TSTP Solution File: ITP340_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 : n028.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 63.53s 9.09s
% Output : Proof 154.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 11:06:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.73/1.06 Prover 0: Warning: Problem contains reals, using incomplete axiomatisation
% 2.73/1.06 Prover 4: Warning: Problem contains reals, using incomplete axiomatisation
% 2.73/1.06 Prover 5: Warning: Problem contains reals, using incomplete axiomatisation
% 2.73/1.07 Prover 1: Warning: Problem contains reals, using incomplete axiomatisation
% 2.73/1.07 Prover 6: Warning: Problem contains reals, using incomplete axiomatisation
% 2.73/1.07 Prover 2: Warning: Problem contains reals, using incomplete axiomatisation
% 2.73/1.07 Prover 3: Warning: Problem contains reals, using incomplete axiomatisation
% 14.29/2.71 Prover 1: Preprocessing ...
% 14.29/2.71 Prover 4: Preprocessing ...
% 14.29/2.74 Prover 6: Preprocessing ...
% 14.29/2.74 Prover 2: Preprocessing ...
% 14.29/2.75 Prover 5: Preprocessing ...
% 14.29/2.75 Prover 0: Preprocessing ...
% 15.25/2.81 Prover 3: Preprocessing ...
% 34.40/5.27 Prover 1: Warning: ignoring some quantifiers
% 34.97/5.30 Prover 3: Warning: ignoring some quantifiers
% 34.97/5.36 Prover 6: Proving ...
% 35.51/5.38 Prover 3: Constructing countermodel ...
% 36.29/5.48 Prover 1: Constructing countermodel ...
% 41.87/6.22 Prover 5: Proving ...
% 42.10/6.32 Prover 4: Warning: ignoring some quantifiers
% 43.27/6.40 Prover 2: Proving ...
% 43.27/6.45 Prover 0: Proving ...
% 43.27/6.53 Prover 4: Constructing countermodel ...
% 63.53/9.09 Prover 3: proved (8446ms)
% 63.53/9.09
% 63.53/9.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.53/9.09
% 63.53/9.09 Prover 6: stopped
% 63.53/9.09 Prover 0: stopped
% 64.21/9.11 Prover 5: stopped
% 64.21/9.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 64.21/9.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 64.21/9.11 Prover 7: Warning: Problem contains reals, using incomplete axiomatisation
% 64.21/9.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 64.21/9.12 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 64.21/9.13 Prover 2: stopped
% 64.21/9.15 Prover 8: Warning: Problem contains reals, using incomplete axiomatisation
% 64.21/9.15 Prover 11: Warning: Problem contains reals, using incomplete axiomatisation
% 64.21/9.16 Prover 10: Warning: Problem contains reals, using incomplete axiomatisation
% 64.21/9.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 64.21/9.18 Prover 13: Warning: Problem contains reals, using incomplete axiomatisation
% 72.92/10.25 Prover 7: Preprocessing ...
% 72.92/10.26 Prover 8: Preprocessing ...
% 72.92/10.26 Prover 10: Preprocessing ...
% 73.60/10.34 Prover 11: Preprocessing ...
% 73.60/10.37 Prover 13: Preprocessing ...
% 80.49/11.26 Prover 10: Warning: ignoring some quantifiers
% 80.49/11.37 Prover 10: Constructing countermodel ...
% 81.82/11.42 Prover 7: Warning: ignoring some quantifiers
% 81.82/11.48 Prover 7: Constructing countermodel ...
% 82.66/11.54 Prover 8: Warning: ignoring some quantifiers
% 83.44/11.63 Prover 8: Constructing countermodel ...
% 84.22/11.70 Prover 13: Warning: ignoring some quantifiers
% 84.22/11.79 Prover 13: Constructing countermodel ...
% 85.82/11.92 Prover 11: Warning: ignoring some quantifiers
% 86.59/12.00 Prover 11: Constructing countermodel ...
% 98.13/13.49 Prover 13: stopped
% 98.13/13.51 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 98.13/13.52 Prover 16: Warning: Problem contains reals, using incomplete axiomatisation
% 103.32/14.18 Prover 16: Preprocessing ...
% 108.43/14.96 Prover 16: Warning: ignoring some quantifiers
% 109.32/15.02 Prover 16: Constructing countermodel ...
% 116.80/15.98 Prover 1: stopped
% 117.34/15.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 117.34/15.99 Prover 19: Warning: Problem contains reals, using incomplete axiomatisation
% 131.87/17.94 Prover 19: Preprocessing ...
% 138.49/18.77 Prover 16: stopped
% 140.95/19.16 Prover 19: Warning: ignoring some quantifiers
% 141.82/19.23 Prover 19: Constructing countermodel ...
% 153.52/20.73 Prover 8: Found proof (size 300)
% 153.52/20.73 Prover 8: proved (11530ms)
% 153.52/20.73 Prover 19: stopped
% 153.52/20.73 Prover 10: stopped
% 153.52/20.73 Prover 11: stopped
% 153.52/20.73 Prover 4: stopped
% 153.52/20.74 Prover 7: stopped
% 153.52/20.74
% 153.52/20.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 153.52/20.74
% 153.88/20.78 % SZS output start Proof for theBenchmark
% 153.88/20.80 Assumptions after simplification:
% 153.88/20.80 ---------------------------------
% 153.88/20.80
% 153.88/20.80 (axiom378)
% 153.88/20.81 Nat_int_fun$(of_nat$) & ! [v0: A_cols_vec_rows_vec$] : ! [v1: Nat$] : ( ~
% 153.88/20.81 (rank$(v0) = v1) | ~ A_cols_vec_rows_vec$(v0) | ? [v2: int] : ? [v3:
% 153.88/20.81 A_iarray_iarray$] : ? [v4: Nat$] : (matrix_to_iarray$(v0) = v3 &
% 153.88/20.81 rank_iarray$(v3) = v4 & fun_app$d(of_nat$, v4) = v2 & fun_app$d(of_nat$,
% 153.88/20.81 v1) = v2 & Nat$(v4) & A_iarray_iarray$(v3)))
% 153.88/20.81
% 153.88/20.81 (axiom38)
% 153.88/20.82 Nat_int_fun$(of_nat$) & ! [v0: Cols$] : ! [v1: Nat$] : ! [v2: Nat$] : !
% 153.88/20.82 [v3: int] : ( ~ (fun_app$d(of_nat$, v1) = v3) | ~ (to_nat$(v0) = v2) | ~
% 153.88/20.82 Cols$(v0) | ~ Nat$(v1) | ? [v4: int] : ? [v5: Cols$] :
% 153.88/20.82 (fun_app$d(of_nat$, v2) = v4 & from_nat$(v1) = v5 & Cols$(v5) & ( ~ (v4 =
% 153.88/20.82 v3) | v5 = v0)))
% 153.88/20.82
% 153.88/20.82 (axiom39)
% 153.88/20.82 Nat_int_fun$(of_nat$) & A_cols_vec_rows_vec$(a$) & Nat$(i$) & ? [v0:
% 153.88/20.82 A_iarray_iarray$] : ? [v1: Nat$] : ? [v2: int] : ? [v3: int] :
% 153.88/20.82 ($lesseq(1, $difference(v2, v3)) & ncols_iarray$(v0) = v1 &
% 153.88/20.82 matrix_to_iarray$(a$) = v0 & fun_app$d(of_nat$, v1) = v2 &
% 153.88/20.82 fun_app$d(of_nat$, i$) = v3 & Nat$(v1) & A_iarray_iarray$(v0))
% 153.88/20.82
% 153.88/20.82 (axiom415)
% 153.88/20.82 ! [v0: A_cols_vec_rows_vec$] : ! [v1: A_rows_vec_cols_vec$] : ( ~
% 153.88/20.82 (transpose$(v0) = v1) | ~ A_cols_vec_rows_vec$(v0) | ? [v2:
% 153.88/20.82 A_iarray_iarray$] : ? [v3: A_iarray_iarray$] : (matrix_to_iarray$a(v1) =
% 153.88/20.82 v2 & transpose_iarray$(v3) = v2 & matrix_to_iarray$(v0) = v3 &
% 153.88/20.82 A_iarray_iarray$(v3) & A_iarray_iarray$(v2)))
% 153.88/20.82
% 153.88/20.82 (axiom431)
% 153.88/20.82 Nat_int_fun$(of_nat$) & Cols_set$(top$) & Nat$(i$) & ? [v0: Nat$] : ? [v1:
% 153.88/20.82 int] : ? [v2: int] : ($lesseq(1, $difference(v1, v2)) & card$(top$) = v0 &
% 153.88/20.82 fun_app$d(of_nat$, v0) = v1 & fun_app$d(of_nat$, i$) = v2 & Nat$(v0))
% 153.88/20.82
% 153.88/20.82 (axiom435)
% 153.88/20.82 Nat_int_fun$(of_nat$) & Cols_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 153.88/20.82 (card$(top$) = v0 & fun_app$d(of_nat$, v0) = v1 & Nat$(v0) & ? [v2:
% 153.88/20.82 Cols_bool_fun$] : ( ~ Cols_bool_fun$(v2) | ? [v3: Cols$] : ? [v4: Nat$]
% 153.88/20.82 : ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & $lesseq(1, $difference(v1,
% 153.88/20.82 v5)) & fun_app$e(v2, v3) = v6 & fun_app$d(of_nat$, v4) = v5 &
% 153.88/20.82 to_nat$(v3) = v4 & Cols$(v3) & Nat$(v4)) | ! [v3: Cols$] : ! [v4: int]
% 153.88/20.82 : (v4 = 0 | ~ (fun_app$e(v2, v3) = v4) | ~ Cols$(v3))) & ? [v2:
% 153.88/20.82 Cols_bool_fun$] : ( ~ Cols_bool_fun$(v2) | ? [v3: Cols$] : ? [v4: int] :
% 153.88/20.82 ( ~ (v4 = 0) & fun_app$e(v2, v3) = v4 & Cols$(v3)) | ! [v3: Cols$] : !
% 153.88/20.82 [v4: Nat$] : ( ~ (to_nat$(v3) = v4) | ~ Cols$(v3) | ? [v5: int] : ?
% 153.88/20.82 [v6: any] : (fun_app$e(v2, v3) = v6 & fun_app$d(of_nat$, v4) = v5 & (v6
% 153.88/20.82 = 0 | ~ ($lesseq(1, $difference(v1, v5))))))))
% 153.88/20.82
% 153.88/20.82 (axiom439)
% 153.88/20.83 Nat_int_fun$(of_nat$) & Cols_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 153.88/20.83 (card$(top$) = v0 & fun_app$d(of_nat$, v0) = v1 & Nat$(v0) & ! [v2:
% 153.88/20.83 A_cols_vec_rows_vec$] : ! [v3: A_iarray_iarray$] : ( ~
% 153.88/20.83 (matrix_to_iarray$(v2) = v3) | ~ A_cols_vec_rows_vec$(v2) | ? [v4: Nat$]
% 153.88/20.83 : (ncols_iarray$(v3) = v4 & fun_app$d(of_nat$, v4) = v1 & Nat$(v4))))
% 153.88/20.83
% 153.88/20.83 (axiom440)
% 153.88/20.83 Nat_int_fun$(of_nat$) & Cols_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 153.88/20.83 (card$(top$) = v0 & fun_app$d(of_nat$, v0) = v1 & Nat$(v0) & ! [v2: Cols$] :
% 153.88/20.83 ! [v3: Nat$] : ( ~ (to_nat$(v2) = v3) | ~ Cols$(v2) | ? [v4: int] :
% 153.88/20.83 ($lesseq(1, $difference(v1, v4)) & fun_app$d(of_nat$, v3) = v4)))
% 153.88/20.83
% 153.88/20.83 (axiom441)
% 153.88/20.83 Nat_int_fun$(of_nat$) & Cols_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 153.88/20.83 (card$(top$) = v0 & fun_app$d(of_nat$, v0) = v1 & Nat$(v0) & ! [v2: Nat$] :
% 153.88/20.83 ! [v3: Nat$] : ! [v4: int] : ! [v5: int] : (v5 = v4 | ~ ($lesseq(1,
% 153.88/20.83 $difference(v1, v5))) | ~ ($lesseq(1, $difference(v1, v4))) | ~
% 153.88/20.83 (fun_app$d(of_nat$, v3) = v5) | ~ (fun_app$d(of_nat$, v2) = v4) | ~
% 153.88/20.83 Nat$(v3) | ~ Nat$(v2) | ? [v6: Cols$] : ? [v7: Cols$] : ( ~ (v7 = v6) &
% 153.88/20.83 from_nat$(v3) = v7 & from_nat$(v2) = v6 & Cols$(v7) & Cols$(v6))))
% 153.88/20.83
% 153.88/20.83 (axiom444)
% 153.88/20.83 Nat_int_fun$(of_nat$) & Cols_set$(top$) & Cols_cols_bool_fun_fun$(less$) & ?
