nat$(v6) | fun_app$s(v0, v6)
% 57.39/8.74 | = 0)) | ? [v3: int] : ( ~ (v3 = 0) & fun_app$s(v0, all_539_0) =
% 57.39/8.74 | v3))
% 57.39/8.74 |
% 57.39/8.74 | ALPHA: (72) implies:
% 57.39/8.74 | (73) nat$(0) = all_539_0
% 57.39/8.74 |
% 57.39/8.74 | DELTA: instantiating (19) with fresh symbols all_542_0, all_542_1, all_542_2,
% 57.39/8.74 | all_542_3, all_542_4, all_542_5, all_542_6, all_542_7, all_542_8 gives:
% 57.39/8.74 | (74) gauss_Jordan_upt_k_iarrays_PA$(all_542_2, ka$) = all_542_1 &
% 57.39/8.74 | matrix_to_iarray$a(a$) = all_542_2 & ncols$(a$) = all_542_8 &
% 57.39/8.74 | gauss_Jordan_upt_k_PA$(a$, ka$) = all_542_5 & fst$k(all_542_5) =
% 57.39/8.74 | all_542_4 & fst$c(all_542_1) = all_542_0 & fun_app$b(of_nat$,
% 57.39/8.74 | all_542_8) = all_542_7 & fun_app$b(of_nat$, ka$) = all_542_6 &
% 57.39/8.74 | matrix_to_iarray$(all_542_4) = all_542_3 & Nat$(all_542_8) &
% 57.39/8.74 | A_c_vec_c_vec_a_b_vec_c_vec_prod$(all_542_5) &
% 57.39/8.74 | A_iarray_iarray$(all_542_0) & A_iarray_iarray$(all_542_2) &
% 57.39/8.74 | A_iarray_iarray$(all_542_3) &
% 57.39/8.74 | A_iarray_iarray_a_iarray_iarray_prod$(all_542_1) &
% 57.39/8.74 | A_c_vec_c_vec$(all_542_4) & (all_542_0 = all_542_3 | ~ ($lesseq(1,
% 57.39/8.74 | $difference(all_542_7, all_542_6))))
% 57.39/8.74 |
% 57.39/8.74 | ALPHA: (74) implies:
% 57.39/8.74 | (75) fun_app$b(of_nat$, ka$) = all_542_6
% 57.39/8.74 |
% 57.39/8.74 | DELTA: instantiating (25) with fresh symbol all_550_0 gives:
% 57.39/8.74 | (76) nat$(0) = all_550_0 & Nat$(all_550_0) & ! [v0: A_iarray_iarray$] : !
% 57.39/8.74 | [v1: Nat$] : ! [v2: Nat$] : ! [v3: A_iarray_iarray$] : ! [v4:
% 57.39/8.74 | Nat_a_iarray_iarray_prod$] : ! [v5:
% 57.39/8.74 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v6: int] : !
% 57.39/8.74 | [v7: Nat$] : ! [v8: Nat_list$] : ! [v9:
% 57.39/8.74 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$] : ! [v10:
% 57.39/8.74 | A_iarray_iarray$] : ! [v11: Nat_a_iarray_iarray_prod$] : ! [v12:
% 57.39/8.74 | A_iarray_iarray$] : ! [v13: A_iarray_iarray_a_iarray_iarray_prod$]
% 57.39/8.74 | : ( ~ (nrows_iarray$(v0) = v2) | ~ (mat_iarray$(one$, v2) = v3) | ~
% 57.39/8.74 | (foldl$a(gauss_Jordan_column_k_iarrays_PA$, v5, v8) = v9) | ~
% 57.39/8.74 | (fst$d(v9) = v10) | ~ (snd$d(v9) = v11) | ~ (pair$d(v3, v4) = v5)
% 57.39/8.74 | | ~ (pair$c(v10, v12) = v13) | ~ (snd$b(v11) = v12) | ~
% 57.39/8.74 | (pair$b(all_550_0, v0) = v4) | ~ (fun_app$b(of_nat$, v1) = v6) | ~
% 57.39/8.74 | (nat$($sum(v6, 1)) = v7) | ~ (upt$(all_550_0, v7) = v8) | ~
% 57.39/8.74 | Nat$(v1) | ~ A_iarray_iarray$(v0) |
% 57.39/8.74 | (gauss_Jordan_upt_k_iarrays_PA$(v0, v1) = v13 &
% 57.39/8.74 | A_iarray_iarray_a_iarray_iarray_prod$(v13)))
% 57.39/8.74 |
% 57.39/8.74 | ALPHA: (76) implies:
% 57.39/8.74 | (77) nat$(0) = all_550_0
% 57.39/8.74 |
% 57.39/8.74 | DELTA: instantiating (14) with fresh symbol all_556_0 gives:
% 57.39/8.74 | (78) nat$(0) = all_556_0 & Nat$(all_556_0) & ! [v0: Nat_bool_fun$] : !
% 57.39/8.74 | [v1: Nat$] : ! [v2: int] : ! [v3: int] : (v2 = 0 | ~ (fun_app$s(v0,
% 57.39/8.74 | all_556_0) = v2) | ~ (fun_app$b(of_nat$, v1) = v3) | ~
% 57.39/8.74 | Nat_bool_fun$(v0) | ~ Nat$(v1) | ? [v4: Nat$] : ? [v5: int] :
% 57.39/8.74 | ($lesseq(v5, v3) & fun_app$s(v0, v4) = 0 & fun_app$b(of_nat$, v4) =
% 57.39/8.74 | v5 & Nat$(v4) & ! [v6: Nat$] : ! [v7: int] : ( ~ ($lesseq(1,
% 57.39/8.74 | $difference(v5, v7))) | ~ (fun_app$b(of_nat$, v6) = v7) |
% 57.39/8.74 | ~ Nat$(v6) | ? [v8: int] : ( ~ (v8 = 0) & fun_app$s(v0, v6) =
% 57.39/8.74 | v8))) | ? [v4: int] : ( ~ (v4 = 0) & fun_app$s(v0, v1) = v4))
% 57.39/8.74 |
% 57.39/8.74 | ALPHA: (78) implies:
% 57.39/8.74 | (79) nat$(0) = all_556_0
% 57.39/8.74 |
% 57.39/8.74 | DELTA: instantiating (26) with fresh symbols all_562_0, all_562_1 gives:
% 57.39/8.74 | (80) mat$(one$) = all_562_1 & nat$(0) = all_562_0 & Nat$(all_562_0) &
% 57.39/8.74 | A_c_vec_c_vec$(all_562_1) & ! [v0: A_b_vec_c_vec$] : ! [v1: Nat$] :
% 57.39/8.74 | ! [v2: Nat_a_b_vec_c_vec_prod$] : ! [v3:
% 57.39/8.74 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v4: int] : ! [v5:
% 57.39/8.74 | Nat$] : ! [v6: Nat_list$] : ! [v7:
% 57.39/8.74 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$] : ! [v8:
% 57.39/8.74 | A_c_vec_c_vec$] : ! [v9: Nat_a_b_vec_c_vec_prod$] : ! [v10:
% 57.39/8.74 | A_b_vec_c_vec$] : ! [v11: A_c_vec_c_vec_a_b_vec_c_vec_prod$] : ( ~
% 57.39/8.74 | (pair$l(v8, v10) = v11) | ~ (snd$(v7) = v9) | ~ (snd$a(v9) = v10)
% 57.39/8.74 | | ~ (pair$a(all_562_0, v0) = v2) | ~ (pair$(all_562_1, v2) = v3) |
% 57.39/8.74 | ~ (fun_app$b(of_nat$, v1) = v4) | ~ (nat$($sum(v4, 1)) = v5) | ~
% 57.39/8.74 | (upt$(all_562_0, v5) = v6) | ~ (foldl$(gauss_Jordan_column_k_PA$,
% 57.39/8.74 | v3, v6) = v7) | ~ (fst$(v7) = v8) | ~ Nat$(v1) | ~
% 57.39/8.74 | A_b_vec_c_vec$(v0) | (gauss_Jordan_upt_k_PA$(v0, v1) = v11 &
% 57.39/8.74 | A_c_vec_c_vec_a_b_vec_c_vec_prod$(v11)))
% 57.39/8.74 |
% 57.39/8.74 | ALPHA: (80) implies:
% 57.39/8.74 | (81) nat$(0) = all_562_0
% 57.39/8.74 | (82) mat$(one$) = all_562_1
% 57.39/8.74 |
% 57.39/8.74 | DELTA: instantiating (21) with fresh symbols all_565_0, all_565_1, all_565_2,
% 57.39/8.74 | all_565_3, all_565_4, all_565_5, all_565_6, all_565_7, all_565_8 gives:
% 57.39/8.74 | (83) snd$l(all_565_5) = all_565_4 &
% 57.39/8.74 | gauss_Jordan_upt_k_iarrays_PA$(all_565_2, ka$) = all_565_1 &
% 57.39/8.74 | matrix_to_iarray$a(all_565_4) = all_565_3 & matrix_to_iarray$a(a$) =
% 57.39/8.74 | all_565_2 & ncols$(a$) = all_565_8 & gauss_Jordan_upt_k_PA$(a$, ka$) =
% 57.39/8.74 | all_565_5 & snd$c(all_565_1) = all_565_0 & fun_app$b(of_nat$,
% 57.39/8.74 | all_565_8) = all_565_7 & fun_app$b(of_nat$, ka$) = all_565_6 &
% 57.39/8.74 | Nat$(all_565_8) & A_b_vec_c_vec$(all_565_4) &
% 57.39/8.74 | A_c_vec_c_vec_a_b_vec_c_vec_prod$(all_565_5) &
% 57.39/8.74 | A_iarray_iarray$(all_565_0) & A_iarray_iarray$(all_565_2) &
% 57.39/8.74 | A_iarray_iarray$(all_565_3) &
% 57.39/8.74 | A_iarray_iarray_a_iarray_iarray_prod$(all_565_1) & (all_565_0 =
% 57.39/8.74 | all_565_3 | ~ ($lesseq(1, $difference(all_565_7, all_565_6))))
% 57.39/8.74 |
% 57.39/8.74 | ALPHA: (83) implies:
% 57.39/8.74 | (84) fun_app$b(of_nat$, ka$) = all_565_6
% 57.39/8.74 |
% 57.39/8.74 | DELTA: instantiating (24) with fresh symbols all_567_0, all_567_1, all_567_2,
% 57.39/8.74 | all_567_3, all_567_4, all_567_5, all_567_6, all_567_7, all_567_8 gives:
% 57.39/8.74 | (85) nrows_iarray$(all_567_8) = all_567_7 & mat_iarray$(one$, all_567_7) =
% 57.39/8.74 | all_567_6 & foldl$a(gauss_Jordan_column_k_iarrays_PA$, all_567_3,
% 57.39/8.74 | all_567_0) = b$ & matrix_to_iarray$a(a$) = all_567_8 &
% 57.39/8.74 | pair$d(all_567_6, all_567_4) = all_567_3 & pair$b(all_567_5,
% 57.39/8.74 | all_567_8) = all_567_4 & fun_app$b(of_nat$, ka$) = all_567_2 &
% 57.39/8.74 | nat$($sum(all_567_2, 1)) = all_567_1 & nat$(0) = all_567_5 &
% 57.39/8.74 | upt$(all_567_5, all_567_1) = all_567_0 &
% 57.39/8.74 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(all_567_3) &
% 57.39/8.74 | Nat_a_iarray_iarray_prod$(all_567_4) & Nat$(all_567_1) &
% 57.39/8.74 | Nat$(all_567_5) & Nat$(all_567_7) & Nat_list$(all_567_0) &
% 57.39/8.74 | A_iarray_iarray$(all_567_6) & A_iarray_iarray$(all_567_8)
% 57.39/8.74 |
% 57.39/8.74 | ALPHA: (85) implies:
% 57.39/8.74 | (86) nat$(0) = all_567_5
% 57.39/8.74 | (87) nat$($sum(all_567_2, 1)) = all_567_1
% 57.39/8.74 | (88) fun_app$b(of_nat$, ka$) = all_567_2
% 57.39/8.74 |
% 57.39/8.74 | DELTA: instantiating (15) with fresh symbol all_569_0 gives:
% 57.39/8.75 | (89) nat$(0) = all_569_0 & Nat$(all_569_0) & ! [v0: Nat_bool_fun$] : !
% 57.39/8.75 | [v1: Nat$] : ! [v2: int] : ! [v3: int] : (v2 = 0 | ~ (fun_app$s(v0,
% 57.39/8.75 | all_569_0) = v2) | ~ (fun_app$b(of_nat$, v1) = v3) | ~
% 57.39/8.75 | Nat_bool_fun$(v0) | ~ Nat$(v1) | ? [v4: Nat$] : ? [v5: int] : ?