% 153.88/20.83 [v0: Nat$] : ? [v1: int] : (card$(top$) = v0 & fun_app$d(of_nat$, v0) = v1 &
% 153.88/20.83 Nat$(v0) & ! [v2: Nat$] : ! [v3: Nat$] : ! [v4: Cols$] : ! [v5:
% 153.88/20.83 Cols_bool_fun$] : ! [v6: Cols$] : ! [v7: int] : (v7 = 0 | ~
% 153.88/20.83 (fun_app$f(less$, v4) = v5) | ~ (fun_app$e(v5, v6) = v7) | ~
% 153.88/20.83 (from_nat$(v3) = v6) | ~ (from_nat$(v2) = v4) | ~ Nat$(v3) | ~ Nat$(v2)
% 153.88/20.83 | ? [v8: int] : ? [v9: int] : (fun_app$d(of_nat$, v3) = v8 &
% 153.88/20.83 fun_app$d(of_nat$, v2) = v9 & ( ~ ($lesseq(1, $difference(v8, v9))) | ~
% 153.88/20.83 ($lesseq(1, $difference(v1, v8)))))))
% 153.88/20.83
% 153.88/20.83 (axiom445)
% 153.88/20.83 Nat_int_fun$(of_nat$) & Cols_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 153.88/20.83 (card$(top$) = v0 & fun_app$d(of_nat$, v0) = v1 & Nat$(v0) & ! [v2: Nat$] :
% 153.88/20.83 ! [v3: int] : ( ~ ($lesseq(1, $difference(v1, v3))) | ~ (fun_app$d(of_nat$,
% 153.88/20.83 v2) = v3) | ~ Nat$(v2) | ? [v4: Cols$] : ? [v5: Nat$] :
% 153.88/20.83 (fun_app$d(of_nat$, v5) = v3 & to_nat$(v4) = v5 & from_nat$(v2) = v4 &
% 153.88/20.83 Cols$(v4) & Nat$(v5))))
% 153.88/20.83
% 153.88/20.83 (axiom446)
% 153.88/20.83 Nat_int_fun$(of_nat$) & Cols_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 153.88/20.83 (card$(top$) = v0 & fun_app$d(of_nat$, v0) = v1 & Nat$(v0) & ! [v2: Nat$] :
% 153.88/20.83 ! [v3: Cols$] : ! [v4: int] : ! [v5: Nat$] : ( ~ ($lesseq(1,
% 153.88/20.83 $difference(v1, v4))) | ~ (fun_app$d(of_nat$, v2) = v4) | ~
% 153.88/20.83 (to_nat$(v3) = v5) | ~ Cols$(v3) | ~ Nat$(v2) | ? [v6: Cols$] : ? [v7:
% 153.88/20.83 int] : (fun_app$d(of_nat$, v5) = v7 & from_nat$(v2) = v6 & Cols$(v6) & (
% 153.88/20.83 ~ (v6 = v3) | v7 = v4))))
% 153.88/20.83
% 153.88/20.83 (axiom447)
% 153.88/20.84 Nat_int_fun$(of_nat$) & Cols_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 153.88/20.84 (card$(top$) = v0 & fun_app$d(of_nat$, v0) = v1 & Nat$(v0) & ! [v2: Nat$] :
% 153.88/20.84 ! [v3: Cols$] : ! [v4: int] : ! [v5: Nat$] : ( ~ ($lesseq(1,
% 153.88/20.84 $difference(v1, v4))) | ~ (fun_app$d(of_nat$, v2) = v4) | ~
% 153.88/20.84 (to_nat$(v3) = v5) | ~ Cols$(v3) | ~ Nat$(v2) | ? [v6: int] : ? [v7:
% 153.88/20.84 Cols$] : (fun_app$d(of_nat$, v5) = v6 & from_nat$(v2) = v7 & Cols$(v7) &
% 153.88/20.84 ( ~ (v7 = v3) | v6 = v4))))
% 153.88/20.84
% 153.88/20.84 (axiom448)
% 153.88/20.84 Nat_int_fun$(of_nat$) & Cols_set$(top$) & Cols_cols_bool_fun_fun$(less_eq$a) &
% 153.88/20.84 ? [v0: Nat$] : ? [v1: int] : (card$(top$) = v0 & fun_app$d(of_nat$, v0) = v1
% 153.88/20.84 & Nat$(v0) & ! [v2: Nat$] : ! [v3: Nat$] : ! [v4: Cols$] : ! [v5:
% 153.88/20.84 Cols_bool_fun$] : ! [v6: Cols$] : ! [v7: int] : (v7 = 0 | ~
% 153.88/20.84 (fun_app$f(less_eq$a, v4) = v5) | ~ (fun_app$e(v5, v6) = v7) | ~
% 153.88/20.84 (from_nat$(v3) = v6) | ~ (from_nat$(v2) = v4) | ~ Nat$(v3) | ~ Nat$(v2)
% 153.88/20.84 | ? [v8: int] : ? [v9: int] : (fun_app$d(of_nat$, v3) = v8 &
% 153.88/20.84 fun_app$d(of_nat$, v2) = v9 & ( ~ ($lesseq(v9, v8)) | ~ ($lesseq(1,
% 153.88/20.84 $difference(v1, v8)))))))
% 153.88/20.84
% 153.88/20.84 (axiom452)
% 153.88/20.84 Nat_int_fun$(of_nat$) & Rows_set$(top$a) & ? [v0: Nat$] : ? [v1: int] :
% 153.88/20.84 (card$a(top$a) = v0 & fun_app$d(of_nat$, v0) = v1 & Nat$(v0) & ! [v2:
% 153.88/20.84 A_cols_vec_rows_vec$] : ! [v3: A_iarray_iarray$] : ( ~
% 153.88/20.84 (matrix_to_iarray$(v2) = v3) | ~ A_cols_vec_rows_vec$(v2) | ? [v4: Nat$]
% 153.88/20.84 : (nrows_iarray$(v3) = v4 & fun_app$d(of_nat$, v4) = v1 & Nat$(v4))))
% 153.88/20.84
% 153.88/20.84 (axiom453)
% 153.88/20.84 Nat_int_fun$(of_nat$) & Rows_set$(top$a) & ? [v0: Nat$] : ? [v1: int] :
% 153.88/20.84 (card$a(top$a) = v0 & fun_app$d(of_nat$, v0) = v1 & Nat$(v0) & ! [v2:
% 153.88/20.84 A_cols_vec_rows_vec$] : ! [v3: A_iarray_iarray$] : ( ~
% 153.88/20.84 (matrix_to_iarray$(v2) = v3) | ~ A_cols_vec_rows_vec$(v2) | ? [v4: Nat$]
% 153.88/20.84 : (length$(v3) = v4 & fun_app$d(of_nat$, v4) = v1 & Nat$(v4))))
% 153.88/20.84
% 153.88/20.84 (axiom468)
% 153.88/20.84 Nat_int_fun$(of_nat$) & Cols_set$(top$) & ? [v0: Nat$] : ? [v1: Nat$] : ?
% 153.88/20.84 [v2: int] : (nat$(0) = v0 & card$(top$) = v1 & fun_app$d(of_nat$, v1) = v2 &
% 153.88/20.84 Nat$(v1) & Nat$(v0) & ! [v3: A_cols_vec_rows_vec$] : ! [v4:
% 153.88/20.84 A_iarray_iarray$] : ( ~ (matrix_to_iarray$(v3) = v4) | ~
% 153.88/20.84 A_cols_vec_rows_vec$(v3) | ? [v5: Nat_a_iarray_fun$] : ? [v6: A_iarray$]
% 153.88/20.84 : ? [v7: Nat$] : (length$a(v6) = v7 & sub$(v4) = v5 & fun_app$ac(v5, v0)
% 153.88/20.84 = v6 & fun_app$d(of_nat$, v7) = v2 & A_iarray$(v6) & Nat$(v7) &
% 153.88/20.84 Nat_a_iarray_fun$(v5))))
% 153.88/20.84
% 153.88/20.84 (axiom484)
% 153.88/20.84 Nat_int_fun$(of_nat$) & Cols$(zero$) & ? [v0: Nat$] : (fun_app$d(of_nat$, v0)
% 153.88/20.84 = 0 & to_nat$(zero$) = v0 & Nat$(v0))
% 153.88/20.84
% 153.88/20.84 (axiom493)
% 153.88/20.84 Cols$(zero$) & Cols_set$(top$) & ? [v0: Nat$] : (card$(top$) = v0 &
% 153.88/20.84 from_nat$(v0) = zero$ & Nat$(v0))
% 153.88/20.84
% 153.88/20.84 (axiom495)
% 153.88/20.84 Nat_int_fun$(of_nat$) & A_cols_vec_rows_vec$(zero$a) & ? [v0: Nat$] :
% 153.88/20.84 (rank$(zero$a) = v0 & fun_app$d(of_nat$, v0) = 0 & Nat$(v0))
% 153.88/20.84
% 153.88/20.84 (axiom497)
% 153.88/20.84 Nat_int_fun$(of_nat$) & Cols_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 153.88/20.84 ($lesseq(1, v1) & card$(top$) = v0 & fun_app$d(of_nat$, v0) = v1 & Nat$(v0))
% 153.88/20.84
% 153.88/20.84 (axiom507)
% 153.88/20.84 Nat_int_fun$(of_nat$) & Cols$(one$) & ? [v0: Nat$] : (fun_app$d(of_nat$, v0)
% 153.88/20.84 = 1 & to_nat$(one$) = v0 & Nat$(v0))
% 153.88/20.84
% 153.88/20.84 (axiom598)
% 153.88/20.84 Nat_int_fun$(of_nat$) & Cols_set$(top$) & ? [v0: Nat$] : ? [v1: int] :
% 153.88/20.84 ($lesseq(1, v1) & card$(top$) = v0 & fun_app$d(of_nat$, v0) = v1 & Nat$(v0))
% 153.88/20.84
% 153.88/20.84 (axiom8)
% 153.88/20.84 Nat_int_fun$(of_nat$) & A_cols_vec_rows_vec$(a$) & Nat$(i$) & ? [v0: int] :
% 153.88/20.84 ? [v1: A_iarray_iarray$] : ? [v2: Nat$] : ? [v3: int] : ($lesseq(v3, v0) &
% 153.88/20.84 matrix_to_iarray$(a$) = v1 & rank_iarray$(v1) = v2 & fun_app$d(of_nat$, v2)
% 153.88/20.84 = v3 & fun_app$d(of_nat$, i$) = v0 & Nat$(v2) & A_iarray_iarray$(v1))
% 153.88/20.84
% 153.88/20.84 (conjecture5)
% 153.88/20.85 Nat_int_fun$(of_nat$) & A_cols_vec_rows_vec$(a$) & Nat$(i$) & ? [v0: Cols$] :
% 153.88/20.85 ? [v1: A_rows_vec_cols_vec$] : ? [v2: A_cols_vec_cols_vec$] : ? [v3:
% 153.88/20.85 A_cols_vec$] : ? [v4: Nat$] : ? [v5: int] : (p_Gauss_Jordan$(v1) = v2 &
% 153.88/20.85 row$(v0, v2) = v3 & rank$(a$) = v4 & transpose$(a$) = v1 &
% 153.88/20.85 fun_app$d(of_nat$, v4) = v5 & from_nat$(i$) = v0 & A_cols_vec_cols_vec$(v2)
% 153.88/20.85 & Cols$(v0) & A_cols_vec$(v3) & Nat$(v4) & A_rows_vec_cols_vec$(v1) & !
% 153.88/20.85 [v6: Cols$] : ( ~ (row$(v6, v2) = v3) | ~ Cols$(v6) | ? [v7: Nat$] : ?
% 153.88/20.85 [v8: int] : ($lesseq(1, $difference(v5, v8)) & fun_app$d(of_nat$, v7) = v8
% 153.88/20.85 & to_nat$(v6) = v7 & Nat$(v7))))
% 153.88/20.85
% 153.88/20.85 (function-axioms)
% 154.25/20.89 ! [v0: A_iarray_iarray$] : ! [v1: A_iarray_iarray$] : ! [v2: A$] : ! [v3:
% 154.25/20.89 Nat$] : ! [v4: Nat$] : ! [v5: A_iarray_iarray$] : (v1 = v0 | ~
% 154.25/20.89 (column_add_iarray$(v5, v4, v3, v2) = v1) | ~ (column_add_iarray$(v5, v4,
% 154.25/20.89 v3, v2) = v0)) & ! [v0: A_cols_vec_rows_vec$] : ! [v1:
% 154.25/20.89 A_cols_vec_rows_vec$] : ! [v2: A$] : ! [v3: Cols$] : ! [v4: Cols$] : !
% 154.25/20.89 [v5: A_cols_vec_rows_vec$] : (v1 = v0 | ~ (column_add$(v5, v4, v3, v2) = v1)
% 154.25/20.89 | ~ (column_add$(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 154.25/20.89 [v1: MultipleValueBool] : ! [v2: Cols_set$] : ! [v3:
% 154.25/20.89 Cols_set_cols_set_bool_fun_fun$] : ! [v4: Cols_set_cols_set_bool_fun_fun$]
% 154.25/20.89 : (v1 = v0 | ~ (ordering_top$(v4, v3, v2) = v1) | ~ (ordering_top$(v4, v3,
% 154.25/20.89 v2) = v0)) & ! [v0: A_iarray_iarray$] : ! [v1: A_iarray_iarray$] : !
% 154.25/20.89 [v2: A$] : ! [v3: Nat$] : ! [v4: A_iarray_iarray$] : (v1 = v0 | ~
% 154.25/20.89 (mult_column_iarray$(v4, v3, v2) = v1) | ~ (mult_column_iarray$(v4, v3, v2)
% 154.25/20.89 = v0)) & ! [v0: A_cols_vec_rows_vec$] : ! [v1: A_cols_vec_rows_vec$] :
% 154.25/20.89 ! [v2: A$] : ! [v3: Cols$] : ! [v4: A_cols_vec_rows_vec$] : (v1 = v0 | ~
% 154.25/20.89 (mult_column$(v4, v3, v2) = v1) | ~ (mult_column$(v4, v3, v2) = v0)) & !
% 154.25/20.89 [v0: $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 154.25/20.89 (real_$quotient(v3, v2) = v1) | ~ (real_$quotient(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 154.25/20.89 (real_$product(v3, v2) = v1) | ~ (real_$product(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 154.25/20.89 (real_$sum(v3, v2) = v1) | ~ (real_$sum(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 154.25/20.89 $real] : (v1 = v0 | ~ (real_$greatereq(v3, v2) = v1) | ~
% 154.25/20.89 (real_$greatereq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 154.25/20.89 MultipleValueBool] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 154.25/20.89 (real_$greater(v3, v2) = v1) | ~ (real_$greater(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 $real] : ! [v1: $real] : ! [v2: $real] : ! [v3: $real] : (v1 = v0 | ~
% 154.25/20.89 (real_$difference(v3, v2) = v1) | ~ (real_$difference(v3, v2) = v0)) & !
% 154.25/20.89 [v0: Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: Nat$] : ! [v3:
% 154.25/20.89 Nat_nat_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$ad(v3, v2) = v1) | ~
% 154.25/20.89 (fun_app$ad(v3, v2) = v0)) & ! [v0: A_iarray_iarray$] : ! [v1:
% 154.25/20.89 A_iarray_iarray$] : ! [v2: Nat$] : ! [v3: Nat_a_iarray_fun$] : (v1 = v0 |
% 154.25/20.89 ~ (of_fun$(v3, v2) = v1) | ~ (of_fun$(v3, v2) = v0)) & ! [v0: A$] : !
% 154.25/20.89 [v1: A$] : ! [v2: Nat$] : ! [v3: A_iarray$] : (v1 = v0 | ~ (sub$a(v3, v2) =
% 154.25/20.89 v1) | ~ (sub$a(v3, v2) = v0)) & ! [v0: A$] : ! [v1: A$] : ! [v2:
% 154.25/20.89 Cols$] : ! [v3: A_cols_vec$] : (v1 = v0 | ~ (vec_nth$a(v3, v2) = v1) | ~
% 154.25/20.89 (vec_nth$a(v3, v2) = v0)) & ! [v0: A_cols_vec$] : ! [v1: A_cols_vec$] : !
% 154.25/20.89 [v2: Rows$] : ! [v3: A_cols_vec_rows_vec$] : (v1 = v0 | ~ (vec_nth$(v3, v2)
% 154.25/20.89 = v1) | ~ (vec_nth$(v3, v2) = v0)) & ! [v0: A_iarray$] : ! [v1:
% 154.25/20.89 A_iarray$] : ! [v2: Nat$] : ! [v3: Nat_a_iarray_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$ac(v3, v2) = v1) | ~ (fun_app$ac(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 A_iarray$] : ! [v1: A_iarray$] : ! [v2: A_iarray_iarray$] : ! [v3: Nat$]
% 154.25/20.89 : (v1 = v0 | ~ (row_iarray$(v3, v2) = v1) | ~ (row_iarray$(v3, v2) = v0)) &
% 154.25/20.89 ! [v0: A_iarray$] : ! [v1: A_iarray$] : ! [v2: A_iarray_iarray$] : ! [v3:
% 154.25/20.89 Nat$] : (v1 = v0 | ~ (column_iarray$(v3, v2) = v1) | ~ (column_iarray$(v3,
% 154.25/20.89 v2) = v0)) & ! [v0: A_iarray_iarray$] : ! [v1: A_iarray_iarray$] : !
% 154.25/20.89 [v2: Nat$] : ! [v3: A_iarray_iarray$] : (v1 = v0 | ~
% 154.25/20.89 (gauss_Jordan_upt_k_iarrays$(v3, v2) = v1) | ~
% 154.25/20.89 (gauss_Jordan_upt_k_iarrays$(v3, v2) = v0)) & ! [v0: A_cols_vec_rows_vec$]
% 154.25/20.89 : ! [v1: A_cols_vec_rows_vec$] : ! [v2: Nat$] : ! [v3:
% 154.25/20.89 A_cols_vec_rows_vec$] : (v1 = v0 | ~ (gauss_Jordan_upt_k$(v3, v2) = v1) |
% 154.25/20.89 ~ (gauss_Jordan_upt_k$(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 154.25/20.89 MultipleValueBool] : ! [v2: Real_real_bool_fun_fun$] : ! [v3:
% 154.25/20.89 Real_real_bool_fun_fun$] : (v1 = v0 | ~ (ordering$a(v3, v2) = v1) | ~
% 154.25/20.89 (ordering$a(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 154.25/20.89 MultipleValueBool] : ! [v2: Int_int_bool_fun_fun$] : ! [v3:
% 154.25/20.89 Int_int_bool_fun_fun$] : (v1 = v0 | ~ (ordering$(v3, v2) = v1) | ~
% 154.25/20.89 (ordering$(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 154.25/20.89 tlbool] : ! [v3: Bool_real_fun$] : (v1 = v0 | ~ (fun_app$ab(v3, v2) = v1)
% 154.25/20.89 | ~ (fun_app$ab(v3, v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 154.25/20.89 tlbool] : ! [v3: Bool_int_fun$] : (v1 = v0 | ~ (fun_app$aa(v3, v2) = v1) |
% 154.25/20.89 ~ (fun_app$aa(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 154.25/20.89 MultipleValueBool] : ! [v2: Real_real_bool_fun_fun$] : ! [v3:
% 154.25/20.89 Real_real_bool_fun_fun$] : (v1 = v0 | ~ (preordering_bdd$a(v3, v2) = v1) |
% 154.25/20.89 ~ (preordering_bdd$a(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 154.25/20.89 MultipleValueBool] : ! [v2: Int_int_bool_fun_fun$] : ! [v3:
% 154.25/20.89 Int_int_bool_fun_fun$] : (v1 = v0 | ~ (preordering_bdd$(v3, v2) = v1) | ~
% 154.25/20.89 (preordering_bdd$(v3, v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2:
% 154.25/20.89 Nat$] : ! [v3: Nat_real_fun$] : (v1 = v0 | ~ (fun_app$z(v3, v2) = v1) | ~
% 154.25/20.89 (fun_app$z(v3, v2) = v0)) & ! [v0: A_rows_vec$] : ! [v1: A_rows_vec$] : !
% 154.25/20.89 [v2: A_rows_vec_cols_vec$] : ! [v3: Cols$] : (v1 = v0 | ~ (row$b(v3, v2) =
% 154.25/20.89 v1) | ~ (row$b(v3, v2) = v0)) & ! [v0: A_rows_vec$] : ! [v1:
% 154.25/20.89 A_rows_vec$] : ! [v2: A_cols_vec_rows_vec$] : ! [v3: Cols$] : (v1 = v0 |
% 154.25/20.89 ~ (column$b(v3, v2) = v1) | ~ (column$b(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 A_cols_vec$] : ! [v1: A_cols_vec$] : ! [v2: A_rows_vec_cols_vec$] : !
% 154.25/20.89 [v3: Rows$] : (v1 = v0 | ~ (column$a(v3, v2) = v1) | ~ (column$a(v3, v2) =
% 154.25/20.89 v0)) & ! [v0: A_cols_vec$] : ! [v1: A_cols_vec$] : ! [v2:
% 154.25/20.89 A_cols_vec_rows_vec$] : ! [v3: Rows$] : (v1 = v0 | ~ (row$a(v3, v2) = v1)
% 154.25/20.89 | ~ (row$a(v3, v2) = v0)) & ! [v0: A_cols_vec$] : ! [v1: A_cols_vec$] :
% 154.25/20.89 ! [v2: A_cols_vec_cols_vec$] : ! [v3: Cols$] : (v1 = v0 | ~ (column$(v3, v2)
% 154.25/20.89 = v1) | ~ (column$(v3, v2) = v0)) & ! [v0: A_cols_vec$] : ! [v1:
% 154.25/20.89 A_cols_vec$] : ! [v2: A_cols_vec_cols_vec$] : ! [v3: Cols$] : (v1 = v0 |
% 154.25/20.89 ~ (row$(v3, v2) = v1) | ~ (row$(v3, v2) = v0)) & ! [v0: Nat$] : ! [v1:
% 154.25/20.89 Nat$] : ! [v2: Nat$] : ! [v3: Nat_nat_fun$] : (v1 = v0 | ~ (fun_app$y(v3,
% 154.25/20.89 v2) = v1) | ~ (fun_app$y(v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 154.25/20.89 ! [v1: MultipleValueBool] : ! [v2: Nat$] : ! [v3: Nat_bool_fun$] : (v1 = v0
% 154.25/20.89 | ~ (fun_app$x(v3, v2) = v1) | ~ (fun_app$x(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 Real_set$] : ! [v1: Real_set$] : ! [v2: Real_set$] : ! [v3:
% 154.25/20.89 Real_set_real_set_fun$] : (v1 = v0 | ~ (fun_app$w(v3, v2) = v1) | ~
% 154.25/20.89 (fun_app$w(v3, v2) = v0)) & ! [v0: Cols_set$] : ! [v1: Cols_set$] : !
% 154.25/20.89 [v2: Real_set$] : ! [v3: Real_set_cols_set_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$v(v3, v2) = v1) | ~ (fun_app$v(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 Bool_int_fun$] : ! [v1: Bool_int_fun$] : ! [v2: Real_set$] : ! [v3:
% 154.25/20.89 Real_set_bool_int_fun_fun$] : (v1 = v0 | ~ (fun_app$u(v3, v2) = v1) | ~
% 154.25/20.89 (fun_app$u(v3, v2) = v0)) & ! [v0: Bool_real_fun$] : ! [v1:
% 154.25/20.89 Bool_real_fun$] : ! [v2: Real_set$] : ! [v3: Real_set_bool_real_fun_fun$]
% 154.25/20.89 : (v1 = v0 | ~ (fun_app$t(v3, v2) = v1) | ~ (fun_app$t(v3, v2) = v0)) & !
% 154.25/20.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Bool_int_fun$]
% 154.25/20.89 : ! [v3: Bool_int_fun$] : (v1 = v0 | ~ (less$e(v3, v2) = v1) | ~
% 154.25/20.89 (less$e(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 154.25/20.89 MultipleValueBool] : ! [v2: Bool_real_fun$] : ! [v3: Bool_real_fun$] : (v1
% 154.25/20.89 = v0 | ~ (less$d(v3, v2) = v1) | ~ (less$d(v3, v2) = v0)) & ! [v0: int] :
% 154.25/20.89 ! [v1: int] : ! [v2: Cols_set$] : ! [v3: Cols_set_int_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$s(v3, v2) = v1) | ~ (fun_app$s(v3, v2) = v0)) & ! [v0: Cols_set$]
% 154.25/20.89 : ! [v1: Cols_set$] : ! [v2: int] : ! [v3: Int_cols_set_fun$] : (v1 = v0 |
% 154.25/20.89 ~ (fun_app$r(v3, v2) = v1) | ~ (fun_app$r(v3, v2) = v0)) & ! [v0: Cols$] :
% 154.25/20.89 ! [v1: Cols$] : ! [v2: Cols$] : ! [v3: Cols_cols_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$q(v3, v2) = v1) | ~ (fun_app$q(v3, v2) = v0)) & ! [v0: $real] :
% 154.25/20.89 ! [v1: $real] : ! [v2: Cols$] : ! [v3: Cols_real_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$p(v3, v2) = v1) | ~ (fun_app$p(v3, v2) = v0)) & ! [v0: int] : !
% 154.25/20.89 [v1: int] : ! [v2: Cols$] : ! [v3: Cols_int_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$o(v3, v2) = v1) | ~ (fun_app$o(v3, v2) = v0)) & ! [v0: Cols$] :
% 154.25/20.89 ! [v1: Cols$] : ! [v2: $real] : ! [v3: Real_cols_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$n(v3, v2) = v1) | ~ (fun_app$n(v3, v2) = v0)) & ! [v0: Cols$] :
% 154.25/20.89 ! [v1: Cols$] : ! [v2: int] : ! [v3: Int_cols_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$m(v3, v2) = v1) | ~ (fun_app$m(v3, v2) = v0)) & ! [v0: $real] :
% 154.25/20.89 ! [v1: $real] : ! [v2: $real] : ! [v3: Real_real_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$l(v3, v2) = v1) | ~ (fun_app$l(v3, v2) = v0)) & ! [v0: int] : !
% 154.25/20.89 [v1: int] : ! [v2: $real] : ! [v3: Real_int_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$k(v3, v2) = v1) | ~ (fun_app$k(v3, v2) = v0)) & ! [v0: $real] :
% 154.25/20.89 ! [v1: $real] : ! [v2: int] : ! [v3: Int_real_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$j(v3, v2) = v1) | ~ (fun_app$j(v3, v2) = v0)) & ! [v0: int] : !
% 154.25/20.89 [v1: int] : ! [v2: int] : ! [v3: Int_int_fun$] : (v1 = v0 | ~
% 154.25/20.89 (fun_app$i(v3, v2) = v1) | ~ (fun_app$i(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Rows$] : ! [v3:
% 154.25/20.89 Rows$] : (v1 = v0 | ~ (less$c(v3, v2) = v1) | ~ (less$c(v3, v2) = v0)) &
% 154.25/20.89 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Real_set$] :
% 154.25/20.89 ! [v3: Real_set$] : (v1 = v0 | ~ (less$b(v3, v2) = v1) | ~ (less$b(v3, v2) =
% 154.25/20.89 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 154.25/20.89 Real_set$] : ! [v3: Real_set$] : (v1 = v0 | ~ (less_eq$e(v3, v2) = v1) |
% 154.25/20.89 ~ (less_eq$e(v3, v2) = v0)) & ! [v0: Cols_set_bool_fun$] : ! [v1:
% 154.25/20.89 Cols_set_bool_fun$] : ! [v2: Cols_set$] : ! [v3:
% 154.25/20.89 Cols_set_cols_set_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$h(v3, v2) = v1) |
% 154.25/20.89 ~ (fun_app$h(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 154.25/20.89 MultipleValueBool] : ! [v2: Cols_set$] : ! [v3: Cols_set_bool_fun$] : (v1
% 154.25/20.89 = v0 | ~ (fun_app$g(v3, v2) = v1) | ~ (fun_app$g(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Bool_int_fun$] :
% 154.25/20.89 ! [v3: Bool_int_fun$] : (v1 = v0 | ~ (less_eq$c(v3, v2) = v1) | ~
% 154.25/20.89 (less_eq$c(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 154.25/20.89 MultipleValueBool] : ! [v2: Bool_real_fun$] : ! [v3: Bool_real_fun$] : (v1
% 154.25/20.89 = v0 | ~ (less_eq$b(v3, v2) = v1) | ~ (less_eq$b(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 Cols_bool_fun$] : ! [v1: Cols_bool_fun$] : ! [v2: Cols$] : ! [v3:
% 154.25/20.89 Cols_cols_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$f(v3, v2) = v1) | ~
% 154.25/20.89 (fun_app$f(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 154.25/20.89 MultipleValueBool] : ! [v2: Cols$] : ! [v3: Cols_bool_fun$] : (v1 = v0 |
% 154.25/20.89 ~ (fun_app$e(v3, v2) = v1) | ~ (fun_app$e(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Rows$] : ! [v3:
% 154.25/20.89 Rows$] : (v1 = v0 | ~ (less_eq$(v3, v2) = v1) | ~ (less_eq$(v3, v2) = v0))
% 154.25/20.89 & ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : ! [v3: Nat_int_fun$] : (v1 =
% 154.25/20.89 v0 | ~ (fun_app$d(v3, v2) = v1) | ~ (fun_app$d(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Real_set$] : !