% 57.39/8.75 | [v6: Nat$] : ($lesseq(1, $difference(v3, v5)) & fun_app$s(v0, v6) =
% 57.39/8.75 | 0 & fun_app$b(of_nat$, v4) = v5 & nat$($sum(v5, 1)) = v6 &
% 57.39/8.75 | Nat$(v6) & Nat$(v4) & ! [v7: Nat$] : ! [v8: int] : ( ~
% 57.39/8.75 | ($lesseq(v8, v5)) | ~ (fun_app$b(of_nat$, v7) = v8) | ~
% 57.39/8.75 | Nat$(v7) | ? [v9: int] : ( ~ (v9 = 0) & fun_app$s(v0, v7) =
% 57.39/8.75 | v9))) | ? [v4: int] : ( ~ (v4 = 0) & fun_app$s(v0, v1) = v4))
% 57.39/8.75 |
% 57.39/8.75 | ALPHA: (89) implies:
% 57.39/8.75 | (90) nat$(0) = all_569_0
% 57.39/8.75 |
% 57.39/8.75 | DELTA: instantiating (6) with fresh symbols all_572_0, all_572_1, all_572_2,
% 57.39/8.75 | all_572_3, all_572_4, all_572_5, all_572_6, all_572_7, all_572_8,
% 57.39/8.75 | all_572_9, all_572_10, all_572_11, all_572_12 gives:
% 57.39/8.75 | (91) $lesseq(all_572_0, all_572_11) & nrows$(a$) = all_572_12 &
% 57.39/8.75 | snd$(all_572_3) = all_572_2 & fst$a(all_572_2) = all_572_1 &
% 57.39/8.75 | mat$(one$) = all_572_10 & pair$a(all_572_9, a$) = all_572_8 &
% 57.39/8.75 | pair$(all_572_10, all_572_8) = all_572_7 & fun_app$b(of_nat$,
% 57.39/8.75 | all_572_1) = all_572_0 & fun_app$b(of_nat$, all_572_12) = all_572_11
% 57.39/8.75 | & fun_app$b(of_nat$, ka$) = all_572_6 & nat$($sum(all_572_6, 1)) =
% 57.39/8.75 | all_572_5 & nat$(0) = all_572_9 & upt$(all_572_9, all_572_5) =
% 57.39/8.75 | all_572_4 & foldl$(gauss_Jordan_column_k_PA$, all_572_7, all_572_4) =
% 57.39/8.75 | all_572_3 & Nat_a_b_vec_c_vec_prod$(all_572_2) &
% 57.39/8.75 | Nat_a_b_vec_c_vec_prod$(all_572_8) &
% 57.39/8.75 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_572_3) &
% 57.39/8.75 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_572_7) &
% 57.39/8.75 | Nat$(all_572_1) & Nat$(all_572_5) & Nat$(all_572_9) & Nat$(all_572_12)
% 57.39/8.75 | & Nat_list$(all_572_4) & A_c_vec_c_vec$(all_572_10)
% 57.39/8.75 |
% 57.39/8.75 | ALPHA: (91) implies:
% 57.39/8.75 | (92) foldl$(gauss_Jordan_column_k_PA$, all_572_7, all_572_4) = all_572_3
% 57.39/8.75 | (93) upt$(all_572_9, all_572_5) = all_572_4
% 57.39/8.75 | (94) nat$(0) = all_572_9
% 57.39/8.75 | (95) nat$($sum(all_572_6, 1)) = all_572_5
% 57.39/8.75 | (96) fun_app$b(of_nat$, ka$) = all_572_6
% 57.39/8.75 | (97) pair$(all_572_10, all_572_8) = all_572_7
% 57.39/8.75 | (98) pair$a(all_572_9, a$) = all_572_8
% 57.39/8.75 | (99) mat$(one$) = all_572_10
% 57.39/8.75 | (100) fst$a(all_572_2) = all_572_1
% 57.39/8.75 | (101) snd$(all_572_3) = all_572_2
% 57.39/8.75 |
% 57.39/8.75 | DELTA: instantiating (4) with fresh symbols all_575_0, all_575_1, all_575_2,
% 57.39/8.75 | all_575_3, all_575_4, all_575_5, all_575_6, all_575_7, all_575_8,
% 57.39/8.75 | all_575_9, all_575_10, all_575_11, all_575_12 gives:
% 57.39/8.75 | (102) gauss_Jordan_upt_k_PA$(a$, all_575_11) = all_575_10 &
% 57.39/8.75 | fst$k(all_575_10) = all_575_9 & mat$(one$) = all_575_7 &
% 57.39/8.75 | pair$a(all_575_6, a$) = all_575_5 & pair$(all_575_7, all_575_5) =
% 57.39/8.75 | all_575_4 & fun_app$b(of_nat$, ka$) = all_575_12 &
% 57.39/8.75 | nat$($sum(all_575_12, 2)) = all_575_3 & nat$($sum(all_575_12, 1)) =
% 57.39/8.75 | all_575_11 & nat$(0) = all_575_6 & upt$(all_575_6, all_575_3) =
% 57.39/8.75 | all_575_2 & foldl$(gauss_Jordan_column_k_PA$, all_575_4, all_575_2) =
% 57.39/8.75 | all_575_1 & fst$(all_575_1) = all_575_0 &
% 57.39/8.75 | matrix_to_iarray$(all_575_0) = all_575_8 &
% 57.39/8.75 | matrix_to_iarray$(all_575_9) = all_575_8 &
% 57.39/8.75 | Nat_a_b_vec_c_vec_prod$(all_575_5) &
% 57.39/8.75 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_575_1) &
% 57.39/8.75 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_575_4) &
% 57.39/8.75 | Nat$(all_575_3) & Nat$(all_575_6) & Nat$(all_575_11) &
% 57.39/8.75 | Nat_list$(all_575_2) & A_c_vec_c_vec_a_b_vec_c_vec_prod$(all_575_10)
% 57.39/8.75 | & A_iarray_iarray$(all_575_8) & A_c_vec_c_vec$(all_575_0) &
% 57.39/8.75 | A_c_vec_c_vec$(all_575_7) & A_c_vec_c_vec$(all_575_9)
% 57.39/8.75 |
% 57.39/8.75 | ALPHA: (102) implies:
% 57.39/8.75 | (103) matrix_to_iarray$(all_575_0) = all_575_8
% 57.39/8.75 | (104) fst$(all_575_1) = all_575_0
% 57.39/8.75 | (105) foldl$(gauss_Jordan_column_k_PA$, all_575_4, all_575_2) = all_575_1
% 57.39/8.75 | (106) upt$(all_575_6, all_575_3) = all_575_2
% 57.39/8.75 | (107) nat$(0) = all_575_6
% 57.39/8.75 | (108) nat$($sum(all_575_12, 1)) = all_575_11
% 57.39/8.75 | (109) nat$($sum(all_575_12, 2)) = all_575_3
% 57.39/8.75 | (110) fun_app$b(of_nat$, ka$) = all_575_12
% 57.39/8.75 | (111) pair$(all_575_7, all_575_5) = all_575_4
% 57.39/8.75 | (112) pair$a(all_575_6, a$) = all_575_5
% 57.39/8.75 | (113) mat$(one$) = all_575_7
% 57.39/8.75 |
% 57.39/8.75 | DELTA: instantiating (5) with fresh symbols all_577_0, all_577_1, all_577_2,
% 57.39/8.75 | all_577_3, all_577_4, all_577_5, all_577_6, all_577_7, all_577_8,
% 57.39/8.75 | all_577_9, all_577_10, all_577_11, all_577_12, all_577_13 gives:
% 57.39/8.75 | (114) gauss_Jordan_upt_k_PA$(a$, all_577_12) = all_577_11 &
% 57.39/8.75 | fst$k(all_577_11) = all_577_10 & mat$(one$) = all_577_8 &
% 57.39/8.75 | pair$a(all_577_7, a$) = all_577_6 & pair$(all_577_8, all_577_6) =
% 57.39/8.75 | all_577_5 & fun_app$b(of_nat$, ka$) = all_577_13 &
% 57.39/8.75 | nat$($sum(all_577_13, 1)) = all_577_12 & nat$(0) = all_577_7 &
% 57.39/8.75 | upt$(all_577_7, all_577_12) = all_577_4 &
% 57.39/8.75 | foldl$(gauss_Jordan_column_k_PA$, all_577_5, all_577_4) = all_577_3 &
% 57.39/8.75 | fun_app$a(gauss_Jordan_column_k_PA$, all_577_3) = all_577_2 &
% 57.39/8.75 | fun_app$(all_577_2, all_577_12) = all_577_1 & fst$(all_577_1) =
% 57.39/8.75 | all_577_0 & matrix_to_iarray$(all_577_0) = all_577_9 &
% 57.39/8.75 | matrix_to_iarray$(all_577_10) = all_577_9 &
% 57.39/8.75 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(all_577_2) &
% 57.39/8.75 | Nat_a_b_vec_c_vec_prod$(all_577_6) &
% 57.39/8.75 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_577_1) &
% 57.39/8.75 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_577_3) &
% 57.39/8.75 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_577_5) &
% 57.39/8.75 | Nat$(all_577_7) & Nat$(all_577_12) & Nat_list$(all_577_4) &
% 57.39/8.75 | A_c_vec_c_vec_a_b_vec_c_vec_prod$(all_577_11) &
% 57.39/8.75 | A_iarray_iarray$(all_577_9) & A_c_vec_c_vec$(all_577_0) &
% 57.39/8.75 | A_c_vec_c_vec$(all_577_8) & A_c_vec_c_vec$(all_577_10)
% 57.39/8.75 |
% 57.39/8.75 | ALPHA: (114) implies:
% 57.39/8.75 | (115) fst$(all_577_1) = all_577_0
% 57.39/8.75 | (116) fun_app$(all_577_2, all_577_12) = all_577_1
% 57.39/8.75 | (117) fun_app$a(gauss_Jordan_column_k_PA$, all_577_3) = all_577_2
% 57.39/8.75 | (118) foldl$(gauss_Jordan_column_k_PA$, all_577_5, all_577_4) = all_577_3
% 57.39/8.75 | (119) upt$(all_577_7, all_577_12) = all_577_4
% 57.39/8.75 | (120) nat$(0) = all_577_7
% 57.39/8.75 | (121) nat$($sum(all_577_13, 1)) = all_577_12
% 57.39/8.75 | (122) fun_app$b(of_nat$, ka$) = all_577_13
% 57.39/8.75 | (123) pair$(all_577_8, all_577_6) = all_577_5
% 57.39/8.75 | (124) pair$a(all_577_7, a$) = all_577_6
% 57.39/8.75 | (125) mat$(one$) = all_577_8
% 57.39/8.75 |
% 57.39/8.75 | DELTA: instantiating (9) with fresh symbols all_579_0, all_579_1, all_579_2,
% 57.39/8.75 | all_579_3, all_579_4, all_579_5, all_579_6, all_579_7, all_579_8,
% 57.39/8.75 | all_579_9, all_579_10, all_579_11, all_579_12, all_579_13, all_579_14
% 57.39/8.75 | gives:
% 57.39/8.76 | (126) ncols$(a$) = all_579_14 & nrows$(a$) = all_579_11 & snd$(all_579_3) =
% 57.39/8.76 | all_579_2 & fst$a(all_579_2) = all_579_1 & mat$(one$) = all_579_9 &
% 57.39/8.76 | pair$a(all_579_8, a$) = all_579_7 & pair$(all_579_9, all_579_7) =
% 57.39/8.76 | all_579_6 & fun_app$b(of_nat$, all_579_1) = all_579_0 &
% 57.39/8.76 | fun_app$b(of_nat$, all_579_11) = all_579_10 & fun_app$b(of_nat$,
% 57.39/8.76 | all_579_14) = all_579_13 & fun_app$b(of_nat$, ka$) = all_579_12 &
% 57.39/8.76 | nat$($sum(all_579_12, 1)) = all_579_5 & nat$(0) = all_579_8 &
% 57.39/8.76 | upt$(all_579_8, all_579_5) = all_579_4 &
% 57.39/8.76 | foldl$(gauss_Jordan_column_k_PA$, all_579_6, all_579_4) = all_579_3 &
% 57.39/8.76 | Nat_a_b_vec_c_vec_prod$(all_579_2) &
% 57.39/8.76 | Nat_a_b_vec_c_vec_prod$(all_579_7) &
% 57.39/8.76 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_579_3) &
% 57.39/8.76 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_579_6) &
% 57.39/8.76 | Nat$(all_579_1) & Nat$(all_579_5) & Nat$(all_579_8) &
% 57.39/8.76 | Nat$(all_579_11) & Nat$(all_579_14) & Nat_list$(all_579_4) &
% 57.39/8.76 | A_c_vec_c_vec$(all_579_9) & ( ~ ($lesseq(1, $difference(all_579_0,
% 57.39/8.76 | all_579_10))) | ~ ($lesseq(1, $difference(all_579_13,
% 57.39/8.76 | all_579_12))))
% 57.39/8.76 |
% 57.39/8.76 | ALPHA: (126) implies:
% 57.39/8.76 | (127) foldl$(gauss_Jordan_column_k_PA$, all_579_6, all_579_4) = all_579_3
% 57.39/8.76 | (128) upt$(all_579_8, all_579_5) = all_579_4
% 57.39/8.76 | (129) nat$(0) = all_579_8
% 57.39/8.76 | (130) nat$($sum(all_579_12, 1)) = all_579_5
% 57.39/8.76 | (131) fun_app$b(of_nat$, ka$) = all_579_12
% 57.39/8.76 | (132) pair$(all_579_9, all_579_7) = all_579_6
% 57.39/8.76 | (133) pair$a(all_579_8, a$) = all_579_7
% 57.39/8.76 | (134) mat$(one$) = all_579_9
% 57.39/8.76 | (135) fst$a(all_579_2) = all_579_1
% 57.39/8.76 | (136) snd$(all_579_3) = all_579_2
% 57.39/8.76 |
% 57.39/8.76 | DELTA: instantiating (12) with fresh symbol all_581_0 gives:
% 57.39/8.76 | (137) nat$(0) = all_581_0 & Nat$(all_581_0) & ! [v0: Nat$] : ! [v1:
% 57.39/8.76 | Nat_bool_fun$] : ! [v2: int] : ! [v3: int] : (v3 = 0 | ~
% 57.39/8.76 | (fun_app$s(v1, all_581_0) = v3) | ~ (fun_app$b(of_nat$, v0) = v2)
% 57.39/8.76 | | ~ Nat_bool_fun$(v1) | ~ Nat$(v0) | ? [v4: Nat$] : ? [v5: int]
% 57.39/8.76 | : ? [v6: Nat$] : ($lesseq(1, $difference(v2, v5)) & fun_app$s(v1,
% 57.39/8.76 | v6) = 0 & fun_app$b(of_nat$, v4) = v5 & nat$($sum(v5, 1)) = v6
% 57.39/8.76 | & Nat$(v6) & Nat$(v4)) | ! [v4: Nat$] : ! [v5: int] : ( ~
% 57.39/8.76 | ($lesseq(v5, v2)) | ~ (fun_app$b(of_nat$, v4) = v5) | ~
% 57.39/8.76 | Nat$(v4) | ? [v6: int] : ( ~ (v6 = 0) & fun_app$s(v1, v4) =
% 57.39/8.76 | v6))) & ! [v0: Nat$] : ! [v1: Nat_bool_fun$] : ! [v2: any] :
% 57.39/8.76 | ! [v3: int] : ( ~ (fun_app$s(v1, all_581_0) = v2) | ~
% 57.39/8.76 | (fun_app$b(of_nat$, v0) = v3) | ~ Nat_bool_fun$(v1) | ~ Nat$(v0)
% 57.39/8.76 | | ? [v4: Nat$] : ? [v5: int] : ($lesseq(v5, v3) & fun_app$s(v1,
% 57.39/8.76 | v4) = 0 & fun_app$b(of_nat$, v4) = v5 & Nat$(v4)) | ( ~ (v2 =
% 57.39/8.76 | 0) & ! [v4: Nat$] : ! [v5: int] : ! [v6: Nat$] : ( ~
% 57.39/8.76 | ($lesseq(1, $difference(v3, v5))) | ~ (fun_app$s(v1, v6) = 0)
% 57.39/8.76 | | ~ (fun_app$b(of_nat$, v4) = v5) | ~ (nat$($sum(v5, 1)) =
% 57.39/8.76 | v6) | ~ Nat$(v4))))
% 57.39/8.76 |
% 57.39/8.76 | ALPHA: (137) implies:
% 57.39/8.76 | (138) nat$(0) = all_581_0
% 57.39/8.76 |
% 57.39/8.76 | DELTA: instantiating (1) with fresh symbols all_584_0, all_584_1, all_584_2,
% 57.39/8.76 | all_584_3, all_584_4, all_584_5, all_584_6, all_584_7, all_584_8,
% 57.39/8.76 | all_584_9, all_584_10, all_584_11, all_584_12, all_584_13, all_584_14,
% 57.39/8.76 | all_584_15 gives:
% 57.39/8.76 | (139) mat$(one$) = all_584_15 & pair$a(all_584_14, a$) = all_584_13 &
% 57.39/8.76 | pair$(all_584_15, all_584_13) = all_584_12 & fun_app$b(of_nat$, ka$)
% 57.39/8.76 | = all_584_11 & nat$($sum(all_584_11, 2)) = all_584_10 &
% 57.39/8.76 | nat$($sum(all_584_11, 1)) = all_584_5 & nat$(0) = all_584_14 &
% 57.39/8.76 | upt$(all_584_14, all_584_5) = all_584_4 & upt$(all_584_14,
% 57.39/8.76 | all_584_10) = all_584_9 & foldl$(gauss_Jordan_column_k_PA$,
% 57.39/8.76 | all_584_12, all_584_4) = all_584_3 &
% 57.39/8.76 | foldl$(gauss_Jordan_column_k_PA$, all_584_12, all_584_9) = all_584_8
% 57.39/8.76 | & fun_app$a(gauss_Jordan_column_k_PA$, all_584_3) = all_584_2 &
% 57.39/8.76 | fun_app$(all_584_2, all_584_5) = all_584_1 & fst$(all_584_1) =
% 57.39/8.76 | all_584_0 & fst$(all_584_8) = all_584_7 &
% 57.39/8.76 | matrix_to_iarray$(all_584_0) = all_584_6 &
% 57.39/8.76 | matrix_to_iarray$(all_584_7) = all_584_6 &
% 57.39/8.76 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(all_584_2) &
% 57.39/8.76 | Nat_a_b_vec_c_vec_prod$(all_584_13) &
% 57.39/8.76 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_584_1) &
% 57.39/8.76 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_584_3) &
% 57.39/8.76 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_584_8) &
% 57.39/8.76 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_584_12) &