% 154.25/20.89 [v3: $real] : (v1 = v0 | ~ (member$(v3, v2) = v1) | ~ (member$(v3, v2) =
% 154.25/20.89 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 154.25/20.89 $real] : ! [v3: $real] : (v1 = v0 | ~ (real_$less(v3, v2) = v1) | ~
% 154.25/20.89 (real_$less(v3, v2) = v0)) & ! [v0: Int_bool_fun$] : ! [v1: Int_bool_fun$]
% 154.25/20.89 : ! [v2: int] : ! [v3: Int_int_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$c(v3,
% 154.25/20.89 v2) = v1) | ~ (fun_app$c(v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 154.25/20.89 ! [v1: MultipleValueBool] : ! [v2: int] : ! [v3: Int_bool_fun$] : (v1 = v0 |
% 154.25/20.89 ~ (fun_app$b(v3, v2) = v1) | ~ (fun_app$b(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 Real_bool_fun$] : ! [v1: Real_bool_fun$] : ! [v2: $real] : ! [v3:
% 154.25/20.89 Real_real_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$a(v3, v2) = v1) | ~
% 154.25/20.89 (fun_app$a(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 154.25/20.89 MultipleValueBool] : ! [v2: $real] : ! [v3: Real_bool_fun$] : (v1 = v0 |
% 154.25/20.89 ~ (fun_app$(v3, v2) = v1) | ~ (fun_app$(v3, v2) = v0)) & ! [v0:
% 154.25/20.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $real] : ! [v3:
% 154.25/20.89 $real] : (v1 = v0 | ~ (real_$lesseq(v3, v2) = v1) | ~ (real_$lesseq(v3,
% 154.25/20.89 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 154.25/20.89 ! [v2: $real] : (v1 = v0 | ~ (real_$is_int(v2) = v1) | ~ (real_$is_int(v2) =
% 154.25/20.89 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 154.25/20.89 $real] : (v1 = v0 | ~ (real_$is_rat(v2) = v1) | ~ (real_$is_rat(v2) = v0))
% 154.25/20.89 & ! [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~
% 154.25/20.89 (real_$floor(v2) = v1) | ~ (real_$floor(v2) = v0)) & ! [v0: $real] : !
% 154.25/20.89 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$ceiling(v2) = v1) | ~
% 154.25/20.89 (real_$ceiling(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: $real]
% 154.25/20.89 : (v1 = v0 | ~ (real_$truncate(v2) = v1) | ~ (real_$truncate(v2) = v0)) & !
% 154.25/20.89 [v0: $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$round(v2)
% 154.25/20.89 = v1) | ~ (real_$round(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2:
% 154.25/20.89 $real] : (v1 = v0 | ~ (real_$to_int(v2) = v1) | ~ (real_$to_int(v2) = v0))
% 154.25/20.89 & ! [v0: $rat] : ! [v1: $rat] : ! [v2: $real] : (v1 = v0 | ~
% 154.25/20.89 (real_$to_rat(v2) = v1) | ~ (real_$to_rat(v2) = v0)) & ! [v0: $real] : !
% 154.25/20.89 [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$to_real(v2) = v1) | ~
% 154.25/20.89 (real_$to_real(v2) = v0)) & ! [v0: $real] : ! [v1: $real] : ! [v2: int] :
% 154.25/20.89 (v1 = v0 | ~ (int_$to_real(v2) = v1) | ~ (int_$to_real(v2) = v0)) & ! [v0:
% 154.25/20.89 $real] : ! [v1: $real] : ! [v2: $real] : (v1 = v0 | ~ (real_$uminus(v2) =
% 154.25/20.89 v1) | ~ (real_$uminus(v2) = v0)) & ! [v0: A_cols_vec_cols_vec$] : !
% 154.25/20.89 [v1: A_cols_vec_cols_vec$] : ! [v2: A_rows_vec_cols_vec$] : (v1 = v0 | ~
% 154.25/20.89 (p_Gauss_Jordan$(v2) = v1) | ~ (p_Gauss_Jordan$(v2) = v0)) & ! [v0: Nat$]
% 154.25/20.89 : ! [v1: Nat$] : ! [v2: A_cols_vec_rows_vec$] : (v1 = v0 | ~ (row_rank$(v2)
% 154.25/20.89 = v1) | ~ (row_rank$(v2) = v0)) & ! [v0: A_cols_vec_rows_vec$] : ! [v1:
% 154.25/20.89 A_cols_vec_rows_vec$] : ! [v2: A_cols_vec_rows_vec$] : (v1 = v0 | ~
% 154.25/20.89 (gauss_Jordan$(v2) = v1) | ~ (gauss_Jordan$(v2) = v0)) & ! [v0: Nat$] : !
% 154.25/20.89 [v1: Nat$] : ! [v2: int] : (v1 = v0 | ~ (nat$(v2) = v1) | ~ (nat$(v2) =
% 154.25/20.89 v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: A_iarray$] : (v1 = v0 | ~
% 154.25/20.89 (length$a(v2) = v1) | ~ (length$a(v2) = v0)) & ! [v0: Nat_a_iarray_fun$] :
% 154.25/20.89 ! [v1: Nat_a_iarray_fun$] : ! [v2: A_iarray_iarray$] : (v1 = v0 | ~
% 154.25/20.89 (sub$(v2) = v1) | ~ (sub$(v2) = v0)) & ! [v0: A_iarray_iarray$] : ! [v1:
% 154.25/20.89 A_iarray_iarray$] : ! [v2: A_cols_vec_cols_vec$] : (v1 = v0 | ~
% 154.25/20.89 (matrix_to_iarray$b(v2) = v1) | ~ (matrix_to_iarray$b(v2) = v0)) & ! [v0:
% 154.25/20.89 A_iarray$] : ! [v1: A_iarray$] : ! [v2: A_cols_vec$] : (v1 = v0 | ~
% 154.25/20.89 (vec_to_iarray$a(v2) = v1) | ~ (vec_to_iarray$a(v2) = v0)) & ! [v0:
% 154.25/20.89 A_iarray$] : ! [v1: A_iarray$] : ! [v2: A_rows_vec$] : (v1 = v0 | ~
% 154.25/20.89 (vec_to_iarray$(v2) = v1) | ~ (vec_to_iarray$(v2) = v0)) & ! [v0: Nat$] :
% 154.25/20.89 ! [v1: Nat$] : ! [v2: A_iarray_iarray$] : (v1 = v0 | ~ (length$(v2) = v1) |
% 154.25/20.89 ~ (length$(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Rows_set$] :
% 154.25/20.89 (v1 = v0 | ~ (card$a(v2) = v1) | ~ (card$a(v2) = v0)) & ! [v0: Nat$] : !
% 154.25/20.89 [v1: Nat$] : ! [v2: A_iarray_iarray$] : (v1 = v0 | ~ (nrows_iarray$(v2) =
% 154.25/20.89 v1) | ~ (nrows_iarray$(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : !
% 154.25/20.89 [v2: A_cols_vec_rows_vec$] : (v1 = v0 | ~ (col_rank$(v2) = v1) | ~
% 154.25/20.89 (col_rank$(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Cols_set$] :
% 154.25/20.89 (v1 = v0 | ~ (card$(v2) = v1) | ~ (card$(v2) = v0)) & ! [v0: Nat$] : !
% 154.25/20.89 [v1: Nat$] : ! [v2: A_cols_vec_rows_vec$] : (v1 = v0 | ~ (ncols$(v2) = v1) |
% 154.25/20.89 ~ (ncols$(v2) = v0)) & ! [v0: A_iarray_set$] : ! [v1: A_iarray_set$] : !
% 154.25/20.89 [v2: A_iarray_iarray$] : (v1 = v0 | ~ (basis_left_null_space_iarrays$(v2) =
% 154.25/20.89 v1) | ~ (basis_left_null_space_iarrays$(v2) = v0)) & ! [v0:
% 154.25/20.89 A_iarray_set$] : ! [v1: A_iarray_set$] : ! [v2: A_iarray_iarray$] : (v1 =
% 154.25/20.89 v0 | ~ (basis_null_space_iarrays$(v2) = v1) | ~
% 154.25/20.89 (basis_null_space_iarrays$(v2) = v0)) & ! [v0: A_iarray_iarray$] : ! [v1:
% 154.25/20.89 A_iarray_iarray$] : ! [v2: A_rows_vec_cols_vec$] : (v1 = v0 | ~
% 154.25/20.89 (matrix_to_iarray$a(v2) = v1) | ~ (matrix_to_iarray$a(v2) = v0)) & ! [v0:
% 154.25/20.89 A_iarray_iarray$] : ! [v1: A_iarray_iarray$] : ! [v2: A_iarray_iarray$] :
% 154.25/20.89 (v1 = v0 | ~ (transpose_iarray$(v2) = v1) | ~ (transpose_iarray$(v2) = v0))
% 154.25/20.89 & ! [v0: A_cols_vec_rows_vec$] : ! [v1: A_cols_vec_rows_vec$] : ! [v2:
% 154.25/20.89 A_iarray_iarray$] : (v1 = v0 | ~ (iarray_to_matrix$(v2) = v1) | ~
% 154.25/20.89 (iarray_to_matrix$(v2) = v0)) & ! [v0: Real_set$] : ! [v1: Real_set$] : !
% 154.25/20.89 [v2: Real_bool_fun$] : (v1 = v0 | ~ (collect$(v2) = v1) | ~ (collect$(v2) =
% 154.25/20.89 v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: A_iarray_iarray$] : (v1 =
% 154.25/20.89 v0 | ~ (ncols_iarray$(v2) = v1) | ~ (ncols_iarray$(v2) = v0)) & ! [v0:
% 154.25/20.89 Nat$] : ! [v1: Nat$] : ! [v2: A_rows_vec_cols_vec$] : (v1 = v0 | ~
% 154.25/20.89 (rank$b(v2) = v1) | ~ (rank$b(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] :
% 154.25/20.89 ! [v2: A_cols_vec_rows_vec$] : (v1 = v0 | ~ (rank$(v2) = v1) | ~ (rank$(v2)
% 154.25/20.89 = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: A_cols_vec_cols_vec$] :
% 154.25/20.89 (v1 = v0 | ~ (rank$a(v2) = v1) | ~ (rank$a(v2) = v0)) & ! [v0:
% 154.25/20.89 A_rows_vec_cols_vec$] : ! [v1: A_rows_vec_cols_vec$] : ! [v2:
% 154.25/20.89 A_cols_vec_rows_vec$] : (v1 = v0 | ~ (transpose$(v2) = v1) | ~
% 154.25/20.89 (transpose$(v2) = v0)) & ! [v0: A_cols_vec_cols_vec$] : ! [v1:
% 154.25/20.89 A_cols_vec_cols_vec$] : ! [v2: A_cols_vec_cols_vec$] : (v1 = v0 | ~
% 154.25/20.89 (transpose$b(v2) = v1) | ~ (transpose$b(v2) = v0)) & ! [v0:
% 154.25/20.89 A_cols_vec_rows_vec$] : ! [v1: A_cols_vec_rows_vec$] : ! [v2:
% 154.25/20.89 A_rows_vec_cols_vec$] : (v1 = v0 | ~ (transpose$a(v2) = v1) | ~
% 154.25/20.89 (transpose$a(v2) = v0)) & ! [v0: A_iarray_iarray$] : ! [v1:
% 154.25/20.89 A_iarray_iarray$] : ! [v2: A_cols_vec_rows_vec$] : (v1 = v0 | ~
% 154.25/20.89 (matrix_to_iarray$(v2) = v1) | ~ (matrix_to_iarray$(v2) = v0)) & ! [v0:
% 154.25/20.89 Nat$] : ! [v1: Nat$] : ! [v2: A_iarray_iarray$] : (v1 = v0 | ~
% 154.25/20.89 (rank_iarray$(v2) = v1) | ~ (rank_iarray$(v2) = v0)) & ! [v0: Nat$] : !
% 154.25/20.89 [v1: Nat$] : ! [v2: Cols$] : (v1 = v0 | ~ (to_nat$(v2) = v1) | ~
% 154.25/20.89 (to_nat$(v2) = v0)) & ! [v0: Cols$] : ! [v1: Cols$] : ! [v2: Nat$] : (v1
% 154.25/20.89 = v0 | ~ (from_nat$(v2) = v1) | ~ (from_nat$(v2) = v0)) & ! [v0: Nat$] :
% 154.25/20.89 ! [v1: Nat$] : ! [v2: Rows$] : (v1 = v0 | ~ (to_nat$a(v2) = v1) | ~
% 154.25/20.89 (to_nat$a(v2) = v0)) & ! [v0: Rows$] : ! [v1: Rows$] : ! [v2: Nat$] : (v1
% 154.25/20.89 = v0 | ~ (from_nat$a(v2) = v1) | ~ (from_nat$a(v2) = v0)) & ! [v0:
% 154.25/20.89 Real_bool_fun$] : ! [v1: Real_bool_fun$] : ! [v2: Real_set$] : (v1 = v0 |
% 154.25/20.89 ~ (uu$(v2) = v1) | ~ (uu$(v2) = v0)) & ? [v0: A$] : ? [v1: Nat$] : ?
% 154.25/20.89 [v2: Nat$] : ? [v3: A_iarray_iarray$] : ? [v4: A_iarray_iarray$] :
% 154.25/20.89 (column_add_iarray$(v3, v2, v1, v0) = v4 & A_iarray_iarray$(v4)) & ? [v0: A$]
% 154.25/20.89 : ? [v1: Cols$] : ? [v2: Cols$] : ? [v3: A_cols_vec_rows_vec$] : ? [v4:
% 154.25/20.89 A_cols_vec_rows_vec$] : (column_add$(v3, v2, v1, v0) = v4 &
% 154.25/20.89 A_cols_vec_rows_vec$(v4)) & ? [v0: Cols_set$] : ? [v1:
% 154.25/20.89 Cols_set_cols_set_bool_fun_fun$] : ? [v2: Cols_set_cols_set_bool_fun_fun$]
% 154.25/20.89 : ? [v3: MultipleValueBool] : (ordering_top$(v2, v1, v0) = v3) & ? [v0: A$]
% 154.25/20.89 : ? [v1: Nat$] : ? [v2: A_iarray_iarray$] : ? [v3: A_iarray_iarray$] :
% 154.25/20.89 (mult_column_iarray$(v2, v1, v0) = v3 & A_iarray_iarray$(v3)) & ? [v0: A$] :
% 154.25/20.89 ? [v1: Cols$] : ? [v2: A_cols_vec_rows_vec$] : ? [v3: A_cols_vec_rows_vec$]
% 154.25/20.89 : (mult_column$(v2, v1, v0) = v3 & A_cols_vec_rows_vec$(v3)) & ? [v0: $real]
% 154.25/20.89 : ? [v1: $real] : ? [v2: $real] : (real_$quotient(v1, v0) = v2) & ? [v0:
% 154.25/20.89 $real] : ? [v1: $real] : ? [v2: $real] : (real_$product(v1, v0) = v2) & ?
% 154.25/20.89 [v0: $real] : ? [v1: $real] : ? [v2: $real] : (real_$sum(v1, v0) = v2) & ?
% 154.25/20.89 [v0: $real] : ? [v1: $real] : ? [v2: MultipleValueBool] :
% 154.25/20.89 (real_$greatereq(v1, v0) = v2) & ? [v0: $real] : ? [v1: $real] : ? [v2:
% 154.25/20.89 MultipleValueBool] : (real_$greater(v1, v0) = v2) & ? [v0: $real] : ? [v1:
% 154.25/20.89 $real] : ? [v2: $real] : (real_$difference(v1, v0) = v2) & ? [v0:
% 154.25/20.89 Real_real_bool_fun_fun$] : ? [v1: Real_real_bool_fun_fun$] : ? [v2:
% 154.25/20.89 MultipleValueBool] : (ordering$a(v1, v0) = v2) & ? [v0:
% 154.25/20.89 Int_int_bool_fun_fun$] : ? [v1: Int_int_bool_fun_fun$] : ? [v2:
% 154.25/20.89 MultipleValueBool] : (ordering$(v1, v0) = v2) & ? [v0: tlbool] : ? [v1:
% 154.25/20.89 Bool_real_fun$] : ? [v2: $real] : (fun_app$ab(v1, v0) = v2) & ? [v0:
% 154.25/20.89 tlbool] : ? [v1: Bool_int_fun$] : ? [v2: int] : (fun_app$aa(v1, v0) = v2)
% 154.25/20.89 & ? [v0: Real_real_bool_fun_fun$] : ? [v1: Real_real_bool_fun_fun$] : ?
% 154.25/20.89 [v2: MultipleValueBool] : (preordering_bdd$a(v1, v0) = v2) & ? [v0:
% 154.25/20.89 Int_int_bool_fun_fun$] : ? [v1: Int_int_bool_fun_fun$] : ? [v2:
% 154.25/20.89 MultipleValueBool] : (preordering_bdd$(v1, v0) = v2) & ? [v0: Nat$] : ?
% 154.25/20.89 [v1: Nat_real_fun$] : ? [v2: $real] : (fun_app$z(v1, v0) = v2) & ? [v0:
% 154.25/20.89 Nat$] : ? [v1: Nat_bool_fun$] : ? [v2: MultipleValueBool] : (fun_app$x(v1,
% 154.25/20.89 v0) = v2) & ? [v0: Bool_int_fun$] : ? [v1: Bool_int_fun$] : ? [v2:
% 154.25/20.89 MultipleValueBool] : (less$e(v1, v0) = v2) & ? [v0: Bool_real_fun$] : ?
% 154.25/20.89 [v1: Bool_real_fun$] : ? [v2: MultipleValueBool] : (less$d(v1, v0) = v2) & ?
% 154.25/20.89 [v0: Cols_set$] : ? [v1: Cols_set_int_fun$] : ? [v2: int] : (fun_app$s(v1,
% 154.25/20.89 v0) = v2) & ? [v0: Cols$] : ? [v1: Cols_real_fun$] : ? [v2: $real] :
% 154.25/20.89 (fun_app$p(v1, v0) = v2) & ? [v0: Cols$] : ? [v1: Cols_int_fun$] : ? [v2:
% 154.25/20.89 int] : (fun_app$o(v1, v0) = v2) & ? [v0: $real] : ? [v1: Real_real_fun$] :
% 154.25/20.89 ? [v2: $real] : (fun_app$l(v1, v0) = v2) & ? [v0: $real] : ? [v1:
% 154.25/20.89 Real_int_fun$] : ? [v2: int] : (fun_app$k(v1, v0) = v2) & ? [v0: int] : ?
% 154.25/20.89 [v1: Int_real_fun$] : ? [v2: $real] : (fun_app$j(v1, v0) = v2) & ? [v0: int]
% 154.25/20.89 : ? [v1: Int_int_fun$] : ? [v2: int] : (fun_app$i(v1, v0) = v2) & ? [v0:
% 154.25/20.89 Rows$] : ? [v1: Rows$] : ? [v2: MultipleValueBool] : (less$c(v1, v0) = v2)
% 154.25/20.89 & ? [v0: Real_set$] : ? [v1: Real_set$] : ? [v2: MultipleValueBool] :
% 154.25/20.89 (less$b(v1, v0) = v2) & ? [v0: Real_set$] : ? [v1: Real_set$] : ? [v2:
% 154.25/20.89 MultipleValueBool] : (less_eq$e(v1, v0) = v2) & ? [v0: Cols_set$] : ? [v1:
% 154.25/20.89 Cols_set_bool_fun$] : ? [v2: MultipleValueBool] : (fun_app$g(v1, v0) = v2)
% 154.25/20.89 & ? [v0: Bool_int_fun$] : ? [v1: Bool_int_fun$] : ? [v2: MultipleValueBool]
% 154.25/20.89 : (less_eq$c(v1, v0) = v2) & ? [v0: Bool_real_fun$] : ? [v1: Bool_real_fun$]
% 154.25/20.89 : ? [v2: MultipleValueBool] : (less_eq$b(v1, v0) = v2) & ? [v0: Cols$] : ?
% 154.25/20.89 [v1: Cols_bool_fun$] : ? [v2: MultipleValueBool] : (fun_app$e(v1, v0) = v2) &
% 154.25/20.89 ? [v0: Rows$] : ? [v1: Rows$] : ? [v2: MultipleValueBool] : (less_eq$(v1,
% 154.25/20.89 v0) = v2) & ? [v0: Nat$] : ? [v1: Nat_int_fun$] : ? [v2: int] :
% 154.25/20.89 (fun_app$d(v1, v0) = v2) & ? [v0: Real_set$] : ? [v1: $real] : ? [v2:
% 154.25/20.89 MultipleValueBool] : (member$(v1, v0) = v2) & ? [v0: $real] : ? [v1:
% 154.25/20.89 $real] : ? [v2: MultipleValueBool] : (real_$less(v1, v0) = v2) & ? [v0:
% 154.25/20.89 int] : ? [v1: Int_bool_fun$] : ? [v2: MultipleValueBool] : (fun_app$b(v1,
% 154.25/20.89 v0) = v2) & ? [v0: $real] : ? [v1: Real_bool_fun$] : ? [v2:
% 154.25/20.89 MultipleValueBool] : (fun_app$(v1, v0) = v2) & ? [v0: $real] : ? [v1:
% 154.25/20.89 $real] : ? [v2: MultipleValueBool] : (real_$lesseq(v1, v0) = v2) & ? [v0:
% 154.25/20.89 Nat$] : ? [v1: Nat_nat_bool_fun_fun$] : ? [v2: Nat_bool_fun$] :
% 154.25/20.89 (fun_app$ad(v1, v0) = v2 & Nat_bool_fun$(v2)) & ? [v0: Nat$] : ? [v1:
% 154.25/20.89 Nat_a_iarray_fun$] : ? [v2: A_iarray_iarray$] : (of_fun$(v1, v0) = v2 &
% 154.25/20.89 A_iarray_iarray$(v2)) & ? [v0: Nat$] : ? [v1: A_iarray$] : ? [v2: A$] :
% 154.25/20.89 (sub$a(v1, v0) = v2 & A$(v2)) & ? [v0: Cols$] : ? [v1: A_cols_vec$] : ?
% 154.25/20.89 [v2: A$] : (vec_nth$a(v1, v0) = v2 & A$(v2)) & ? [v0: Rows$] : ? [v1:
% 154.25/20.89 A_cols_vec_rows_vec$] : ? [v2: A_cols_vec$] : (vec_nth$(v1, v0) = v2 &
% 154.25/20.89 A_cols_vec$(v2)) & ? [v0: Nat$] : ? [v1: Nat_a_iarray_fun$] : ? [v2:
% 154.25/20.89 A_iarray$] : (fun_app$ac(v1, v0) = v2 & A_iarray$(v2)) & ? [v0:
% 154.25/20.89 A_iarray_iarray$] : ? [v1: Nat$] : ? [v2: A_iarray$] : (row_iarray$(v1,
% 154.25/20.89 v0) = v2 & A_iarray$(v2)) & ? [v0: A_iarray_iarray$] : ? [v1: Nat$] : ?
% 154.25/20.89 [v2: A_iarray$] : (column_iarray$(v1, v0) = v2 & A_iarray$(v2)) & ? [v0:
% 154.25/20.89 Nat$] : ? [v1: A_iarray_iarray$] : ? [v2: A_iarray_iarray$] :
% 154.25/20.89 (gauss_Jordan_upt_k_iarrays$(v1, v0) = v2 & A_iarray_iarray$(v2)) & ? [v0:
% 154.25/20.89 Nat$] : ? [v1: A_cols_vec_rows_vec$] : ? [v2: A_cols_vec_rows_vec$] :
% 154.25/20.89 (gauss_Jordan_upt_k$(v1, v0) = v2 & A_cols_vec_rows_vec$(v2)) & ? [v0:
% 154.25/20.89 A_rows_vec_cols_vec$] : ? [v1: Cols$] : ? [v2: A_rows_vec$] : (row$b(v1,
% 154.25/20.89 v0) = v2 & A_rows_vec$(v2)) & ? [v0: A_cols_vec_rows_vec$] : ? [v1:
% 154.25/20.89 Cols$] : ? [v2: A_rows_vec$] : (column$b(v1, v0) = v2 & A_rows_vec$(v2)) &
% 154.25/20.89 ? [v0: A_rows_vec_cols_vec$] : ? [v1: Rows$] : ? [v2: A_cols_vec$] :
% 154.25/20.89 (column$a(v1, v0) = v2 & A_cols_vec$(v2)) & ? [v0: A_cols_vec_rows_vec$] : ?
% 154.25/20.89 [v1: Rows$] : ? [v2: A_cols_vec$] : (row$a(v1, v0) = v2 & A_cols_vec$(v2)) &
% 154.25/20.89 ? [v0: A_cols_vec_cols_vec$] : ? [v1: Cols$] : ? [v2: A_cols_vec$] :
% 154.25/20.89 (column$(v1, v0) = v2 & A_cols_vec$(v2)) & ? [v0: A_cols_vec_cols_vec$] : ?
% 154.25/20.89 [v1: Cols$] : ? [v2: A_cols_vec$] : (row$(v1, v0) = v2 & A_cols_vec$(v2)) &
% 154.25/20.89 ? [v0: Nat$] : ? [v1: Nat_nat_fun$] : ? [v2: Nat$] : (fun_app$y(v1, v0) = v2
% 154.25/20.89 & Nat$(v2)) & ? [v0: Real_set$] : ? [v1: Real_set_real_set_fun$] : ? [v2:
% 154.25/20.89 Real_set$] : (fun_app$w(v1, v0) = v2 & Real_set$(v2)) & ? [v0: Real_set$] :
% 154.25/20.89 ? [v1: Real_set_cols_set_fun$] : ? [v2: Cols_set$] : (fun_app$v(v1, v0) = v2
% 154.25/20.89 & Cols_set$(v2)) & ? [v0: Real_set$] : ? [v1: Real_set_bool_int_fun_fun$]
% 154.25/20.89 : ? [v2: Bool_int_fun$] : (fun_app$u(v1, v0) = v2 & Bool_int_fun$(v2)) & ?
% 154.25/20.89 [v0: Real_set$] : ? [v1: Real_set_bool_real_fun_fun$] : ? [v2:
% 154.25/20.89 Bool_real_fun$] : (fun_app$t(v1, v0) = v2 & Bool_real_fun$(v2)) & ? [v0:
% 154.25/20.89 int] : ? [v1: Int_cols_set_fun$] : ? [v2: Cols_set$] : (fun_app$r(v1, v0)
% 154.25/20.89 = v2 & Cols_set$(v2)) & ? [v0: Cols$] : ? [v1: Cols_cols_fun$] : ? [v2:
% 154.25/20.89 Cols$] : (fun_app$q(v1, v0) = v2 & Cols$(v2)) & ? [v0: $real] : ? [v1:
% 154.25/20.89 Real_cols_fun$] : ? [v2: Cols$] : (fun_app$n(v1, v0) = v2 & Cols$(v2)) & ?
% 154.25/20.89 [v0: int] : ? [v1: Int_cols_fun$] : ? [v2: Cols$] : (fun_app$m(v1, v0) = v2
% 154.25/20.89 & Cols$(v2)) & ? [v0: Cols_set$] : ? [v1: Cols_set_cols_set_bool_fun_fun$]
% 154.25/20.89 : ? [v2: Cols_set_bool_fun$] : (fun_app$h(v1, v0) = v2 &
% 154.25/20.89 Cols_set_bool_fun$(v2)) & ? [v0: Cols$] : ? [v1: Cols_cols_bool_fun_fun$]
% 154.25/20.89 : ? [v2: Cols_bool_fun$] : (fun_app$f(v1, v0) = v2 & Cols_bool_fun$(v2)) & ?