% 57.39/8.76 | Nat$(all_584_5) & Nat$(all_584_10) & Nat$(all_584_14) &
% 57.39/8.76 | Nat_list$(all_584_4) & Nat_list$(all_584_9) &
% 57.39/8.76 | A_iarray_iarray$(all_584_6) & A_c_vec_c_vec$(all_584_0) &
% 57.39/8.76 | A_c_vec_c_vec$(all_584_7) & A_c_vec_c_vec$(all_584_15)
% 57.39/8.76 |
% 57.39/8.76 | ALPHA: (139) implies:
% 57.39/8.76 | (140) matrix_to_iarray$(all_584_7) = all_584_6
% 57.39/8.76 | (141) matrix_to_iarray$(all_584_0) = all_584_6
% 57.39/8.76 | (142) fst$(all_584_8) = all_584_7
% 57.39/8.76 | (143) fst$(all_584_1) = all_584_0
% 57.39/8.76 | (144) fun_app$(all_584_2, all_584_5) = all_584_1
% 57.39/8.76 | (145) fun_app$a(gauss_Jordan_column_k_PA$, all_584_3) = all_584_2
% 57.39/8.76 | (146) foldl$(gauss_Jordan_column_k_PA$, all_584_12, all_584_9) = all_584_8
% 57.39/8.76 | (147) foldl$(gauss_Jordan_column_k_PA$, all_584_12, all_584_4) = all_584_3
% 57.39/8.76 | (148) upt$(all_584_14, all_584_10) = all_584_9
% 57.39/8.76 | (149) upt$(all_584_14, all_584_5) = all_584_4
% 57.39/8.76 | (150) nat$(0) = all_584_14
% 57.39/8.76 | (151) nat$($sum(all_584_11, 1)) = all_584_5
% 57.39/8.76 | (152) nat$($sum(all_584_11, 2)) = all_584_10
% 57.39/8.76 | (153) fun_app$b(of_nat$, ka$) = all_584_11
% 57.39/8.76 | (154) pair$(all_584_15, all_584_13) = all_584_12
% 57.39/8.76 | (155) pair$a(all_584_14, a$) = all_584_13
% 57.39/8.76 | (156) mat$(one$) = all_584_15
% 57.39/8.76 |
% 57.39/8.76 | DELTA: instantiating (13) with fresh symbol all_586_0 gives:
% 57.39/8.77 | (157) nat$(0) = all_586_0 & Nat$(all_586_0) & ! [v0: Nat$] : ! [v1:
% 57.39/8.77 | Nat_bool_fun$] : ! [v2: int] : ! [v3: any] : ( ~ (fun_app$s(v1,
% 57.39/8.77 | all_586_0) = v3) | ~ (fun_app$b(of_nat$, v0) = v2) | ~
% 57.39/8.77 | Nat_bool_fun$(v1) | ~ Nat$(v0) | ? [v4: Nat$] : ? [v5: int] : ?
% 57.39/8.77 | [v6: int] : ( ~ (v6 = 0) & $lesseq(v5, v2) & fun_app$s(v1, v4) = v6
% 57.39/8.77 | & fun_app$b(of_nat$, v4) = v5 & Nat$(v4)) | (v3 = 0 & ! [v4:
% 57.39/8.77 | Nat$] : ! [v5: int] : ! [v6: Nat$] : ! [v7: int] : (v7 = 0 |
% 57.39/8.77 | ~ ($lesseq(1, $difference(v2, v5))) | ~ (fun_app$s(v1, v6) =
% 57.39/8.77 | v7) | ~ (fun_app$b(of_nat$, v4) = v5) | ~ (nat$($sum(v5,
% 57.39/8.77 | 1)) = v6) | ~ Nat$(v4)))) & ! [v0: Nat$] : ! [v1:
% 57.39/8.77 | Nat_bool_fun$] : ! [v2: int] : ( ~ (fun_app$s(v1, all_586_0) = 0)
% 57.39/8.77 | | ~ (fun_app$b(of_nat$, v0) = v2) | ~ Nat_bool_fun$(v1) | ~
% 57.39/8.77 | Nat$(v0) | ? [v3: Nat$] : ? [v4: int] : ? [v5: Nat$] : ? [v6:
% 57.39/8.77 | int] : ( ~ (v6 = 0) & $lesseq(1, $difference(v2, v4)) &
% 57.39/8.77 | fun_app$s(v1, v5) = v6 & fun_app$b(of_nat$, v3) = v4 &
% 57.39/8.77 | nat$($sum(v4, 1)) = v5 & Nat$(v5) & Nat$(v3)) | ! [v3: Nat$] :
% 57.39/8.77 | ! [v4: int] : ( ~ ($lesseq(v4, v2)) | ~ (fun_app$b(of_nat$, v3) =
% 57.39/8.77 | v4) | ~ Nat$(v3) | fun_app$s(v1, v3) = 0))
% 57.39/8.77 |
% 57.39/8.77 | ALPHA: (157) implies:
% 57.39/8.77 | (158) nat$(0) = all_586_0
% 57.39/8.77 |
% 57.39/8.77 | DELTA: instantiating (17) with fresh symbol all_589_0 gives:
% 57.39/8.77 | (159) nat$(0) = all_589_0 & Nat$(all_589_0) & ! [v0:
% 57.39/8.77 | Nat_nat_bool_fun_fun$] : ! [v1: Nat$] : ! [v2: Nat$] : ! [v3:
% 57.39/8.77 | Nat_bool_fun$] : ! [v4: int] : (v4 = 0 | ~ (fun_app$t(v0, v1) =
% 57.39/8.77 | v3) | ~ (fun_app$s(v3, v2) = v4) | ~ Nat$(v2) | ~ Nat$(v1) |
% 57.39/8.77 | ~ Nat_nat_bool_fun_fun$(v0) | ? [v5: Nat$] : ? [v6: Nat$] : ?
% 57.39/8.77 | [v7: Nat_bool_fun$] : ? [v8: int] : ? [v9: Nat$] : ? [v10:
% 57.39/8.77 | Nat_bool_fun$] : ? [v11: int] : ? [v12: Nat$] : ? [v13: int] :
% 57.39/8.77 | ( ~ (v13 = 0) & fun_app$t(v0, v9) = v10 & fun_app$t(v0, v5) = v7 &
% 57.39/8.77 | fun_app$s(v10, v12) = v13 & fun_app$s(v7, v6) = 0 &
% 57.39/8.77 | fun_app$b(of_nat$, v6) = v11 & fun_app$b(of_nat$, v5) = v8 &
% 57.39/8.77 | nat$($sum(v11, 1)) = v12 & nat$($sum(v8, 1)) = v9 &
% 57.39/8.77 | Nat_bool_fun$(v10) & Nat_bool_fun$(v7) & Nat$(v12) & Nat$(v9) &
% 57.39/8.77 | Nat$(v6) & Nat$(v5)) | ? [v5: Nat$] : ? [v6: Nat_bool_fun$] :
% 57.39/8.77 | ? [v7: int] : ( ~ (v7 = 0) & fun_app$t(v0, v5) = v6 & fun_app$s(v6,
% 57.39/8.77 | all_589_0) = v7 & Nat_bool_fun$(v6) & Nat$(v5)) | ? [v5:
% 57.39/8.77 | Nat_bool_fun$] : (fun_app$t(v0, all_589_0) = v5 &
% 57.39/8.77 | Nat_bool_fun$(v5) & ? [v6: Nat$] : ? [v7: int] : ? [v8: Nat$]
% 57.39/8.77 | : ? [v9: int] : ( ~ (v9 = 0) & fun_app$s(v5, v8) = v9 &
% 57.39/8.77 | fun_app$b(of_nat$, v6) = v7 & nat$($sum(v7, 1)) = v8 & Nat$(v8)
% 57.39/8.77 | & Nat$(v6))))
% 57.39/8.77 |
% 57.39/8.77 | ALPHA: (159) implies:
% 57.39/8.77 | (160) nat$(0) = all_589_0
% 57.39/8.77 |
% 57.39/8.77 | DELTA: instantiating (23) with fresh symbols all_592_0, all_592_1, all_592_2,
% 57.39/8.77 | all_592_3, all_592_4, all_592_5, all_592_6, all_592_7, all_592_8,
% 57.39/8.77 | all_592_9, all_592_10, all_592_11, all_592_12, all_592_13, all_592_14,
% 57.39/8.77 | all_592_15, all_592_16, all_592_17, all_592_18 gives:
% 57.39/8.77 | (161) nrows_iarray$(all_592_7) = all_592_6 & mat_iarray$(one$, all_592_6) =
% 57.39/8.77 | all_592_5 & foldl$a(gauss_Jordan_column_k_iarrays_PA$, all_592_3,
% 57.39/8.77 | all_592_12) = all_592_2 & matrix_to_iarray$a(a$) = all_592_7 &
% 57.39/8.77 | snd$d(all_592_2) = all_592_1 & pair$d(all_592_5, all_592_4) =
% 57.39/8.77 | all_592_3 & fst$b(all_592_1) = all_592_0 & pair$b(all_592_17,
% 57.39/8.77 | all_592_7) = all_592_4 & snd$(all_592_11) = all_592_10 &
% 57.39/8.77 | fst$a(all_592_10) = all_592_9 & mat$(one$) = all_592_18 &
% 57.39/8.77 | pair$a(all_592_17, a$) = all_592_16 & pair$(all_592_18, all_592_16) =
% 57.39/8.77 | all_592_15 & fun_app$b(of_nat$, all_592_0) = all_592_8 &
% 57.39/8.77 | fun_app$b(of_nat$, all_592_9) = all_592_8 & fun_app$b(of_nat$, ka$) =
% 57.39/8.77 | all_592_14 & nat$($sum(all_592_14, 1)) = all_592_13 & nat$(0) =
% 57.39/8.77 | all_592_17 & upt$(all_592_17, all_592_13) = all_592_12 &
% 57.39/8.77 | foldl$(gauss_Jordan_column_k_PA$, all_592_15, all_592_12) =
% 57.39/8.77 | all_592_11 &
% 57.39/8.77 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(all_592_2) &
% 57.39/8.77 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(all_592_3) &
% 57.39/8.77 | Nat_a_b_vec_c_vec_prod$(all_592_10) &
% 57.39/8.77 | Nat_a_b_vec_c_vec_prod$(all_592_16) &
% 57.39/8.77 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_592_11) &
% 57.39/8.77 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_592_15) &
% 57.39/8.77 | Nat_a_iarray_iarray_prod$(all_592_1) &
% 57.39/8.77 | Nat_a_iarray_iarray_prod$(all_592_4) & Nat$(all_592_0) &
% 57.39/8.77 | Nat$(all_592_6) & Nat$(all_592_9) & Nat$(all_592_13) &
% 57.39/8.77 | Nat$(all_592_17) & Nat_list$(all_592_12) &
% 57.39/8.77 | A_iarray_iarray$(all_592_5) & A_iarray_iarray$(all_592_7) &
% 57.39/8.77 | A_c_vec_c_vec$(all_592_18)
% 57.39/8.77 |
% 57.39/8.77 | ALPHA: (161) implies:
% 57.39/8.77 | (162) foldl$(gauss_Jordan_column_k_PA$, all_592_15, all_592_12) =
% 57.39/8.77 | all_592_11
% 57.39/8.77 | (163) upt$(all_592_17, all_592_13) = all_592_12
% 57.39/8.77 | (164) nat$(0) = all_592_17
% 57.39/8.77 | (165) nat$($sum(all_592_14, 1)) = all_592_13
% 57.39/8.77 | (166) fun_app$b(of_nat$, ka$) = all_592_14
% 57.39/8.77 | (167) pair$(all_592_18, all_592_16) = all_592_15
% 57.39/8.77 | (168) pair$a(all_592_17, a$) = all_592_16
% 57.39/8.77 | (169) mat$(one$) = all_592_18
% 57.39/8.77 | (170) fst$a(all_592_10) = all_592_9
% 57.39/8.77 | (171) snd$(all_592_11) = all_592_10
% 57.39/8.77 |
% 57.39/8.77 | DELTA: instantiating (22) with fresh symbols all_594_0, all_594_1, all_594_2,
% 57.39/8.77 | all_594_3, all_594_4, all_594_5, all_594_6, all_594_7, all_594_8,
% 57.39/8.77 | all_594_9, all_594_10, all_594_11, all_594_12, all_594_13, all_594_14,
% 57.39/8.77 | all_594_15, all_594_16, all_594_17, all_594_18, all_594_19, all_594_20,
% 57.39/8.77 | all_594_21 gives:
% 57.39/8.77 | (172) nrows_iarray$(all_594_8) = all_594_7 & mat_iarray$(one$, all_594_7) =
% 57.39/8.77 | all_594_6 & foldl$a(gauss_Jordan_column_k_iarrays_PA$, all_594_4,
% 57.39/8.77 | all_594_13) = all_594_3 & matrix_to_iarray$a(a$) = all_594_8 &
% 57.39/8.77 | ncols$(a$) = all_594_21 & snd$d(all_594_3) = all_594_2 &
% 57.39/8.77 | pair$d(all_594_6, all_594_5) = all_594_4 & fst$b(all_594_2) =
% 57.39/8.77 | all_594_1 & pair$b(all_594_17, all_594_8) = all_594_5 &
% 57.39/8.77 | snd$(all_594_12) = all_594_11 & fst$a(all_594_11) = all_594_10 &
% 57.39/8.77 | mat$(one$) = all_594_18 & pair$a(all_594_17, a$) = all_594_16 &
% 57.39/8.77 | pair$(all_594_18, all_594_16) = all_594_15 & fun_app$b(of_nat$,
% 57.39/8.77 | all_594_1) = all_594_0 & fun_app$b(of_nat$, all_594_10) = all_594_9
% 57.39/8.77 | & fun_app$b(of_nat$, all_594_21) = all_594_20 & fun_app$b(of_nat$,
% 57.39/8.77 | ka$) = all_594_19 & nat$($sum(all_594_19, 1)) = all_594_14 &
% 57.39/8.77 | nat$(0) = all_594_17 & upt$(all_594_17, all_594_14) = all_594_13 &
% 57.39/8.77 | foldl$(gauss_Jordan_column_k_PA$, all_594_15, all_594_13) =
% 57.39/8.77 | all_594_12 &
% 57.39/8.77 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(all_594_3) &
% 57.39/8.77 | A_iarray_iarray_nat_a_iarray_iarray_prod_prod$(all_594_4) &
% 57.39/8.77 | Nat_a_b_vec_c_vec_prod$(all_594_11) &
% 57.39/8.77 | Nat_a_b_vec_c_vec_prod$(all_594_16) &
% 57.39/8.77 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_594_12) &
% 57.39/8.77 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_594_15) &
% 57.39/8.77 | Nat_a_iarray_iarray_prod$(all_594_2) &
% 57.39/8.77 | Nat_a_iarray_iarray_prod$(all_594_5) & Nat$(all_594_1) &
% 57.39/8.77 | Nat$(all_594_7) & Nat$(all_594_10) & Nat$(all_594_14) &
% 57.39/8.77 | Nat$(all_594_17) & Nat$(all_594_21) & Nat_list$(all_594_13) &
% 57.39/8.77 | A_iarray_iarray$(all_594_6) & A_iarray_iarray$(all_594_8) &
% 57.39/8.77 | A_c_vec_c_vec$(all_594_18) & (all_594_0 = all_594_9 | ~ ($lesseq(1,
% 57.39/8.77 | $difference(all_594_20, all_594_19))))
% 57.39/8.77 |
% 57.39/8.77 | ALPHA: (172) implies:
% 57.39/8.77 | (173) foldl$(gauss_Jordan_column_k_PA$, all_594_15, all_594_13) =
% 57.39/8.77 | all_594_12
% 57.39/8.77 | (174) upt$(all_594_17, all_594_14) = all_594_13
% 57.39/8.77 | (175) nat$(0) = all_594_17
% 57.39/8.77 | (176) nat$($sum(all_594_19, 1)) = all_594_14
% 57.39/8.77 | (177) fun_app$b(of_nat$, ka$) = all_594_19
% 57.39/8.77 | (178) pair$(all_594_18, all_594_16) = all_594_15
% 57.39/8.77 | (179) pair$a(all_594_17, a$) = all_594_16
% 57.39/8.77 | (180) mat$(one$) = all_594_18
% 57.39/8.77 | (181) fst$a(all_594_11) = all_594_10
% 57.39/8.77 | (182) snd$(all_594_12) = all_594_11
% 57.39/8.77 |
% 57.39/8.77 | DELTA: instantiating (27) with fresh symbols all_596_0, all_596_1, all_596_2,
% 57.39/8.77 | all_596_3, all_596_4, all_596_5, all_596_6, all_596_7, all_596_8,
% 57.39/8.77 | all_596_9, all_596_10, all_596_11, all_596_12, all_596_13, all_596_14,
% 57.39/8.77 | all_596_15, all_596_16, all_596_17, all_596_18, all_596_19, all_596_20,
% 57.39/8.77 | all_596_21 gives:
% 57.39/8.78 | (183) ~ (all_596_0 = all_596_10) & snd$(all_596_14) = all_596_8 &
% 57.39/8.78 | fst$a(all_596_8) = all_596_7 & snd$a(all_596_8) = all_596_6 &
% 57.39/8.78 | mat$(one$) = all_596_21 & pair$a(all_596_7, all_596_6) = all_596_5 &
% 57.39/8.78 | pair$a(all_596_20, a$) = all_596_19 & pair$(all_596_9, all_596_5) =
% 57.39/8.78 | all_596_4 & pair$(all_596_21, all_596_19) = all_596_18 &
% 57.39/8.78 | fun_app$b(of_nat$, ka$) = all_596_17 & nat$($sum(all_596_17, 1)) =
% 57.39/8.78 | all_596_16 & nat$(0) = all_596_20 & upt$(all_596_20, all_596_16) =
% 57.39/8.78 | all_596_15 & foldl$(gauss_Jordan_column_k_PA$, all_596_18,
% 57.39/8.78 | all_596_15) = all_596_14 & fun_app$a(gauss_Jordan_column_k_PA$,
% 57.39/8.78 | all_596_4) = all_596_3 & fun_app$a(gauss_Jordan_column_k_PA$,
% 57.39/8.78 | all_596_14) = all_596_13 & fun_app$(all_596_3, all_596_16) =
% 57.39/8.78 | all_596_2 & fun_app$(all_596_13, all_596_16) = all_596_12 &
% 57.39/8.78 | fst$(all_596_2) = all_596_1 & fst$(all_596_12) = all_596_11 &
% 57.39/8.78 | fst$(all_596_14) = all_596_9 & matrix_to_iarray$(all_596_1) =
% 57.39/8.78 | all_596_0 & matrix_to_iarray$(all_596_11) = all_596_10 &
% 57.39/8.78 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(all_596_3) &
% 57.39/8.78 | Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$(all_596_13) &
% 57.39/8.78 | Nat_a_b_vec_c_vec_prod$(all_596_5) &
% 57.39/8.78 | Nat_a_b_vec_c_vec_prod$(all_596_8) &
% 57.39/8.78 | Nat_a_b_vec_c_vec_prod$(all_596_19) &
% 57.39/8.78 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_596_2) &