% 154.25/20.89 [v0: int] : ? [v1: Int_int_bool_fun_fun$] : ? [v2: Int_bool_fun$] :
% 154.25/20.89 (fun_app$c(v1, v0) = v2 & Int_bool_fun$(v2)) & ? [v0: $real] : ? [v1:
% 154.25/20.89 Real_real_bool_fun_fun$] : ? [v2: Real_bool_fun$] : (fun_app$a(v1, v0) = v2
% 154.25/20.89 & Real_bool_fun$(v2)) & ? [v0: $real] : ? [v1: MultipleValueBool] :
% 154.25/20.89 (real_$is_int(v0) = v1) & ? [v0: $real] : ? [v1: MultipleValueBool] :
% 154.25/20.89 (real_$is_rat(v0) = v1) & ? [v0: $real] : ? [v1: $real] : (real_$floor(v0) =
% 154.25/20.89 v1) & ? [v0: $real] : ? [v1: $real] : (real_$ceiling(v0) = v1) & ? [v0:
% 154.25/20.89 $real] : ? [v1: $real] : (real_$truncate(v0) = v1) & ? [v0: $real] : ?
% 154.25/20.89 [v1: $real] : (real_$round(v0) = v1) & ? [v0: $real] : ? [v1: int] :
% 154.25/20.89 (real_$to_int(v0) = v1) & ? [v0: $real] : ? [v1: $rat] : (real_$to_rat(v0) =
% 154.25/20.89 v1) & ? [v0: $real] : ? [v1: $real] : (real_$to_real(v0) = v1) & ? [v0:
% 154.25/20.89 int] : ? [v1: $real] : (int_$to_real(v0) = v1) & ? [v0: $real] : ? [v1:
% 154.25/20.89 $real] : (real_$uminus(v0) = v1) & ? [v0: A_rows_vec_cols_vec$] : ? [v1:
% 154.25/20.89 A_cols_vec_cols_vec$] : (p_Gauss_Jordan$(v0) = v1 &
% 154.25/20.89 A_cols_vec_cols_vec$(v1)) & ? [v0: A_cols_vec_rows_vec$] : ? [v1: Nat$] :
% 154.25/20.89 (row_rank$(v0) = v1 & Nat$(v1)) & ? [v0: A_cols_vec_rows_vec$] : ? [v1:
% 154.25/20.89 A_cols_vec_rows_vec$] : (gauss_Jordan$(v0) = v1 & A_cols_vec_rows_vec$(v1))
% 154.25/20.89 & ? [v0: int] : ? [v1: Nat$] : (nat$(v0) = v1 & Nat$(v1)) & ? [v0:
% 154.25/20.89 A_iarray$] : ? [v1: Nat$] : (length$a(v0) = v1 & Nat$(v1)) & ? [v0:
% 154.25/20.89 A_iarray_iarray$] : ? [v1: Nat_a_iarray_fun$] : (sub$(v0) = v1 &
% 154.25/20.89 Nat_a_iarray_fun$(v1)) & ? [v0: A_cols_vec_cols_vec$] : ? [v1:
% 154.25/20.89 A_iarray_iarray$] : (matrix_to_iarray$b(v0) = v1 & A_iarray_iarray$(v1)) &
% 154.25/20.89 ? [v0: A_cols_vec$] : ? [v1: A_iarray$] : (vec_to_iarray$a(v0) = v1 &
% 154.25/20.89 A_iarray$(v1)) & ? [v0: A_rows_vec$] : ? [v1: A_iarray$] :
% 154.25/20.89 (vec_to_iarray$(v0) = v1 & A_iarray$(v1)) & ? [v0: A_iarray_iarray$] : ?
% 154.25/20.89 [v1: Nat$] : (length$(v0) = v1 & Nat$(v1)) & ? [v0: Rows_set$] : ? [v1:
% 154.25/20.89 Nat$] : (card$a(v0) = v1 & Nat$(v1)) & ? [v0: A_iarray_iarray$] : ? [v1:
% 154.25/20.89 Nat$] : (nrows_iarray$(v0) = v1 & Nat$(v1)) & ? [v0: A_cols_vec_rows_vec$]
% 154.25/20.89 : ? [v1: Nat$] : (col_rank$(v0) = v1 & Nat$(v1)) & ? [v0: Cols_set$] : ?
% 154.25/20.89 [v1: Nat$] : (card$(v0) = v1 & Nat$(v1)) & ? [v0: A_cols_vec_rows_vec$] : ?
% 154.25/20.89 [v1: Nat$] : (ncols$(v0) = v1 & Nat$(v1)) & ? [v0: A_iarray_iarray$] : ?
% 154.25/20.89 [v1: A_iarray_set$] : (basis_left_null_space_iarrays$(v0) = v1 &
% 154.25/20.89 A_iarray_set$(v1)) & ? [v0: A_iarray_iarray$] : ? [v1: A_iarray_set$] :
% 154.25/20.89 (basis_null_space_iarrays$(v0) = v1 & A_iarray_set$(v1)) & ? [v0:
% 154.25/20.89 A_rows_vec_cols_vec$] : ? [v1: A_iarray_iarray$] : (matrix_to_iarray$a(v0)
% 154.25/20.89 = v1 & A_iarray_iarray$(v1)) & ? [v0: A_iarray_iarray$] : ? [v1:
% 154.25/20.89 A_iarray_iarray$] : (transpose_iarray$(v0) = v1 & A_iarray_iarray$(v1)) & ?
% 154.25/20.89 [v0: A_iarray_iarray$] : ? [v1: A_cols_vec_rows_vec$] :
% 154.25/20.89 (iarray_to_matrix$(v0) = v1 & A_cols_vec_rows_vec$(v1)) & ? [v0:
% 154.25/20.89 Real_bool_fun$] : ? [v1: Real_set$] : (collect$(v0) = v1 & Real_set$(v1)) &
% 154.25/20.89 ? [v0: A_iarray_iarray$] : ? [v1: Nat$] : (ncols_iarray$(v0) = v1 &
% 154.25/20.89 Nat$(v1)) & ? [v0: A_rows_vec_cols_vec$] : ? [v1: Nat$] : (rank$b(v0) = v1
% 154.25/20.89 & Nat$(v1)) & ? [v0: A_cols_vec_rows_vec$] : ? [v1: Nat$] : (rank$(v0) =
% 154.25/20.90 v1 & Nat$(v1)) & ? [v0: A_cols_vec_cols_vec$] : ? [v1: Nat$] : (rank$a(v0)
% 154.25/20.90 = v1 & Nat$(v1)) & ? [v0: A_cols_vec_rows_vec$] : ? [v1:
% 154.25/20.90 A_rows_vec_cols_vec$] : (transpose$(v0) = v1 & A_rows_vec_cols_vec$(v1)) &
% 154.25/20.90 ? [v0: A_cols_vec_cols_vec$] : ? [v1: A_cols_vec_cols_vec$] :
% 154.25/20.90 (transpose$b(v0) = v1 & A_cols_vec_cols_vec$(v1)) & ? [v0:
% 154.25/20.90 A_rows_vec_cols_vec$] : ? [v1: A_cols_vec_rows_vec$] : (transpose$a(v0) =
% 154.25/20.90 v1 & A_cols_vec_rows_vec$(v1)) & ? [v0: A_cols_vec_rows_vec$] : ? [v1:
% 154.25/20.90 A_iarray_iarray$] : (matrix_to_iarray$(v0) = v1 & A_iarray_iarray$(v1)) & ?
% 154.25/20.90 [v0: A_iarray_iarray$] : ? [v1: Nat$] : (rank_iarray$(v0) = v1 & Nat$(v1)) &
% 154.25/20.90 ? [v0: Cols$] : ? [v1: Nat$] : (to_nat$(v0) = v1 & Nat$(v1)) & ? [v0: Nat$]
% 154.25/20.90 : ? [v1: Cols$] : (from_nat$(v0) = v1 & Cols$(v1)) & ? [v0: Rows$] : ? [v1:
% 154.25/20.90 Nat$] : (to_nat$a(v0) = v1 & Nat$(v1)) & ? [v0: Nat$] : ? [v1: Rows$] :
% 154.25/20.90 (from_nat$a(v0) = v1 & Rows$(v1)) & ? [v0: Real_set$] : ? [v1:
% 154.25/20.90 Real_bool_fun$] : (uu$(v0) = v1 & Real_bool_fun$(v1))
% 154.25/20.90
% 154.25/20.90 Further assumptions not needed in the proof:
% 154.25/20.90 --------------------------------------------
% 154.25/20.90 axiom0, axiom1, axiom10, axiom100, axiom101, axiom102, axiom103, axiom104,
% 154.25/20.90 axiom105, axiom106, axiom107, axiom108, axiom109, axiom11, axiom110, axiom111,
% 154.25/20.90 axiom112, axiom113, axiom114, axiom115, axiom116, axiom117, axiom118, axiom119,
% 154.25/20.90 axiom12, axiom120, axiom121, axiom122, axiom123, axiom124, axiom125, axiom126,
% 154.25/20.90 axiom127, axiom128, axiom129, axiom13, axiom130, axiom131, axiom132, axiom133,
% 154.25/20.90 axiom134, axiom135, axiom136, axiom137, axiom138, axiom139, axiom14, axiom140,
% 154.25/20.90 axiom141, axiom142, axiom143, axiom144, axiom145, axiom146, axiom147, axiom148,
% 154.25/20.90 axiom149, axiom15, axiom150, axiom151, axiom152, axiom153, axiom154, axiom155,
% 154.25/20.90 axiom156, axiom157, axiom158, axiom159, axiom16, axiom160, axiom161, axiom162,
% 154.25/20.90 axiom163, axiom164, axiom165, axiom166, axiom167, axiom168, axiom169, axiom17,
% 154.25/20.90 axiom170, axiom171, axiom172, axiom173, axiom174, axiom175, axiom176, axiom177,
% 154.25/20.90 axiom178, axiom179, axiom18, axiom180, axiom181, axiom182, axiom183, axiom184,
% 154.25/20.90 axiom185, axiom186, axiom187, axiom188, axiom189, axiom19, axiom190, axiom191,
% 154.25/20.90 axiom192, axiom193, axiom194, axiom195, axiom196, axiom197, axiom198, axiom199,
% 154.25/20.90 axiom2, axiom20, axiom200, axiom201, axiom202, axiom203, axiom204, axiom205,
% 154.25/20.90 axiom206, axiom207, axiom208, axiom209, axiom21, axiom210, axiom211, axiom212,
% 154.25/20.90 axiom213, axiom214, axiom215, axiom216, axiom217, axiom218, axiom219, axiom22,
% 154.25/20.90 axiom220, axiom221, axiom222, axiom223, axiom224, axiom225, axiom226, axiom227,
% 154.25/20.90 axiom228, axiom229, axiom23, axiom230, axiom231, axiom232, axiom233, axiom234,
% 154.25/20.90 axiom235, axiom236, axiom237, axiom238, axiom239, axiom24, axiom240, axiom241,
% 154.25/20.90 axiom242, axiom243, axiom244, axiom245, axiom246, axiom247, axiom248, axiom249,
% 154.25/20.90 axiom25, axiom250, axiom251, axiom252, axiom253, axiom254, axiom255, axiom256,
% 154.25/20.90 axiom257, axiom258, axiom259, axiom26, axiom260, axiom261, axiom262, axiom263,
% 154.25/20.90 axiom264, axiom265, axiom266, axiom267, axiom268, axiom269, axiom27, axiom270,
% 154.25/20.90 axiom271, axiom272, axiom273, axiom274, axiom275, axiom276, axiom277, axiom278,
% 154.25/20.90 axiom279, axiom28, axiom280, axiom281, axiom282, axiom283, axiom284, axiom285,
% 154.25/20.90 axiom286, axiom287, axiom288, axiom289, axiom29, axiom290, axiom291, axiom292,
% 154.25/20.90 axiom293, axiom294, axiom295, axiom296, axiom297, axiom298, axiom299, axiom3,
% 154.25/20.90 axiom30, axiom300, axiom301, axiom302, axiom303, axiom304, axiom305, axiom306,
% 154.25/20.90 axiom307, axiom308, axiom309, axiom31, axiom310, axiom311, axiom312, axiom313,
% 154.25/20.90 axiom314, axiom315, axiom316, axiom317, axiom318, axiom319, axiom32, axiom320,
% 154.25/20.90 axiom321, axiom322, axiom323, axiom324, axiom325, axiom326, axiom327, axiom328,
% 154.25/20.90 axiom329, axiom33, axiom330, axiom331, axiom332, axiom333, axiom334, axiom335,
% 154.25/20.90 axiom336, axiom337, axiom338, axiom339, axiom34, axiom340, axiom341, axiom342,
% 154.25/20.90 axiom343, axiom344, axiom345, axiom346, axiom347, axiom348, axiom349, axiom35,
% 154.25/20.90 axiom350, axiom351, axiom352, axiom353, axiom354, axiom355, axiom356, axiom357,
% 154.25/20.90 axiom358, axiom359, axiom36, axiom360, axiom361, axiom362, axiom363, axiom364,
% 154.25/20.90 axiom365, axiom366, axiom367, axiom368, axiom369, axiom37, axiom370, axiom371,
% 154.25/20.90 axiom372, axiom373, axiom374, axiom375, axiom376, axiom377, axiom379, axiom380,
% 154.25/20.90 axiom381, axiom382, axiom383, axiom384, axiom385, axiom386, axiom387, axiom388,
% 154.25/20.90 axiom389, axiom390, axiom391, axiom392, axiom393, axiom394, axiom395, axiom396,
% 154.25/20.90 axiom397, axiom398, axiom399, axiom4, axiom40, axiom400, axiom401, axiom402,
% 154.25/20.90 axiom403, axiom404, axiom405, axiom406, axiom407, axiom408, axiom409, axiom41,
% 154.25/20.90 axiom410, axiom411, axiom412, axiom413, axiom414, axiom416, axiom417, axiom418,
% 154.25/20.90 axiom419, axiom42, axiom420, axiom421, axiom422, axiom423, axiom424, axiom425,
% 154.25/20.90 axiom426, axiom427, axiom428, axiom429, axiom43, axiom430, axiom432, axiom433,
% 154.25/20.90 axiom434, axiom436, axiom437, axiom438, axiom44, axiom442, axiom443, axiom449,
% 154.25/20.90 axiom45, axiom450, axiom451, axiom454, axiom455, axiom456, axiom457, axiom458,
% 154.25/20.90 axiom459, axiom46, axiom460, axiom461, axiom462, axiom463, axiom464, axiom465,
% 154.25/20.90 axiom466, axiom467, axiom469, axiom47, axiom470, axiom471, axiom472, axiom473,
% 154.25/20.90 axiom474, axiom475, axiom476, axiom477, axiom478, axiom479, axiom48, axiom480,
% 154.25/20.90 axiom481, axiom482, axiom483, axiom485, axiom486, axiom487, axiom488, axiom489,
% 154.25/20.90 axiom49, axiom490, axiom491, axiom492, axiom494, axiom496, axiom498, axiom499,
% 154.25/20.90 axiom50, axiom500, axiom501, axiom502, axiom503, axiom504, axiom505, axiom506,
% 154.25/20.90 axiom508, axiom509, axiom51, axiom510, axiom511, axiom512, axiom513, axiom514,
% 154.25/20.90 axiom515, axiom516, axiom517, axiom518, axiom519, axiom52, axiom520, axiom521,
% 154.25/20.90 axiom522, axiom523, axiom524, axiom525, axiom526, axiom527, axiom528, axiom529,
% 154.25/20.90 axiom53, axiom530, axiom531, axiom532, axiom533, axiom534, axiom535, axiom536,
% 154.25/20.90 axiom537, axiom538, axiom539, axiom54, axiom540, axiom541, axiom542, axiom543,
% 154.25/20.90 axiom544, axiom545, axiom546, axiom547, axiom548, axiom549, axiom55, axiom550,
% 154.25/20.90 axiom551, axiom552, axiom553, axiom554, axiom555, axiom556, axiom557, axiom558,
% 154.25/20.90 axiom559, axiom56, axiom560, axiom561, axiom562, axiom563, axiom564, axiom565,
% 154.25/20.90 axiom566, axiom567, axiom568, axiom569, axiom57, axiom570, axiom571, axiom572,
% 154.25/20.90 axiom573, axiom574, axiom575, axiom576, axiom577, axiom578, axiom579, axiom58,
% 154.25/20.90 axiom580, axiom581, axiom582, axiom583, axiom584, axiom585, axiom586, axiom587,
% 154.25/20.90 axiom588, axiom589, axiom59, axiom590, axiom591, axiom592, axiom593, axiom594,
% 154.25/20.90 axiom595, axiom596, axiom597, axiom599, axiom6, axiom60, axiom600, axiom601,
% 154.25/20.90 axiom602, axiom603, axiom604, axiom605, axiom606, axiom607, axiom608, axiom609,
% 154.25/20.90 axiom61, axiom610, axiom611, axiom612, axiom613, axiom614, axiom615, axiom616,
% 154.25/20.90 axiom62, axiom63, axiom64, axiom65, axiom66, axiom67, axiom68, axiom69, axiom7,
% 154.25/20.90 axiom70, axiom71, axiom72, axiom73, axiom74, axiom75, axiom76, axiom77, axiom78,
% 154.25/20.90 axiom79, axiom80, axiom81, axiom82, axiom83, axiom84, axiom85, axiom86, axiom87,
% 154.25/20.90 axiom88, axiom89, axiom9, axiom90, axiom91, axiom92, axiom93, axiom94, axiom95,
% 154.25/20.90 axiom96, axiom97, axiom98, axiom99, formula_618, formula_619
% 154.25/20.90
% 154.25/20.90 Those formulas are unsatisfiable:
% 154.25/20.90 ---------------------------------
% 154.25/20.90
% 154.25/20.90 Begin of proof
% 154.25/20.90 |
% 154.25/20.90 | ALPHA: (axiom8) implies:
% 154.25/20.90 | (1) ? [v0: int] : ? [v1: A_iarray_iarray$] : ? [v2: Nat$] : ? [v3: int]
% 154.25/20.90 | : ($lesseq(v3, v0) & matrix_to_iarray$(a$) = v1 & rank_iarray$(v1) = v2
% 154.25/20.90 | & fun_app$d(of_nat$, v2) = v3 & fun_app$d(of_nat$, i$) = v0 &
% 154.25/20.90 | Nat$(v2) & A_iarray_iarray$(v1))
% 154.25/20.90 |
% 154.25/20.90 | ALPHA: (axiom38) implies:
% 154.25/20.90 | (2) ! [v0: Cols$] : ! [v1: Nat$] : ! [v2: Nat$] : ! [v3: int] : ( ~
% 154.25/20.90 | (fun_app$d(of_nat$, v1) = v3) | ~ (to_nat$(v0) = v2) | ~ Cols$(v0)
% 154.25/20.90 | | ~ Nat$(v1) | ? [v4: int] : ? [v5: Cols$] : (fun_app$d(of_nat$,
% 154.25/20.90 | v2) = v4 & from_nat$(v1) = v5 & Cols$(v5) & ( ~ (v4 = v3) | v5 =
% 154.25/20.90 | v0)))
% 154.25/20.90 |
% 154.25/20.90 | ALPHA: (axiom39) implies:
% 154.25/20.91 | (3) ? [v0: A_iarray_iarray$] : ? [v1: Nat$] : ? [v2: int] : ? [v3: int]
% 154.25/20.91 | : ($lesseq(1, $difference(v2, v3)) & ncols_iarray$(v0) = v1 &
% 154.25/20.91 | matrix_to_iarray$(a$) = v0 & fun_app$d(of_nat$, v1) = v2 &
% 154.25/20.91 | fun_app$d(of_nat$, i$) = v3 & Nat$(v1) & A_iarray_iarray$(v0))
% 154.25/20.91 |
% 154.25/20.91 | ALPHA: (axiom378) implies:
% 154.25/20.91 | (4) ! [v0: A_cols_vec_rows_vec$] : ! [v1: Nat$] : ( ~ (rank$(v0) = v1) |
% 154.25/20.91 | ~ A_cols_vec_rows_vec$(v0) | ? [v2: int] : ? [v3: A_iarray_iarray$]
% 154.25/20.91 | : ? [v4: Nat$] : (matrix_to_iarray$(v0) = v3 & rank_iarray$(v3) = v4
% 154.25/20.91 | & fun_app$d(of_nat$, v4) = v2 & fun_app$d(of_nat$, v1) = v2 &
% 154.25/20.91 | Nat$(v4) & A_iarray_iarray$(v3)))
% 154.25/20.91 |
% 154.25/20.91 | ALPHA: (axiom431) implies:
% 154.25/20.91 | (5) ? [v0: Nat$] : ? [v1: int] : ? [v2: int] : ($lesseq(1,
% 154.25/20.91 | $difference(v1, v2)) & card$(top$) = v0 & fun_app$d(of_nat$, v0) =
% 154.25/20.91 | v1 & fun_app$d(of_nat$, i$) = v2 & Nat$(v0))
% 154.25/20.91 |
% 154.25/20.91 | ALPHA: (axiom435) implies:
% 154.25/20.91 | (6) ? [v0: Nat$] : ? [v1: int] : (card$(top$) = v0 & fun_app$d(of_nat$,
% 154.25/20.91 | v0) = v1 & Nat$(v0) & ? [v2: Cols_bool_fun$] : ( ~
% 154.25/20.91 | Cols_bool_fun$(v2) | ? [v3: Cols$] : ? [v4: Nat$] : ? [v5: int]
% 154.25/20.91 | : ? [v6: int] : ( ~ (v6 = 0) & $lesseq(1, $difference(v1, v5)) &
% 154.25/20.91 | fun_app$e(v2, v3) = v6 & fun_app$d(of_nat$, v4) = v5 &
% 154.25/20.91 | to_nat$(v3) = v4 & Cols$(v3) & Nat$(v4)) | ! [v3: Cols$] : !
% 154.25/20.91 | [v4: int] : (v4 = 0 | ~ (fun_app$e(v2, v3) = v4) | ~ Cols$(v3)))
% 154.25/20.91 | & ? [v2: Cols_bool_fun$] : ( ~ Cols_bool_fun$(v2) | ? [v3: Cols$] :
% 154.25/20.91 | ? [v4: int] : ( ~ (v4 = 0) & fun_app$e(v2, v3) = v4 & Cols$(v3)) |
% 154.25/20.91 | ! [v3: Cols$] : ! [v4: Nat$] : ( ~ (to_nat$(v3) = v4) | ~
% 154.25/20.91 | Cols$(v3) | ? [v5: int] : ? [v6: any] : (fun_app$e(v2, v3) = v6
% 154.25/20.91 | & fun_app$d(of_nat$, v4) = v5 & (v6 = 0 | ~ ($lesseq(1,
% 154.25/20.91 | $difference(v1, v5))))))))
% 154.25/20.91 |
% 154.25/20.91 | ALPHA: (axiom439) implies:
% 154.25/20.91 | (7) ? [v0: Nat$] : ? [v1: int] : (card$(top$) = v0 & fun_app$d(of_nat$,
% 154.25/20.91 | v0) = v1 & Nat$(v0) & ! [v2: A_cols_vec_rows_vec$] : ! [v3:
% 154.25/20.91 | A_iarray_iarray$] : ( ~ (matrix_to_iarray$(v2) = v3) | ~
% 154.25/20.91 | A_cols_vec_rows_vec$(v2) | ? [v4: Nat$] : (ncols_iarray$(v3) = v4
% 154.25/20.91 | & fun_app$d(of_nat$, v4) = v1 & Nat$(v4))))
% 154.25/20.91 |
% 154.25/20.91 | ALPHA: (axiom440) implies:
% 154.25/20.91 | (8) ? [v0: Nat$] : ? [v1: int] : (card$(top$) = v0 & fun_app$d(of_nat$,
% 154.25/20.91 | v0) = v1 & Nat$(v0) & ! [v2: Cols$] : ! [v3: Nat$] : ( ~
% 154.25/20.91 | (to_nat$(v2) = v3) | ~ Cols$(v2) | ? [v4: int] : ($lesseq(1,
% 154.25/20.91 | $difference(v1, v4)) & fun_app$d(of_nat$, v3) = v4)))
% 154.25/20.91 |
% 154.25/20.91 | ALPHA: (axiom441) implies:
% 154.25/20.91 | (9) ? [v0: Nat$] : ? [v1: int] : (card$(top$) = v0 & fun_app$d(of_nat$,
% 154.25/20.91 | v0) = v1 & Nat$(v0) & ! [v2: Nat$] : ! [v3: Nat$] : ! [v4: int]
% 154.25/20.91 | : ! [v5: int] : (v5 = v4 | ~ ($lesseq(1, $difference(v1, v5))) | ~
% 154.25/20.91 | ($lesseq(1, $difference(v1, v4))) | ~ (fun_app$d(of_nat$, v3) =
% 154.25/20.91 | v5) | ~ (fun_app$d(of_nat$, v2) = v4) | ~ Nat$(v3) | ~
% 154.25/20.91 | Nat$(v2) | ? [v6: Cols$] : ? [v7: Cols$] : ( ~ (v7 = v6) &
% 154.25/20.91 | from_nat$(v3) = v7 & from_nat$(v2) = v6 & Cols$(v7) &
% 154.25/20.91 | Cols$(v6))))
% 154.25/20.91 |
% 154.25/20.91 | ALPHA: (axiom444) implies:
% 154.25/20.91 | (10) ? [v0: Nat$] : ? [v1: int] : (card$(top$) = v0 & fun_app$d(of_nat$,
% 154.25/20.91 | v0) = v1 & Nat$(v0) & ! [v2: Nat$] : ! [v3: Nat$] : ! [v4:
% 154.25/20.91 | Cols$] : ! [v5: Cols_bool_fun$] : ! [v6: Cols$] : ! [v7: int] :
% 154.25/20.91 | (v7 = 0 | ~ (fun_app$f(less$, v4) = v5) | ~ (fun_app$e(v5, v6) =
% 154.25/20.91 | v7) | ~ (from_nat$(v3) = v6) | ~ (from_nat$(v2) = v4) | ~
% 154.25/20.91 | Nat$(v3) | ~ Nat$(v2) | ? [v8: int] : ? [v9: int] :
% 154.25/20.91 | (fun_app$d(of_nat$, v3) = v8 & fun_app$d(of_nat$, v2) = v9 & ( ~
% 154.25/20.91 | ($lesseq(1, $difference(v8, v9))) | ~ ($lesseq(1,
% 154.25/20.91 | $difference(v1, v8)))))))
% 154.25/20.91 |
% 154.25/20.91 | ALPHA: (axiom445) implies:
% 154.25/20.91 | (11) ? [v0: Nat$] : ? [v1: int] : (card$(top$) = v0 & fun_app$d(of_nat$,
% 154.25/20.91 | v0) = v1 & Nat$(v0) & ! [v2: Nat$] : ! [v3: int] : ( ~
% 154.25/20.91 | ($lesseq(1, $difference(v1, v3))) | ~ (fun_app$d(of_nat$, v2) =
% 154.25/20.91 | v3) | ~ Nat$(v2) | ? [v4: Cols$] : ? [v5: Nat$] :
% 154.25/20.91 | (fun_app$d(of_nat$, v5) = v3 & to_nat$(v4) = v5 & from_nat$(v2) =
% 154.25/20.91 | v4 & Cols$(v4) & Nat$(v5))))
% 154.25/20.91 |
% 154.25/20.91 | ALPHA: (axiom446) implies:
% 154.25/20.91 | (12) ? [v0: Nat$] : ? [v1: int] : (card$(top$) = v0 & fun_app$d(of_nat$,
% 154.25/20.91 | v0) = v1 & Nat$(v0) & ! [v2: Nat$] : ! [v3: Cols$] : ! [v4:
% 154.25/20.91 | int] : ! [v5: Nat$] : ( ~ ($lesseq(1, $difference(v1, v4))) | ~
% 154.25/20.91 | (fun_app$d(of_nat$, v2) = v4) | ~ (to_nat$(v3) = v5) | ~
% 154.25/20.91 | Cols$(v3) | ~ Nat$(v2) | ? [v6: Cols$] : ? [v7: int] :
% 154.25/20.91 | (fun_app$d(of_nat$, v5) = v7 & from_nat$(v2) = v6 & Cols$(v6) & (
% 154.25/20.91 | ~ (v6 = v3) | v7 = v4))))
% 154.25/20.91 |
% 154.25/20.91 | ALPHA: (axiom447) implies:
% 154.25/20.92 | (13) ? [v0: Nat$] : ? [v1: int] : (card$(top$) = v0 & fun_app$d(of_nat$,
% 154.25/20.92 | v0) = v1 & Nat$(v0) & ! [v2: Nat$] : ! [v3: Cols$] : ! [v4:
% 154.25/20.92 | int] : ! [v5: Nat$] : ( ~ ($lesseq(1, $difference(v1, v4))) | ~
% 154.25/20.92 | (fun_app$d(of_nat$, v2) = v4) | ~ (to_nat$(v3) = v5) | ~
% 154.25/20.92 | Cols$(v3) | ~ Nat$(v2) | ? [v6: int] : ? [v7: Cols$] :
% 154.25/20.92 | (fun_app$d(of_nat$, v5) = v6 & from_nat$(v2) = v7 & Cols$(v7) & (
% 154.25/20.92 | ~ (v7 = v3) | v6 = v4))))
% 154.25/20.92 |
% 154.25/20.92 | ALPHA: (axiom448) implies:
% 154.25/20.92 | (14) ? [v0: Nat$] : ? [v1: int] : (card$(top$) = v0 & fun_app$d(of_nat$,
% 154.25/20.92 | v0) = v1 & Nat$(v0) & ! [v2: Nat$] : ! [v3: Nat$] : ! [v4:
% 154.25/20.92 | Cols$] : ! [v5: Cols_bool_fun$] : ! [v6: Cols$] : ! [v7: int] :
% 154.25/20.92 | (v7 = 0 | ~ (fun_app$f(less_eq$a, v4) = v5) | ~ (fun_app$e(v5, v6)
% 154.25/20.92 | = v7) | ~ (from_nat$(v3) = v6) | ~ (from_nat$(v2) = v4) | ~
% 154.25/20.92 | Nat$(v3) | ~ Nat$(v2) | ? [v8: int] : ? [v9: int] :
% 154.25/20.92 | (fun_app$d(of_nat$, v3) = v8 & fun_app$d(of_nat$, v2) = v9 & ( ~
% 154.25/20.92 | ($lesseq(v9, v8)) | ~ ($lesseq(1, $difference(v1, v8)))))))
% 154.25/20.92 |
% 154.25/20.92 | ALPHA: (axiom452) implies:
% 154.25/20.92 | (15) ? [v0: Nat$] : ? [v1: int] : (card$a(top$a) = v0 &
% 154.25/20.92 | fun_app$d(of_nat$, v0) = v1 & Nat$(v0) & ! [v2:
% 154.25/20.92 | A_cols_vec_rows_vec$] : ! [v3: A_iarray_iarray$] : ( ~
% 154.25/20.92 | (matrix_to_iarray$(v2) = v3) | ~ A_cols_vec_rows_vec$(v2) | ?