% 57.39/8.78 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_596_4) &
% 57.39/8.78 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_596_12) &
% 57.39/8.78 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_596_14) &
% 57.39/8.78 | A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$(all_596_18) &
% 57.39/8.78 | Nat$(all_596_7) & Nat$(all_596_16) & Nat$(all_596_20) &
% 57.39/8.78 | A_b_vec_c_vec$(all_596_6) & Nat_list$(all_596_15) &
% 57.39/8.78 | A_iarray_iarray$(all_596_0) & A_iarray_iarray$(all_596_10) &
% 57.39/8.78 | A_c_vec_c_vec$(all_596_1) & A_c_vec_c_vec$(all_596_9) &
% 57.39/8.78 | A_c_vec_c_vec$(all_596_11) & A_c_vec_c_vec$(all_596_21)
% 57.39/8.78 |
% 57.39/8.78 | ALPHA: (183) implies:
% 57.39/8.78 | (184) ~ (all_596_0 = all_596_10)
% 57.39/8.78 | (185) matrix_to_iarray$(all_596_11) = all_596_10
% 57.39/8.78 | (186) matrix_to_iarray$(all_596_1) = all_596_0
% 57.39/8.78 | (187) fst$(all_596_14) = all_596_9
% 57.39/8.78 | (188) fst$(all_596_12) = all_596_11
% 57.39/8.78 | (189) fst$(all_596_2) = all_596_1
% 57.39/8.78 | (190) fun_app$(all_596_13, all_596_16) = all_596_12
% 57.39/8.78 | (191) fun_app$(all_596_3, all_596_16) = all_596_2
% 57.39/8.78 | (192) fun_app$a(gauss_Jordan_column_k_PA$, all_596_14) = all_596_13
% 57.39/8.78 | (193) fun_app$a(gauss_Jordan_column_k_PA$, all_596_4) = all_596_3
% 57.39/8.78 | (194) foldl$(gauss_Jordan_column_k_PA$, all_596_18, all_596_15) =
% 57.39/8.78 | all_596_14
% 57.39/8.78 | (195) upt$(all_596_20, all_596_16) = all_596_15
% 57.39/8.78 | (196) nat$(0) = all_596_20
% 57.39/8.78 | (197) nat$($sum(all_596_17, 1)) = all_596_16
% 57.39/8.78 | (198) fun_app$b(of_nat$, ka$) = all_596_17
% 57.39/8.78 | (199) pair$(all_596_21, all_596_19) = all_596_18
% 57.39/8.78 | (200) pair$(all_596_9, all_596_5) = all_596_4
% 57.39/8.78 | (201) pair$a(all_596_20, a$) = all_596_19
% 57.39/8.78 | (202) pair$a(all_596_7, all_596_6) = all_596_5
% 57.39/8.78 | (203) mat$(one$) = all_596_21
% 57.39/8.78 | (204) snd$a(all_596_8) = all_596_6
% 57.39/8.78 | (205) fst$a(all_596_8) = all_596_7
% 57.39/8.78 | (206) snd$(all_596_14) = all_596_8
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (29) with all_410_1, all_492_4, a$a, simplifying
% 57.39/8.78 | with (43), (53) gives:
% 57.39/8.78 | (207) all_492_4 = all_410_1
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_522_5, all_539_0, 0, simplifying with
% 57.39/8.78 | (64), (73) gives:
% 57.39/8.78 | (208) all_539_0 = all_522_5
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_504_0, all_539_0, 0, simplifying with
% 57.39/8.78 | (60), (73) gives:
% 57.39/8.78 | (209) all_539_0 = all_504_0
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_562_0, all_567_5, 0, simplifying with
% 57.39/8.78 | (81), (86) gives:
% 57.39/8.78 | (210) all_567_5 = all_562_0
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_562_0, all_569_0, 0, simplifying with
% 57.39/8.78 | (81), (90) gives:
% 57.39/8.78 | (211) all_569_0 = all_562_0
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_569_0, all_577_7, 0, simplifying with
% 57.39/8.78 | (90), (120) gives:
% 57.39/8.78 | (212) all_577_7 = all_569_0
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_556_0, all_577_7, 0, simplifying with
% 57.39/8.78 | (79), (120) gives:
% 57.39/8.78 | (213) all_577_7 = all_556_0
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_575_6, all_579_8, 0, simplifying with
% 57.39/8.78 | (107), (129) gives:
% 57.39/8.78 | (214) all_579_8 = all_575_6
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_569_0, all_581_0, 0, simplifying with
% 57.39/8.78 | (90), (138) gives:
% 57.39/8.78 | (215) all_581_0 = all_569_0
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_550_0, all_581_0, 0, simplifying with
% 57.39/8.78 | (77), (138) gives:
% 57.39/8.78 | (216) all_581_0 = all_550_0
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_539_0, all_581_0, 0, simplifying with
% 57.39/8.78 | (73), (138) gives:
% 57.39/8.78 | (217) all_581_0 = all_539_0
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_579_8, all_584_14, 0, simplifying
% 57.39/8.78 | with (129), (150) gives:
% 57.39/8.78 | (218) all_584_14 = all_579_8
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_575_6, all_589_0, 0, simplifying with
% 57.39/8.78 | (107), (160) gives:
% 57.39/8.78 | (219) all_589_0 = all_575_6
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_572_9, all_589_0, 0, simplifying with
% 57.39/8.78 | (94), (160) gives:
% 57.39/8.78 | (220) all_589_0 = all_572_9
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_567_5, all_589_0, 0, simplifying with
% 57.39/8.78 | (86), (160) gives:
% 57.39/8.78 | (221) all_589_0 = all_567_5
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_592_17, all_594_17, 0, simplifying
% 57.39/8.78 | with (164), (175) gives:
% 57.39/8.78 | (222) all_594_17 = all_592_17
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_586_0, all_594_17, 0, simplifying
% 57.39/8.78 | with (158), (175) gives:
% 57.39/8.78 | (223) all_594_17 = all_586_0
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_584_14, all_594_17, 0, simplifying
% 57.39/8.78 | with (150), (175) gives:
% 57.39/8.78 | (224) all_594_17 = all_584_14
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_592_17, all_596_20, 0, simplifying
% 57.39/8.78 | with (164), (196) gives:
% 57.39/8.78 | (225) all_596_20 = all_592_17
% 57.39/8.78 |
% 57.39/8.78 | GROUND_INST: instantiating (30) with all_527_0, all_596_20, 0, simplifying
% 57.39/8.78 | with (71), (196) gives:
% 57.39/8.78 | (226) all_596_20 = all_527_0
% 57.39/8.78 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_522_2, all_565_6, ka$, of_nat$,
% 57.39/8.79 | simplifying with (66), (84) gives:
% 57.39/8.79 | (227) all_565_6 = all_522_2
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_412_0, all_565_6, ka$, of_nat$,
% 57.39/8.79 | simplifying with (45), (84) gives:
% 57.39/8.79 | (228) all_565_6 = all_412_0
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_572_6, all_575_12, ka$, of_nat$,
% 57.39/8.79 | simplifying with (96), (110) gives:
% 57.39/8.79 | (229) all_575_12 = all_572_6
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_575_12, all_577_13, ka$, of_nat$,
% 57.39/8.79 | simplifying with (110), (122) gives:
% 57.39/8.79 | (230) all_577_13 = all_575_12
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_575_12, all_579_12, ka$, of_nat$,
% 57.39/8.79 | simplifying with (110), (131) gives:
% 57.39/8.79 | (231) all_579_12 = all_575_12
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_565_6, all_579_12, ka$, of_nat$,
% 57.39/8.79 | simplifying with (84), (131) gives:
% 57.39/8.79 | (232) all_579_12 = all_565_6
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_579_12, all_584_11, ka$, of_nat$,
% 57.39/8.79 | simplifying with (131), (153) gives:
% 57.39/8.79 | (233) all_584_11 = all_579_12
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_584_11, all_592_14, ka$, of_nat$,
% 57.39/8.79 | simplifying with (153), (166) gives:
% 57.39/8.79 | (234) all_592_14 = all_584_11
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_592_14, all_594_19, ka$, of_nat$,
% 57.39/8.79 | simplifying with (166), (177) gives:
% 57.39/8.79 | (235) all_594_19 = all_592_14
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_567_2, all_594_19, ka$, of_nat$,
% 57.39/8.79 | simplifying with (88), (177) gives:
% 57.39/8.79 | (236) all_594_19 = all_567_2
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_577_13, all_596_17, ka$, of_nat$,
% 57.39/8.79 | simplifying with (122), (198) gives:
% 57.39/8.79 | (237) all_596_17 = all_577_13
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (38) with all_542_6, all_596_17, ka$, of_nat$,
% 57.39/8.79 | simplifying with (75), (198) gives:
% 57.39/8.79 | (238) all_596_17 = all_542_6
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (31) with all_562_1, all_577_8, one$, simplifying
% 57.39/8.79 | with (82), (125) gives:
% 57.39/8.79 | (239) all_577_8 = all_562_1
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (31) with all_577_8, all_579_9, one$, simplifying
% 57.39/8.79 | with (125), (134) gives:
% 57.39/8.79 | (240) all_579_9 = all_577_8
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (31) with all_579_9, all_584_15, one$, simplifying
% 57.39/8.79 | with (134), (156) gives:
% 57.39/8.79 | (241) all_584_15 = all_579_9
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (31) with all_572_10, all_584_15, one$, simplifying
% 57.39/8.79 | with (99), (156) gives:
% 57.39/8.79 | (242) all_584_15 = all_572_10
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (31) with all_577_8, all_592_18, one$, simplifying
% 57.39/8.79 | with (125), (169) gives:
% 57.39/8.79 | (243) all_592_18 = all_577_8
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (31) with all_577_8, all_594_18, one$, simplifying
% 57.39/8.79 | with (125), (180) gives:
% 57.39/8.79 | (244) all_594_18 = all_577_8
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (31) with all_522_6, all_594_18, one$, simplifying
% 57.39/8.79 | with (69), (180) gives:
% 57.39/8.79 | (245) all_594_18 = all_522_6
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (31) with all_592_18, all_596_21, one$, simplifying
% 57.39/8.79 | with (169), (203) gives:
% 57.39/8.79 | (246) all_596_21 = all_592_18
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (31) with all_575_7, all_596_21, one$, simplifying
% 57.39/8.79 | with (113), (203) gives:
% 57.39/8.79 | (247) all_596_21 = all_575_7
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (34) with all_490_4, all_492_3, a$a, simplifying
% 57.39/8.79 | with (51), (58) gives:
% 57.39/8.79 | (248) all_492_3 = all_490_4
% 57.39/8.79 |
% 57.39/8.79 | GROUND_INST: instantiating (34) with all_488_3, all_492_3, a$a, simplifying
% 57.39/8.79 | with (48), (58) gives:
% 57.39/8.79 | (249) all_492_3 = all_488_3
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (237), (238) imply:
% 57.39/8.79 | (250) all_577_13 = all_542_6
% 57.39/8.79 |
% 57.39/8.79 | SIMP: (250) implies:
% 57.39/8.79 | (251) all_577_13 = all_542_6
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (225), (226) imply:
% 57.39/8.79 | (252) all_592_17 = all_527_0
% 57.39/8.79 |
% 57.39/8.79 | SIMP: (252) implies:
% 57.39/8.79 | (253) all_592_17 = all_527_0
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (246), (247) imply:
% 57.39/8.79 | (254) all_592_18 = all_575_7
% 57.39/8.79 |
% 57.39/8.79 | SIMP: (254) implies:
% 57.39/8.79 | (255) all_592_18 = all_575_7
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (222), (223) imply:
% 57.39/8.79 | (256) all_592_17 = all_586_0
% 57.39/8.79 |
% 57.39/8.79 | SIMP: (256) implies:
% 57.39/8.79 | (257) all_592_17 = all_586_0
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (223), (224) imply:
% 57.39/8.79 | (258) all_586_0 = all_584_14
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (244), (245) imply:
% 57.39/8.79 | (259) all_577_8 = all_522_6
% 57.39/8.79 |
% 57.39/8.79 | SIMP: (259) implies:
% 57.39/8.79 | (260) all_577_8 = all_522_6
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (235), (236) imply:
% 57.39/8.79 | (261) all_592_14 = all_567_2
% 57.39/8.79 |
% 57.39/8.79 | SIMP: (261) implies:
% 57.39/8.79 | (262) all_592_14 = all_567_2
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (234), (262) imply:
% 57.39/8.79 | (263) all_584_11 = all_567_2
% 57.39/8.79 |
% 57.39/8.79 | SIMP: (263) implies:
% 57.39/8.79 | (264) all_584_11 = all_567_2
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (253), (257) imply:
% 57.39/8.79 | (265) all_586_0 = all_527_0
% 57.39/8.79 |
% 57.39/8.79 | SIMP: (265) implies:
% 57.39/8.79 | (266) all_586_0 = all_527_0
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (243), (255) imply:
% 57.39/8.79 | (267) all_577_8 = all_575_7
% 57.39/8.79 |
% 57.39/8.79 | SIMP: (267) implies:
% 57.39/8.79 | (268) all_577_8 = all_575_7
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (220), (221) imply:
% 57.39/8.79 | (269) all_572_9 = all_567_5
% 57.39/8.79 |
% 57.39/8.79 | COMBINE_EQS: (219), (220) imply:
% 57.39/8.79 | (270) all_575_6 = all_572_9
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (270) implies:
% 57.39/8.80 | (271) all_575_6 = all_572_9
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (258), (266) imply:
% 57.39/8.80 | (272) all_584_14 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (272) implies:
% 57.39/8.80 | (273) all_584_14 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (233), (264) imply:
% 57.39/8.80 | (274) all_579_12 = all_567_2
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (274) implies:
% 57.39/8.80 | (275) all_579_12 = all_567_2
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (218), (273) imply:
% 57.39/8.80 | (276) all_579_8 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (276) implies:
% 57.39/8.80 | (277) all_579_8 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (241), (242) imply:
% 57.39/8.80 | (278) all_579_9 = all_572_10
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (278) implies:
% 57.39/8.80 | (279) all_579_9 = all_572_10
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (215), (216) imply:
% 57.39/8.80 | (280) all_569_0 = all_550_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (280) implies:
% 57.39/8.80 | (281) all_569_0 = all_550_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (216), (217) imply:
% 57.39/8.80 | (282) all_550_0 = all_539_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (214), (277) imply:
% 57.39/8.80 | (283) all_575_6 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (283) implies:
% 57.39/8.80 | (284) all_575_6 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (240), (279) imply:
% 57.39/8.80 | (285) all_577_8 = all_572_10
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (285) implies:
% 57.39/8.80 | (286) all_577_8 = all_572_10
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (231), (275) imply:
% 57.39/8.80 | (287) all_575_12 = all_567_2
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (287) implies:
% 57.39/8.80 | (288) all_575_12 = all_567_2
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (232), (275) imply:
% 57.39/8.80 | (289) all_567_2 = all_565_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (212), (213) imply:
% 57.39/8.80 | (290) all_569_0 = all_556_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (290) implies:
% 57.39/8.80 | (291) all_569_0 = all_556_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (239), (268) imply:
% 57.39/8.80 | (292) all_575_7 = all_562_1
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (260), (268) imply:
% 57.39/8.80 | (293) all_575_7 = all_522_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (268), (286) imply:
% 57.39/8.80 | (294) all_575_7 = all_572_10
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (230), (251) imply:
% 57.39/8.80 | (295) all_575_12 = all_542_6
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (295) implies:
% 57.39/8.80 | (296) all_575_12 = all_542_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (271), (284) imply:
% 57.39/8.80 | (297) all_572_9 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (297) implies:
% 57.39/8.80 | (298) all_572_9 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (292), (294) imply:
% 57.39/8.80 | (299) all_572_10 = all_562_1
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (293), (294) imply:
% 57.39/8.80 | (300) all_572_10 = all_522_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (229), (296) imply:
% 57.39/8.80 | (301) all_572_6 = all_542_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (229), (288) imply:
% 57.39/8.80 | (302) all_572_6 = all_567_2
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (301), (302) imply:
% 57.39/8.80 | (303) all_567_2 = all_542_6
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (303) implies:
% 57.39/8.80 | (304) all_567_2 = all_542_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (269), (298) imply:
% 57.39/8.80 | (305) all_567_5 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (305) implies:
% 57.39/8.80 | (306) all_567_5 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (299), (300) imply:
% 57.39/8.80 | (307) all_562_1 = all_522_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (211), (291) imply:
% 57.39/8.80 | (308) all_562_0 = all_556_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (308) implies:
% 57.39/8.80 | (309) all_562_0 = all_556_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (281), (291) imply:
% 57.39/8.80 | (310) all_556_0 = all_550_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (289), (304) imply:
% 57.39/8.80 | (311) all_565_6 = all_542_6
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (311) implies:
% 57.39/8.80 | (312) all_565_6 = all_542_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (210), (306) imply:
% 57.39/8.80 | (313) all_562_0 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (313) implies:
% 57.39/8.80 | (314) all_562_0 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (227), (312) imply:
% 57.39/8.80 | (315) all_542_6 = all_522_2
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (228), (312) imply:
% 57.39/8.80 | (316) all_542_6 = all_412_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (309), (314) imply:
% 57.39/8.80 | (317) all_556_0 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (317) implies:
% 57.39/8.80 | (318) all_556_0 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (310), (318) imply:
% 57.39/8.80 | (319) all_550_0 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (319) implies:
% 57.39/8.80 | (320) all_550_0 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (282), (320) imply:
% 57.39/8.80 | (321) all_539_0 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | SIMP: (321) implies:
% 57.39/8.80 | (322) all_539_0 = all_527_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (315), (316) imply:
% 57.39/8.80 | (323) all_522_2 = all_412_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (208), (322) imply:
% 57.39/8.80 | (324) all_527_0 = all_522_5
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (209), (322) imply:
% 57.39/8.80 | (325) all_527_0 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (324), (325) imply:
% 57.39/8.80 | (326) all_522_5 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (248), (249) imply:
% 57.39/8.80 | (327) all_490_4 = all_488_3
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (318), (325) imply:
% 57.39/8.80 | (328) all_556_0 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (304), (316) imply:
% 57.39/8.80 | (329) all_567_2 = all_412_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (298), (325) imply:
% 57.39/8.80 | (330) all_572_9 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (301), (316) imply:
% 57.39/8.80 | (331) all_572_6 = all_412_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (229), (331) imply:
% 57.39/8.80 | (332) all_575_12 = all_412_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (284), (325) imply:
% 57.39/8.80 | (333) all_575_6 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (251), (316) imply:
% 57.39/8.80 | (334) all_577_13 = all_412_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (213), (328) imply:
% 57.39/8.80 | (335) all_577_7 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (275), (329) imply:
% 57.39/8.80 | (336) all_579_12 = all_412_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (279), (300) imply:
% 57.39/8.80 | (337) all_579_9 = all_522_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (277), (325) imply:
% 57.39/8.80 | (338) all_579_8 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (242), (300) imply:
% 57.39/8.80 | (339) all_584_15 = all_522_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (273), (325) imply:
% 57.39/8.80 | (340) all_584_14 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (264), (329) imply:
% 57.39/8.80 | (341) all_584_11 = all_412_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (266), (325) imply:
% 57.39/8.80 | (342) all_586_0 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (255), (293) imply:
% 57.39/8.80 | (343) all_592_18 = all_522_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (253), (325) imply:
% 57.39/8.80 | (344) all_592_17 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (262), (329) imply:
% 57.39/8.80 | (345) all_592_14 = all_412_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (236), (329) imply:
% 57.39/8.80 | (346) all_594_19 = all_412_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (223), (342) imply:
% 57.39/8.80 | (347) all_594_17 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (247), (293) imply:
% 57.39/8.80 | (348) all_596_21 = all_522_6
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (226), (325) imply:
% 57.39/8.80 | (349) all_596_20 = all_504_0
% 57.39/8.80 |
% 57.39/8.80 | COMBINE_EQS: (238), (316) imply:
% 57.39/8.80 | (350) all_596_17 = all_412_0
% 57.39/8.80 |
% 57.39/8.80 | REDUCE: (57), (249) imply:
% 57.39/8.80 | (351) fst$a(all_488_3) = all_492_2
% 57.39/8.80 |
% 57.39/8.80 | REDUCE: (50), (327) imply:
% 57.39/8.80 | (352) fst$a(all_488_3) = all_490_3
% 57.39/8.80 |
% 57.39/8.80 | REDUCE: (56), (249) imply:
% 57.39/8.80 | (353) snd$a(all_488_3) = all_492_1
% 57.39/8.80 |
% 57.39/8.80 | REDUCE: (201), (349) imply:
% 57.39/8.80 | (354) pair$a(all_504_0, a$) = all_596_19
% 57.39/8.80 |
% 57.39/8.80 | REDUCE: (179), (347) imply:
% 57.39/8.80 | (355) pair$a(all_504_0, a$) = all_594_16
% 57.39/8.80 |
% 57.39/8.80 | REDUCE: (168), (344) imply:
% 57.39/8.80 | (356) pair$a(all_504_0, a$) = all_592_16
% 57.39/8.80 |
% 57.39/8.80 | REDUCE: (155), (340) imply:
% 57.39/8.80 | (357) pair$a(all_504_0, a$) = all_584_13
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (133), (338) imply:
% 57.39/8.81 | (358) pair$a(all_504_0, a$) = all_579_7
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (124), (335) imply:
% 57.39/8.81 | (359) pair$a(all_504_0, a$) = all_577_6
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (112), (333) imply:
% 57.39/8.81 | (360) pair$a(all_504_0, a$) = all_575_5
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (98), (330) imply:
% 57.39/8.81 | (361) pair$a(all_504_0, a$) = all_572_8
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (68), (326) imply:
% 57.39/8.81 | (362) pair$a(all_504_0, a$) = all_522_4
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (199), (348) imply:
% 57.39/8.81 | (363) pair$(all_522_6, all_596_19) = all_596_18
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (178), (245) imply:
% 57.39/8.81 | (364) pair$(all_522_6, all_594_16) = all_594_15
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (167), (343) imply:
% 57.39/8.81 | (365) pair$(all_522_6, all_592_16) = all_592_15
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (154), (339) imply:
% 57.39/8.81 | (366) pair$(all_522_6, all_584_13) = all_584_12
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (132), (337) imply:
% 57.39/8.81 | (367) pair$(all_522_6, all_579_7) = all_579_6
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (123), (260) imply:
% 57.39/8.81 | (368) pair$(all_522_6, all_577_6) = all_577_5
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (111), (293) imply:
% 57.39/8.81 | (369) pair$(all_522_6, all_575_5) = all_575_4
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (97), (300) imply:
% 57.39/8.81 | (370) pair$(all_522_6, all_572_8) = all_572_7
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (54), (207) imply:
% 57.39/8.81 | (371) pair$(all_410_1, all_492_0) = a$a
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (197), (350) imply:
% 57.39/8.81 | (372) nat$($sum(all_412_0, 1)) = all_596_16
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (176), (346) imply:
% 57.39/8.81 | (373) nat$($sum(all_412_0, 1)) = all_594_14
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (165), (345) imply:
% 57.39/8.81 | (374) nat$($sum(all_412_0, 1)) = all_592_13
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (152), (341) imply:
% 57.39/8.81 | (375) nat$($sum(all_412_0, 2)) = all_584_10
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (151), (341) imply:
% 57.39/8.81 | (376) nat$($sum(all_412_0, 1)) = all_584_5
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (130), (336) imply:
% 57.39/8.81 | (377) nat$($sum(all_412_0, 1)) = all_579_5
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (121), (334) imply:
% 57.39/8.81 | (378) nat$($sum(all_412_0, 1)) = all_577_12
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (109), (332) imply:
% 57.39/8.81 | (379) nat$($sum(all_412_0, 2)) = all_575_3
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (108), (332) imply:
% 57.39/8.81 | (380) nat$($sum(all_412_0, 1)) = all_575_11
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (95), (331) imply:
% 57.39/8.81 | (381) nat$($sum(all_412_0, 1)) = all_572_5
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (87), (329) imply:
% 57.39/8.81 | (382) nat$($sum(all_412_0, 1)) = all_567_1
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (65), (323) imply:
% 57.39/8.81 | (383) nat$($sum(all_412_0, 1)) = all_522_1
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (195), (349) imply:
% 57.39/8.81 | (384) upt$(all_504_0, all_596_16) = all_596_15
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (174), (347) imply:
% 57.39/8.81 | (385) upt$(all_504_0, all_594_14) = all_594_13
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (163), (344) imply:
% 57.39/8.81 | (386) upt$(all_504_0, all_592_13) = all_592_12
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (149), (340) imply:
% 57.39/8.81 | (387) upt$(all_504_0, all_584_5) = all_584_4
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (148), (340) imply:
% 57.39/8.81 | (388) upt$(all_504_0, all_584_10) = all_584_9
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (128), (338) imply:
% 57.39/8.81 | (389) upt$(all_504_0, all_579_5) = all_579_4
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (119), (335) imply:
% 57.39/8.81 | (390) upt$(all_504_0, all_577_12) = all_577_4
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (106), (333) imply:
% 57.39/8.81 | (391) upt$(all_504_0, all_575_3) = all_575_2
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (93), (330) imply:
% 57.39/8.81 | (392) upt$(all_504_0, all_572_5) = all_572_4
% 57.39/8.81 |
% 57.39/8.81 | REDUCE: (63), (326) imply:
% 57.39/8.81 | (393) upt$(all_504_0, all_522_1) = all_522_0
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (30) with all_572_5, all_575_11, $sum(all_412_0,
% 57.39/8.81 | 1), simplifying with (380), (381) gives:
% 57.39/8.81 | (394) all_575_11 = all_572_5
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (30) with all_577_12, all_579_5, $sum(all_412_0,
% 57.39/8.81 | 1), simplifying with (377), (378) gives:
% 57.39/8.81 | (395) all_579_5 = all_577_12
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (30) with all_575_11, all_579_5, $sum(all_412_0,
% 57.39/8.81 | 1), simplifying with (377), (380) gives:
% 57.39/8.81 | (396) all_579_5 = all_575_11
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (30) with all_579_5, all_592_13, $sum(all_412_0,
% 57.39/8.81 | 1), simplifying with (374), (377) gives:
% 57.39/8.81 | (397) all_592_13 = all_579_5
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (30) with all_584_5, all_594_14, $sum(all_412_0,
% 57.39/8.81 | 1), simplifying with (373), (376) gives:
% 57.39/8.81 | (398) all_594_14 = all_584_5
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (30) with all_572_5, all_594_14, $sum(all_412_0,
% 57.39/8.81 | 1), simplifying with (373), (381) gives:
% 57.39/8.81 | (399) all_594_14 = all_572_5
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (30) with all_522_1, all_594_14, $sum(all_412_0,
% 57.39/8.81 | 1), simplifying with (373), (383) gives:
% 57.39/8.81 | (400) all_594_14 = all_522_1
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (30) with all_592_13, all_596_16, $sum(all_412_0,
% 57.39/8.81 | 1), simplifying with (372), (374) gives:
% 57.39/8.81 | (401) all_596_16 = all_592_13
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (30) with all_567_1, all_596_16, $sum(all_412_0,
% 57.39/8.81 | 1), simplifying with (372), (382) gives:
% 57.39/8.81 | (402) all_596_16 = all_567_1
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (30) with all_575_3, all_584_10, $sum(all_412_0,
% 57.39/8.81 | 2), simplifying with (375), (379) gives:
% 57.39/8.81 | (403) all_584_10 = all_575_3
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (40) with all_572_8, all_577_6, a$, all_504_0,
% 57.39/8.81 | simplifying with (359), (361) gives:
% 57.39/8.81 | (404) all_577_6 = all_572_8
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (40) with all_577_6, all_584_13, a$, all_504_0,
% 57.39/8.81 | simplifying with (357), (359) gives:
% 57.39/8.81 | (405) all_584_13 = all_577_6
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (40) with all_522_4, all_584_13, a$, all_504_0,
% 57.39/8.81 | simplifying with (357), (362) gives:
% 57.39/8.81 | (406) all_584_13 = all_522_4
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (40) with all_584_13, all_592_16, a$, all_504_0,
% 57.39/8.81 | simplifying with (356), (357) gives:
% 57.39/8.81 | (407) all_592_16 = all_584_13
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (40) with all_577_6, all_594_16, a$, all_504_0,
% 57.39/8.81 | simplifying with (355), (359) gives:
% 57.39/8.81 | (408) all_594_16 = all_577_6
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (40) with all_575_5, all_594_16, a$, all_504_0,
% 57.39/8.81 | simplifying with (355), (360) gives:
% 57.39/8.81 | (409) all_594_16 = all_575_5
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (40) with all_592_16, all_596_19, a$, all_504_0,
% 57.39/8.81 | simplifying with (354), (356) gives:
% 57.39/8.81 | (410) all_596_19 = all_592_16
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (40) with all_579_7, all_596_19, a$, all_504_0,
% 57.39/8.81 | simplifying with (354), (358) gives:
% 57.39/8.81 | (411) all_596_19 = all_579_7
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (32) with all_488_2, all_492_1, all_488_3,
% 57.39/8.81 | simplifying with (47), (353) gives:
% 57.39/8.81 | (412) all_492_1 = all_488_2
% 57.39/8.81 |
% 57.39/8.81 | GROUND_INST: instantiating (33) with all_490_3, all_492_2, all_488_3,
% 57.39/8.81 | simplifying with (351), (352) gives:
% 57.39/8.81 | (413) all_492_2 = all_490_3
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (401), (402) imply:
% 57.39/8.81 | (414) all_592_13 = all_567_1
% 57.39/8.81 |
% 57.39/8.81 | SIMP: (414) implies:
% 57.39/8.81 | (415) all_592_13 = all_567_1
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (410), (411) imply:
% 57.39/8.81 | (416) all_592_16 = all_579_7
% 57.39/8.81 |
% 57.39/8.81 | SIMP: (416) implies:
% 57.39/8.81 | (417) all_592_16 = all_579_7
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (398), (399) imply:
% 57.39/8.81 | (418) all_584_5 = all_572_5
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (398), (400) imply:
% 57.39/8.81 | (419) all_584_5 = all_522_1
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (408), (409) imply:
% 57.39/8.81 | (420) all_577_6 = all_575_5
% 57.39/8.81 |
% 57.39/8.81 | SIMP: (420) implies:
% 57.39/8.81 | (421) all_577_6 = all_575_5
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (397), (415) imply:
% 57.39/8.81 | (422) all_579_5 = all_567_1
% 57.39/8.81 |
% 57.39/8.81 | SIMP: (422) implies:
% 57.39/8.81 | (423) all_579_5 = all_567_1
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (407), (417) imply:
% 57.39/8.81 | (424) all_584_13 = all_579_7
% 57.39/8.81 |
% 57.39/8.81 | SIMP: (424) implies:
% 57.39/8.81 | (425) all_584_13 = all_579_7
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (418), (419) imply:
% 57.39/8.81 | (426) all_572_5 = all_522_1
% 57.39/8.81 |
% 57.39/8.81 | SIMP: (426) implies:
% 57.39/8.81 | (427) all_572_5 = all_522_1
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (405), (425) imply:
% 57.39/8.81 | (428) all_579_7 = all_577_6
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (406), (425) imply:
% 57.39/8.81 | (429) all_579_7 = all_522_4
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (395), (423) imply:
% 57.39/8.81 | (430) all_577_12 = all_567_1
% 57.39/8.81 |
% 57.39/8.81 | COMBINE_EQS: (395), (396) imply:
% 57.39/8.82 | (431) all_577_12 = all_575_11
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (428), (429) imply:
% 57.39/8.82 | (432) all_577_6 = all_522_4
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (432) implies:
% 57.39/8.82 | (433) all_577_6 = all_522_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (421), (433) imply:
% 57.39/8.82 | (434) all_575_5 = all_522_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (404), (421) imply:
% 57.39/8.82 | (435) all_575_5 = all_572_8
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (430), (431) imply:
% 57.39/8.82 | (436) all_575_11 = all_567_1
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (436) implies:
% 57.39/8.82 | (437) all_575_11 = all_567_1
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (434), (435) imply:
% 57.39/8.82 | (438) all_572_8 = all_522_4
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (438) implies:
% 57.39/8.82 | (439) all_572_8 = all_522_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (394), (437) imply:
% 57.39/8.82 | (440) all_572_5 = all_567_1
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (440) implies:
% 57.39/8.82 | (441) all_572_5 = all_567_1
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (427), (441) imply:
% 57.39/8.82 | (442) all_567_1 = all_522_1
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (442) implies:
% 57.39/8.82 | (443) all_567_1 = all_522_1
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (430), (443) imply:
% 57.39/8.82 | (444) all_577_12 = all_522_1
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (395), (444) imply:
% 57.39/8.82 | (445) all_579_5 = all_522_1
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (417), (429) imply:
% 57.39/8.82 | (446) all_592_16 = all_522_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (415), (443) imply:
% 57.39/8.82 | (447) all_592_13 = all_522_1
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (409), (434) imply:
% 57.39/8.82 | (448) all_594_16 = all_522_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (411), (429) imply:
% 57.39/8.82 | (449) all_596_19 = all_522_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (402), (443) imply:
% 57.39/8.82 | (450) all_596_16 = all_522_1
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (55), (412), (413) imply:
% 57.39/8.82 | (451) pair$a(all_490_3, all_488_2) = all_492_0
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (363), (449) imply:
% 57.39/8.82 | (452) pair$(all_522_6, all_522_4) = all_596_18
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (364), (448) imply:
% 57.39/8.82 | (453) pair$(all_522_6, all_522_4) = all_594_15
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (365), (446) imply:
% 57.39/8.82 | (454) pair$(all_522_6, all_522_4) = all_592_15
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (366), (406) imply:
% 57.39/8.82 | (455) pair$(all_522_6, all_522_4) = all_584_12
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (367), (429) imply:
% 57.39/8.82 | (456) pair$(all_522_6, all_522_4) = all_579_6
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (368), (433) imply:
% 57.39/8.82 | (457) pair$(all_522_6, all_522_4) = all_577_5
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (369), (434) imply:
% 57.39/8.82 | (458) pair$(all_522_6, all_522_4) = all_575_4
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (370), (439) imply:
% 57.39/8.82 | (459) pair$(all_522_6, all_522_4) = all_572_7
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (384), (450) imply:
% 57.39/8.82 | (460) upt$(all_504_0, all_522_1) = all_596_15
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (385), (400) imply:
% 57.39/8.82 | (461) upt$(all_504_0, all_522_1) = all_594_13
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (386), (447) imply:
% 57.39/8.82 | (462) upt$(all_504_0, all_522_1) = all_592_12
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (387), (419) imply:
% 57.39/8.82 | (463) upt$(all_504_0, all_522_1) = all_584_4
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (388), (403) imply:
% 57.39/8.82 | (464) upt$(all_504_0, all_575_3) = all_584_9
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (389), (445) imply:
% 57.39/8.82 | (465) upt$(all_504_0, all_522_1) = all_579_4
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (390), (444) imply:
% 57.39/8.82 | (466) upt$(all_504_0, all_522_1) = all_577_4
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (392), (427) imply:
% 57.39/8.82 | (467) upt$(all_504_0, all_522_1) = all_572_4
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (191), (450) imply:
% 57.39/8.82 | (468) fun_app$(all_596_3, all_522_1) = all_596_2
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (190), (450) imply:
% 57.39/8.82 | (469) fun_app$(all_596_13, all_522_1) = all_596_12
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (144), (419) imply:
% 57.39/8.82 | (470) fun_app$(all_584_2, all_522_1) = all_584_1
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (116), (444) imply:
% 57.39/8.82 | (471) fun_app$(all_577_2, all_522_1) = all_577_1
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (37) with all_522_0, all_579_4, all_522_1,
% 57.39/8.82 | all_504_0, simplifying with (393), (465) gives:
% 57.39/8.82 | (472) all_579_4 = all_522_0
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (37) with all_579_4, all_594_13, all_522_1,
% 57.39/8.82 | all_504_0, simplifying with (461), (465) gives:
% 57.39/8.82 | (473) all_594_13 = all_579_4
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (37) with all_572_4, all_594_13, all_522_1,
% 57.39/8.82 | all_504_0, simplifying with (461), (467) gives:
% 57.39/8.82 | (474) all_594_13 = all_572_4
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (37) with all_592_12, all_596_15, all_522_1,
% 57.39/8.82 | all_504_0, simplifying with (460), (462) gives:
% 57.39/8.82 | (475) all_596_15 = all_592_12
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (37) with all_584_4, all_596_15, all_522_1,
% 57.39/8.82 | all_504_0, simplifying with (460), (463) gives:
% 57.39/8.82 | (476) all_596_15 = all_584_4
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (37) with all_579_4, all_596_15, all_522_1,
% 57.39/8.82 | all_504_0, simplifying with (460), (465) gives:
% 57.39/8.82 | (477) all_596_15 = all_579_4
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (37) with all_577_4, all_596_15, all_522_1,
% 57.39/8.82 | all_504_0, simplifying with (460), (466) gives:
% 57.39/8.82 | (478) all_596_15 = all_577_4
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (37) with all_575_2, all_584_9, all_575_3,
% 57.39/8.82 | all_504_0, simplifying with (391), (464) gives:
% 57.39/8.82 | (479) all_584_9 = all_575_2
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (39) with all_522_3, all_584_12, all_522_4,
% 57.39/8.82 | all_522_6, simplifying with (67), (455) gives:
% 57.39/8.82 | (480) all_584_12 = all_522_3
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (39) with all_577_5, all_584_12, all_522_4,
% 57.39/8.82 | all_522_6, simplifying with (455), (457) gives:
% 57.39/8.82 | (481) all_584_12 = all_577_5
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (39) with all_579_6, all_592_15, all_522_4,
% 57.39/8.82 | all_522_6, simplifying with (454), (456) gives:
% 57.39/8.82 | (482) all_592_15 = all_579_6
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (39) with all_577_5, all_592_15, all_522_4,
% 57.39/8.82 | all_522_6, simplifying with (454), (457) gives:
% 57.39/8.82 | (483) all_592_15 = all_577_5
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (39) with all_584_12, all_594_15, all_522_4,
% 57.39/8.82 | all_522_6, simplifying with (453), (455) gives:
% 57.39/8.82 | (484) all_594_15 = all_584_12
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (39) with all_575_4, all_594_15, all_522_4,
% 57.39/8.82 | all_522_6, simplifying with (453), (458) gives:
% 57.39/8.82 | (485) all_594_15 = all_575_4
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (39) with all_592_15, all_596_18, all_522_4,
% 57.39/8.82 | all_522_6, simplifying with (452), (454) gives:
% 57.39/8.82 | (486) all_596_18 = all_592_15
% 57.39/8.82 |
% 57.39/8.82 | GROUND_INST: instantiating (39) with all_572_7, all_596_18, all_522_4,
% 57.39/8.82 | all_522_6, simplifying with (452), (459) gives:
% 57.39/8.82 | (487) all_596_18 = all_572_7
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (475), (477) imply:
% 57.39/8.82 | (488) all_592_12 = all_579_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (475), (476) imply:
% 57.39/8.82 | (489) all_592_12 = all_584_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (475), (478) imply:
% 57.39/8.82 | (490) all_592_12 = all_577_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (486), (487) imply:
% 57.39/8.82 | (491) all_592_15 = all_572_7
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (491) implies:
% 57.39/8.82 | (492) all_592_15 = all_572_7
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (473), (474) imply:
% 57.39/8.82 | (493) all_579_4 = all_572_4
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (493) implies:
% 57.39/8.82 | (494) all_579_4 = all_572_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (484), (485) imply:
% 57.39/8.82 | (495) all_584_12 = all_575_4
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (495) implies:
% 57.39/8.82 | (496) all_584_12 = all_575_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (489), (490) imply:
% 57.39/8.82 | (497) all_584_4 = all_577_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (488), (489) imply:
% 57.39/8.82 | (498) all_584_4 = all_579_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (482), (483) imply:
% 57.39/8.82 | (499) all_579_6 = all_577_5
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (482), (492) imply:
% 57.39/8.82 | (500) all_579_6 = all_572_7
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (497), (498) imply:
% 57.39/8.82 | (501) all_579_4 = all_577_4
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (501) implies:
% 57.39/8.82 | (502) all_579_4 = all_577_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (480), (496) imply:
% 57.39/8.82 | (503) all_575_4 = all_522_3
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (481), (496) imply:
% 57.39/8.82 | (504) all_577_5 = all_575_4
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (504) implies:
% 57.39/8.82 | (505) all_577_5 = all_575_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (472), (502) imply:
% 57.39/8.82 | (506) all_577_4 = all_522_0
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (494), (502) imply:
% 57.39/8.82 | (507) all_577_4 = all_572_4
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (499), (500) imply:
% 57.39/8.82 | (508) all_577_5 = all_572_7
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (508) implies:
% 57.39/8.82 | (509) all_577_5 = all_572_7
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (506), (507) imply:
% 57.39/8.82 | (510) all_572_4 = all_522_0
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (505), (509) imply:
% 57.39/8.82 | (511) all_575_4 = all_572_7
% 57.39/8.82 |
% 57.39/8.82 | SIMP: (511) implies:
% 57.39/8.82 | (512) all_575_4 = all_572_7
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (503), (512) imply:
% 57.39/8.82 | (513) all_572_7 = all_522_3
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (509), (513) imply:
% 57.39/8.82 | (514) all_577_5 = all_522_3
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (500), (513) imply:
% 57.39/8.82 | (515) all_579_6 = all_522_3
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (497), (506) imply:
% 57.39/8.82 | (516) all_584_4 = all_522_0
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (482), (515) imply:
% 57.39/8.82 | (517) all_592_15 = all_522_3
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (489), (516) imply:
% 57.39/8.82 | (518) all_592_12 = all_522_0
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (485), (503) imply:
% 57.39/8.82 | (519) all_594_15 = all_522_3
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (474), (510) imply:
% 57.39/8.82 | (520) all_594_13 = all_522_0
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (487), (513) imply:
% 57.39/8.82 | (521) all_596_18 = all_522_3
% 57.39/8.82 |
% 57.39/8.82 | COMBINE_EQS: (475), (518) imply:
% 57.39/8.82 | (522) all_596_15 = all_522_0
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (194), (521), (522) imply:
% 57.39/8.82 | (523) foldl$(gauss_Jordan_column_k_PA$, all_522_3, all_522_0) = all_596_14
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (173), (519), (520) imply:
% 57.39/8.82 | (524) foldl$(gauss_Jordan_column_k_PA$, all_522_3, all_522_0) = all_594_12
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (162), (517), (518) imply:
% 57.39/8.82 | (525) foldl$(gauss_Jordan_column_k_PA$, all_522_3, all_522_0) = all_592_11
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (147), (480), (516) imply:
% 57.39/8.82 | (526) foldl$(gauss_Jordan_column_k_PA$, all_522_3, all_522_0) = all_584_3
% 57.39/8.82 |
% 57.39/8.82 | REDUCE: (146), (479), (480) imply:
% 57.39/8.83 | (527) foldl$(gauss_Jordan_column_k_PA$, all_522_3, all_575_2) = all_584_8
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (127), (472), (515) imply:
% 57.39/8.83 | (528) foldl$(gauss_Jordan_column_k_PA$, all_522_3, all_522_0) = all_579_3
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (118), (506), (514) imply:
% 57.39/8.83 | (529) foldl$(gauss_Jordan_column_k_PA$, all_522_3, all_522_0) = all_577_3
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (105), (503) imply:
% 57.39/8.83 | (530) foldl$(gauss_Jordan_column_k_PA$, all_522_3, all_575_2) = all_575_1
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (92), (510), (513) imply:
% 57.39/8.83 | (531) foldl$(gauss_Jordan_column_k_PA$, all_522_3, all_522_0) = all_572_3
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (41) with all_577_3, all_579_3, all_522_0,
% 57.39/8.83 | all_522_3, gauss_Jordan_column_k_PA$, simplifying with (528),
% 57.39/8.83 | (529) gives:
% 57.39/8.83 | (532) all_579_3 = all_577_3
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (41) with all_579_3, all_584_3, all_522_0,
% 57.39/8.83 | all_522_3, gauss_Jordan_column_k_PA$, simplifying with (526),
% 57.39/8.83 | (528) gives:
% 57.39/8.83 | (533) all_584_3 = all_579_3
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (41) with all_584_3, all_592_11, all_522_0,
% 57.39/8.83 | all_522_3, gauss_Jordan_column_k_PA$, simplifying with (525),
% 57.39/8.83 | (526) gives:
% 57.39/8.83 | (534) all_592_11 = all_584_3
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (41) with a$a, all_594_12, all_522_0, all_522_3,
% 57.39/8.83 | gauss_Jordan_column_k_PA$, simplifying with (62), (524) gives:
% 57.39/8.83 | (535) all_594_12 = a$a
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (41) with all_577_3, all_594_12, all_522_0,
% 57.39/8.83 | all_522_3, gauss_Jordan_column_k_PA$, simplifying with (524),
% 57.39/8.83 | (529) gives:
% 57.39/8.83 | (536) all_594_12 = all_577_3
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (41) with all_592_11, all_596_14, all_522_0,
% 57.39/8.83 | all_522_3, gauss_Jordan_column_k_PA$, simplifying with (523),
% 57.39/8.83 | (525) gives:
% 57.39/8.83 | (537) all_596_14 = all_592_11
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (41) with all_572_3, all_596_14, all_522_0,
% 57.39/8.83 | all_522_3, gauss_Jordan_column_k_PA$, simplifying with (523),
% 57.39/8.83 | (531) gives:
% 57.39/8.83 | (538) all_596_14 = all_572_3
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (41) with all_575_1, all_584_8, all_575_2,
% 57.39/8.83 | all_522_3, gauss_Jordan_column_k_PA$, simplifying with (527),
% 57.39/8.83 | (530) gives:
% 57.39/8.83 | (539) all_584_8 = all_575_1
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (537), (538) imply:
% 57.39/8.83 | (540) all_592_11 = all_572_3
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (540) implies:
% 57.39/8.83 | (541) all_592_11 = all_572_3
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (535), (536) imply:
% 57.39/8.83 | (542) all_577_3 = a$a
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (542) implies:
% 57.39/8.83 | (543) all_577_3 = a$a
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (534), (541) imply:
% 57.39/8.83 | (544) all_584_3 = all_572_3
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (544) implies:
% 57.39/8.83 | (545) all_584_3 = all_572_3
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (533), (545) imply:
% 57.39/8.83 | (546) all_579_3 = all_572_3
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (546) implies:
% 57.39/8.83 | (547) all_579_3 = all_572_3
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (532), (547) imply:
% 57.39/8.83 | (548) all_577_3 = all_572_3
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (548) implies:
% 57.39/8.83 | (549) all_577_3 = all_572_3
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (543), (549) imply:
% 57.39/8.83 | (550) all_572_3 = a$a
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (547), (550) imply:
% 57.39/8.83 | (551) all_579_3 = a$a
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (545), (550) imply:
% 57.39/8.83 | (552) all_584_3 = a$a
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (541), (550) imply:
% 57.39/8.83 | (553) all_592_11 = a$a
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (538), (550) imply:
% 57.39/8.83 | (554) all_596_14 = a$a
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (206), (554) imply:
% 57.39/8.83 | (555) snd$(a$a) = all_596_8
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (182), (535) imply:
% 57.39/8.83 | (556) snd$(a$a) = all_594_11
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (171), (553) imply:
% 57.39/8.83 | (557) snd$(a$a) = all_592_10
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (136), (551) imply:
% 57.39/8.83 | (558) snd$(a$a) = all_579_2
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (101), (550) imply:
% 57.39/8.83 | (559) snd$(a$a) = all_572_2
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (192), (554) imply:
% 57.39/8.83 | (560) fun_app$a(gauss_Jordan_column_k_PA$, a$a) = all_596_13
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (145), (552) imply:
% 57.39/8.83 | (561) fun_app$a(gauss_Jordan_column_k_PA$, a$a) = all_584_2
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (117), (543) imply:
% 57.39/8.83 | (562) fun_app$a(gauss_Jordan_column_k_PA$, a$a) = all_577_2
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (187), (554) imply:
% 57.39/8.83 | (563) fst$(a$a) = all_596_9
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (142), (539) imply:
% 57.39/8.83 | (564) fst$(all_575_1) = all_584_7
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (29) with all_410_1, all_596_9, a$a, simplifying
% 57.39/8.83 | with (43), (563) gives:
% 57.39/8.83 | (565) all_596_9 = all_410_1
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (29) with all_575_0, all_584_7, all_575_1,
% 57.39/8.83 | simplifying with (104), (564) gives:
% 57.39/8.83 | (566) all_584_7 = all_575_0
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (36) with all_584_2, all_596_13, a$a,
% 57.39/8.83 | gauss_Jordan_column_k_PA$, simplifying with (560), (561) gives:
% 57.39/8.83 | (567) all_596_13 = all_584_2
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (36) with all_577_2, all_596_13, a$a,
% 57.39/8.83 | gauss_Jordan_column_k_PA$, simplifying with (560), (562) gives:
% 57.39/8.83 | (568) all_596_13 = all_577_2
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (34) with all_488_3, all_592_10, a$a, simplifying
% 57.39/8.83 | with (48), (557) gives:
% 57.39/8.83 | (569) all_592_10 = all_488_3
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (34) with all_572_2, all_594_11, a$a, simplifying
% 57.39/8.83 | with (556), (559) gives:
% 57.39/8.83 | (570) all_594_11 = all_572_2
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (34) with all_594_11, all_596_8, a$a, simplifying
% 57.39/8.83 | with (555), (556) gives:
% 57.39/8.83 | (571) all_596_8 = all_594_11
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (34) with all_592_10, all_596_8, a$a, simplifying
% 57.39/8.83 | with (555), (557) gives:
% 57.39/8.83 | (572) all_596_8 = all_592_10
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (34) with all_579_2, all_596_8, a$a, simplifying
% 57.39/8.83 | with (555), (558) gives:
% 57.39/8.83 | (573) all_596_8 = all_579_2
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (571), (573) imply:
% 57.39/8.83 | (574) all_594_11 = all_579_2
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (574) implies:
% 57.39/8.83 | (575) all_594_11 = all_579_2
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (572), (573) imply:
% 57.39/8.83 | (576) all_592_10 = all_579_2
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (576) implies:
% 57.39/8.83 | (577) all_592_10 = all_579_2
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (567), (568) imply:
% 57.39/8.83 | (578) all_584_2 = all_577_2
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (578) implies:
% 57.39/8.83 | (579) all_584_2 = all_577_2
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (570), (575) imply:
% 57.39/8.83 | (580) all_579_2 = all_572_2
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (580) implies:
% 57.39/8.83 | (581) all_579_2 = all_572_2
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (569), (577) imply:
% 57.39/8.83 | (582) all_579_2 = all_488_3
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (582) implies:
% 57.39/8.83 | (583) all_579_2 = all_488_3
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (581), (583) imply:
% 57.39/8.83 | (584) all_572_2 = all_488_3
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (584) implies:
% 57.39/8.83 | (585) all_572_2 = all_488_3
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (570), (585) imply:
% 57.39/8.83 | (586) all_594_11 = all_488_3
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (573), (583) imply:
% 57.39/8.83 | (587) all_596_8 = all_488_3
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (205), (587) imply:
% 57.39/8.83 | (588) fst$a(all_488_3) = all_596_7
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (181), (586) imply:
% 57.39/8.83 | (589) fst$a(all_488_3) = all_594_10
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (170), (569) imply:
% 57.39/8.83 | (590) fst$a(all_488_3) = all_592_9
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (135), (583) imply:
% 57.39/8.83 | (591) fst$a(all_488_3) = all_579_1
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (100), (585) imply:
% 57.39/8.83 | (592) fst$a(all_488_3) = all_572_1
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (204), (587) imply:
% 57.39/8.83 | (593) snd$a(all_488_3) = all_596_6
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (200), (565) imply:
% 57.39/8.83 | (594) pair$(all_410_1, all_596_5) = all_596_4
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (469), (568) imply:
% 57.39/8.83 | (595) fun_app$(all_577_2, all_522_1) = all_596_12
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (470), (579) imply:
% 57.39/8.83 | (596) fun_app$(all_577_2, all_522_1) = all_584_1
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (140), (566) imply:
% 57.39/8.83 | (597) matrix_to_iarray$(all_575_0) = all_584_6
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (28) with all_575_8, all_584_6, all_575_0,
% 57.39/8.83 | simplifying with (103), (597) gives:
% 57.39/8.83 | (598) all_584_6 = all_575_8
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (35) with all_577_1, all_596_12, all_522_1,
% 57.39/8.83 | all_577_2, simplifying with (471), (595) gives:
% 57.39/8.83 | (599) all_596_12 = all_577_1
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (35) with all_584_1, all_596_12, all_522_1,
% 57.39/8.83 | all_577_2, simplifying with (595), (596) gives:
% 57.39/8.83 | (600) all_596_12 = all_584_1
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (32) with all_488_2, all_596_6, all_488_3,
% 57.39/8.83 | simplifying with (47), (593) gives:
% 57.39/8.83 | (601) all_596_6 = all_488_2
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (33) with all_490_3, all_579_1, all_488_3,
% 57.39/8.83 | simplifying with (352), (591) gives:
% 57.39/8.83 | (602) all_579_1 = all_490_3
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (33) with all_579_1, all_592_9, all_488_3,
% 57.39/8.83 | simplifying with (590), (591) gives:
% 57.39/8.83 | (603) all_592_9 = all_579_1
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (33) with all_592_9, all_594_10, all_488_3,
% 57.39/8.83 | simplifying with (589), (590) gives:
% 57.39/8.83 | (604) all_594_10 = all_592_9
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (33) with all_594_10, all_596_7, all_488_3,
% 57.39/8.83 | simplifying with (588), (589) gives:
% 57.39/8.83 | (605) all_596_7 = all_594_10
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (33) with all_572_1, all_596_7, all_488_3,
% 57.39/8.83 | simplifying with (588), (592) gives:
% 57.39/8.83 | (606) all_596_7 = all_572_1
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (605), (606) imply:
% 57.39/8.83 | (607) all_594_10 = all_572_1
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (607) implies:
% 57.39/8.83 | (608) all_594_10 = all_572_1
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (599), (600) imply:
% 57.39/8.83 | (609) all_584_1 = all_577_1
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (604), (608) imply:
% 57.39/8.83 | (610) all_592_9 = all_572_1
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (610) implies:
% 57.39/8.83 | (611) all_592_9 = all_572_1
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (603), (611) imply:
% 57.39/8.83 | (612) all_579_1 = all_572_1
% 57.39/8.83 |
% 57.39/8.83 | SIMP: (612) implies:
% 57.39/8.83 | (613) all_579_1 = all_572_1
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (602), (613) imply:
% 57.39/8.83 | (614) all_572_1 = all_490_3
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (606), (614) imply:
% 57.39/8.83 | (615) all_596_7 = all_490_3
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (202), (601), (615) imply:
% 57.39/8.83 | (616) pair$a(all_490_3, all_488_2) = all_596_5
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (188), (599) imply:
% 57.39/8.83 | (617) fst$(all_577_1) = all_596_11
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (143), (609) imply:
% 57.39/8.83 | (618) fst$(all_577_1) = all_584_0
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (141), (598) imply:
% 57.39/8.83 | (619) matrix_to_iarray$(all_584_0) = all_575_8
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (29) with all_577_0, all_596_11, all_577_1,
% 57.39/8.83 | simplifying with (115), (617) gives:
% 57.39/8.83 | (620) all_596_11 = all_577_0
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (29) with all_584_0, all_596_11, all_577_1,
% 57.39/8.83 | simplifying with (617), (618) gives:
% 57.39/8.83 | (621) all_596_11 = all_584_0
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (40) with all_492_0, all_596_5, all_488_2,
% 57.39/8.83 | all_490_3, simplifying with (451), (616) gives:
% 57.39/8.83 | (622) all_596_5 = all_492_0
% 57.39/8.83 |
% 57.39/8.83 | COMBINE_EQS: (620), (621) imply:
% 57.39/8.83 | (623) all_584_0 = all_577_0
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (594), (622) imply:
% 57.39/8.83 | (624) pair$(all_410_1, all_492_0) = all_596_4
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (185), (620) imply:
% 57.39/8.83 | (625) matrix_to_iarray$(all_577_0) = all_596_10
% 57.39/8.83 |
% 57.39/8.83 | REDUCE: (619), (623) imply:
% 57.39/8.83 | (626) matrix_to_iarray$(all_577_0) = all_575_8
% 57.39/8.83 |
% 57.39/8.83 | GROUND_INST: instantiating (28) with all_575_8, all_596_10, all_577_0,
% 57.39/8.83 | simplifying with (625), (626) gives:
% 57.39/8.83 | (627) all_596_10 = all_575_8
% 57.39/8.83 |
% 57.39/8.84 | GROUND_INST: instantiating (39) with a$a, all_596_4, all_492_0, all_410_1,
% 57.39/8.84 | simplifying with (371), (624) gives:
% 57.39/8.84 | (628) all_596_4 = a$a
% 57.39/8.84 |
% 57.39/8.84 | REDUCE: (184), (627) imply:
% 57.39/8.84 | (629) ~ (all_596_0 = all_575_8)
% 57.39/8.84 |
% 57.39/8.84 | REDUCE: (193), (628) imply:
% 57.39/8.84 | (630) fun_app$a(gauss_Jordan_column_k_PA$, a$a) = all_596_3
% 57.39/8.84 |
% 57.39/8.84 | GROUND_INST: instantiating (36) with all_577_2, all_596_3, a$a,
% 57.39/8.84 | gauss_Jordan_column_k_PA$, simplifying with (562), (630) gives:
% 57.39/8.84 | (631) all_596_3 = all_577_2
% 57.39/8.84 |
% 57.39/8.84 | REDUCE: (468), (631) imply:
% 57.39/8.84 | (632) fun_app$(all_577_2, all_522_1) = all_596_2
% 57.39/8.84 |
% 57.39/8.84 | GROUND_INST: instantiating (35) with all_577_1, all_596_2, all_522_1,
% 57.39/8.84 | all_577_2, simplifying with (471), (632) gives:
% 57.39/8.84 | (633) all_596_2 = all_577_1
% 57.39/8.84 |
% 57.39/8.84 | REDUCE: (189), (633) imply:
% 57.39/8.84 | (634) fst$(all_577_1) = all_596_1
% 57.39/8.84 |
% 57.39/8.84 | GROUND_INST: instantiating (29) with all_577_0, all_596_1, all_577_1,
% 57.39/8.84 | simplifying with (115), (634) gives:
% 57.39/8.84 | (635) all_596_1 = all_577_0
% 57.39/8.84 |
% 57.39/8.84 | REDUCE: (186), (635) imply:
% 57.39/8.84 | (636) matrix_to_iarray$(all_577_0) = all_596_0
% 57.39/8.84 |
% 57.39/8.84 | GROUND_INST: instantiating (28) with all_575_8, all_596_0, all_577_0,
% 57.39/8.84 | simplifying with (626), (636) gives:
% 57.39/8.84 | (637) all_596_0 = all_575_8
% 57.39/8.84 |
% 57.39/8.84 | REDUCE: (629), (637) imply:
% 57.39/8.84 | (638) $false
% 57.39/8.84 |
% 57.39/8.84 | CLOSE: (638) is inconsistent.
% 57.39/8.84 |
% 57.39/8.84 End of proof
% 57.39/8.84 % SZS output end Proof for theBenchmark
% 57.39/8.84
% 57.39/8.84 8232ms
%------------------------------------------------------------------------------