% 154.25/20.92 | [v4: Nat$] : (nrows_iarray$(v3) = v4 & fun_app$d(of_nat$, v4) = v1
% 154.25/20.92 | & Nat$(v4))))
% 154.25/20.92 |
% 154.25/20.92 | ALPHA: (axiom453) implies:
% 154.25/20.92 | (16) ? [v0: Nat$] : ? [v1: int] : (card$a(top$a) = v0 &
% 154.25/20.92 | fun_app$d(of_nat$, v0) = v1 & Nat$(v0) & ! [v2:
% 154.25/20.92 | A_cols_vec_rows_vec$] : ! [v3: A_iarray_iarray$] : ( ~
% 154.25/20.92 | (matrix_to_iarray$(v2) = v3) | ~ A_cols_vec_rows_vec$(v2) | ?
% 154.25/20.92 | [v4: Nat$] : (length$(v3) = v4 & fun_app$d(of_nat$, v4) = v1 &
% 154.25/20.92 | Nat$(v4))))
% 154.25/20.92 |
% 154.25/20.92 | ALPHA: (axiom468) implies:
% 154.25/20.92 | (17) ? [v0: Nat$] : ? [v1: Nat$] : ? [v2: int] : (nat$(0) = v0 &
% 154.25/20.92 | card$(top$) = v1 & fun_app$d(of_nat$, v1) = v2 & Nat$(v1) & Nat$(v0)
% 154.25/20.92 | & ! [v3: A_cols_vec_rows_vec$] : ! [v4: A_iarray_iarray$] : ( ~
% 154.25/20.92 | (matrix_to_iarray$(v3) = v4) | ~ A_cols_vec_rows_vec$(v3) | ?
% 154.25/20.92 | [v5: Nat_a_iarray_fun$] : ? [v6: A_iarray$] : ? [v7: Nat$] :
% 154.25/20.92 | (length$a(v6) = v7 & sub$(v4) = v5 & fun_app$ac(v5, v0) = v6 &
% 154.25/20.92 | fun_app$d(of_nat$, v7) = v2 & A_iarray$(v6) & Nat$(v7) &
% 154.25/20.92 | Nat_a_iarray_fun$(v5))))
% 154.25/20.92 |
% 154.25/20.92 | ALPHA: (axiom484) implies:
% 154.25/20.92 | (18) ? [v0: Nat$] : (fun_app$d(of_nat$, v0) = 0 & to_nat$(zero$) = v0 &
% 154.25/20.92 | Nat$(v0))
% 154.25/20.92 |
% 154.25/20.92 | ALPHA: (axiom493) implies:
% 154.25/20.92 | (19) Cols$(zero$)
% 154.25/20.92 | (20) ? [v0: Nat$] : (card$(top$) = v0 & from_nat$(v0) = zero$ & Nat$(v0))
% 154.25/20.92 |
% 154.25/20.92 | ALPHA: (axiom495) implies:
% 154.25/20.92 | (21) ? [v0: Nat$] : (rank$(zero$a) = v0 & fun_app$d(of_nat$, v0) = 0 &
% 154.25/20.92 | Nat$(v0))
% 154.25/20.92 |
% 154.25/20.92 | ALPHA: (axiom507) implies:
% 154.25/20.92 | (22) Cols$(one$)
% 154.44/20.92 | (23) ? [v0: Nat$] : (fun_app$d(of_nat$, v0) = 1 & to_nat$(one$) = v0 &
% 154.44/20.92 | Nat$(v0))
% 154.44/20.92 |
% 154.44/20.92 | ALPHA: (axiom598) implies:
% 154.44/20.92 | (24) ? [v0: Nat$] : ? [v1: int] : ($lesseq(1, v1) & card$(top$) = v0 &
% 154.44/20.92 | fun_app$d(of_nat$, v0) = v1 & Nat$(v0))
% 154.44/20.92 |
% 154.44/20.92 | ALPHA: (conjecture5) implies:
% 154.44/20.92 | (25) Nat$(i$)
% 154.44/20.92 | (26) A_cols_vec_rows_vec$(a$)
% 154.44/20.92 | (27) ? [v0: Cols$] : ? [v1: A_rows_vec_cols_vec$] : ? [v2:
% 154.44/20.92 | A_cols_vec_cols_vec$] : ? [v3: A_cols_vec$] : ? [v4: Nat$] : ?
% 154.44/20.92 | [v5: int] : (p_Gauss_Jordan$(v1) = v2 & row$(v0, v2) = v3 & rank$(a$)
% 154.44/20.92 | = v4 & transpose$(a$) = v1 & fun_app$d(of_nat$, v4) = v5 &
% 154.44/20.92 | from_nat$(i$) = v0 & A_cols_vec_cols_vec$(v2) & Cols$(v0) &
% 154.44/20.92 | A_cols_vec$(v3) & Nat$(v4) & A_rows_vec_cols_vec$(v1) & ! [v6:
% 154.44/20.92 | Cols$] : ( ~ (row$(v6, v2) = v3) | ~ Cols$(v6) | ? [v7: Nat$] :
% 154.44/20.92 | ? [v8: int] : ($lesseq(1, $difference(v5, v8)) &
% 154.44/20.92 | fun_app$d(of_nat$, v7) = v8 & to_nat$(v6) = v7 & Nat$(v7))))
% 154.44/20.92 |
% 154.44/20.92 | ALPHA: (function-axioms) implies:
% 154.44/20.92 | (28) ! [v0: Cols$] : ! [v1: Cols$] : ! [v2: Nat$] : (v1 = v0 | ~
% 154.44/20.92 | (from_nat$(v2) = v1) | ~ (from_nat$(v2) = v0))
% 154.44/20.92 | (29) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Cols$] : (v1 = v0 | ~
% 154.44/20.92 | (to_nat$(v2) = v1) | ~ (to_nat$(v2) = v0))
% 154.44/20.92 | (30) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: A_iarray_iarray$] : (v1 = v0 |
% 154.44/20.92 | ~ (rank_iarray$(v2) = v1) | ~ (rank_iarray$(v2) = v0))
% 154.44/20.92 | (31) ! [v0: A_iarray_iarray$] : ! [v1: A_iarray_iarray$] : ! [v2:
% 154.44/20.92 | A_cols_vec_rows_vec$] : (v1 = v0 | ~ (matrix_to_iarray$(v2) = v1) |
% 154.44/20.92 | ~ (matrix_to_iarray$(v2) = v0))
% 154.44/20.93 | (32) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Cols_set$] : (v1 = v0 | ~
% 154.44/20.93 | (card$(v2) = v1) | ~ (card$(v2) = v0))
% 154.44/20.93 | (33) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Rows_set$] : (v1 = v0 | ~
% 154.44/20.93 | (card$a(v2) = v1) | ~ (card$a(v2) = v0))
% 154.44/20.93 | (34) ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : ! [v3: Nat_int_fun$] :
% 154.44/20.93 | (v1 = v0 | ~ (fun_app$d(v3, v2) = v1) | ~ (fun_app$d(v3, v2) = v0))
% 154.44/20.93 |
% 154.44/20.93 | DELTA: instantiating (20) with fresh symbol all_741_0 gives:
% 154.44/20.93 | (35) card$(top$) = all_741_0 & from_nat$(all_741_0) = zero$ &
% 154.44/20.93 | Nat$(all_741_0)
% 154.44/20.93 |
% 154.44/20.93 | ALPHA: (35) implies:
% 154.44/20.93 | (36) card$(top$) = all_741_0
% 154.44/20.93 |
% 154.44/20.93 | DELTA: instantiating (21) with fresh symbol all_745_0 gives:
% 154.44/20.93 | (37) rank$(zero$a) = all_745_0 & fun_app$d(of_nat$, all_745_0) = 0 &
% 154.44/20.93 | Nat$(all_745_0)
% 154.44/20.93 |
% 154.44/20.93 | ALPHA: (37) implies:
% 154.44/20.93 | (38) Nat$(all_745_0)
% 154.44/20.93 | (39) fun_app$d(of_nat$, all_745_0) = 0
% 154.44/20.93 |
% 154.44/20.93 | DELTA: instantiating (23) with fresh symbol all_747_0 gives:
% 154.44/20.93 | (40) fun_app$d(of_nat$, all_747_0) = 1 & to_nat$(one$) = all_747_0 &
% 154.44/20.93 | Nat$(all_747_0)
% 154.44/20.93 |
% 154.44/20.93 | ALPHA: (40) implies:
% 154.44/20.93 | (41) Nat$(all_747_0)
% 154.44/20.93 | (42) to_nat$(one$) = all_747_0
% 154.44/20.93 | (43) fun_app$d(of_nat$, all_747_0) = 1
% 154.44/20.93 |
% 154.44/20.93 | DELTA: instantiating (18) with fresh symbol all_749_0 gives:
% 154.44/20.93 | (44) fun_app$d(of_nat$, all_749_0) = 0 & to_nat$(zero$) = all_749_0 &
% 154.44/20.93 | Nat$(all_749_0)
% 154.44/20.93 |
% 154.44/20.93 | ALPHA: (44) implies:
% 154.44/20.93 | (45) Nat$(all_749_0)
% 154.44/20.93 | (46) to_nat$(zero$) = all_749_0
% 154.44/20.93 | (47) fun_app$d(of_nat$, all_749_0) = 0
% 154.44/20.93 |
% 154.44/20.93 | DELTA: instantiating (24) with fresh symbols all_751_0, all_751_1 gives:
% 154.44/20.93 | (48) $lesseq(1, all_751_0) & card$(top$) = all_751_1 & fun_app$d(of_nat$,
% 154.44/20.93 | all_751_1) = all_751_0 & Nat$(all_751_1)
% 154.44/20.93 |
% 154.44/20.93 | ALPHA: (48) implies:
% 154.44/20.93 | (49) Nat$(all_751_1)
% 154.44/20.93 | (50) fun_app$d(of_nat$, all_751_1) = all_751_0
% 154.44/20.93 | (51) card$(top$) = all_751_1
% 154.44/20.93 |
% 154.44/20.93 | DELTA: instantiating (24) with fresh symbols all_754_0, all_754_1 gives:
% 154.44/20.93 | (52) $lesseq(1, all_754_0) & card$(top$) = all_754_1 & fun_app$d(of_nat$,
% 154.44/20.93 | all_754_1) = all_754_0 & Nat$(all_754_1)
% 154.44/20.93 |
% 154.44/20.93 | ALPHA: (52) implies:
% 154.44/20.93 | (53) fun_app$d(of_nat$, all_754_1) = all_754_0
% 154.44/20.93 | (54) card$(top$) = all_754_1
% 154.44/20.93 |
% 154.44/20.93 | DELTA: instantiating (5) with fresh symbols all_762_0, all_762_1, all_762_2
% 154.44/20.93 | gives:
% 154.44/20.93 | (55) $lesseq(1, $difference(all_762_1, all_762_0)) & card$(top$) =
% 154.44/20.93 | all_762_2 & fun_app$d(of_nat$, all_762_2) = all_762_1 &
% 154.44/20.93 | fun_app$d(of_nat$, i$) = all_762_0 & Nat$(all_762_2)
% 154.44/20.93 |
% 154.44/20.93 | ALPHA: (55) implies:
% 154.44/20.93 | (56) $lesseq(1, $difference(all_762_1, all_762_0))
% 154.44/20.93 | (57) fun_app$d(of_nat$, i$) = all_762_0
% 154.44/20.93 | (58) fun_app$d(of_nat$, all_762_2) = all_762_1
% 154.44/20.93 | (59) card$(top$) = all_762_2
% 154.44/20.93 |
% 154.44/20.93 | DELTA: instantiating (1) with fresh symbols all_768_0, all_768_1, all_768_2,
% 154.44/20.93 | all_768_3 gives:
% 154.44/20.93 | (60) $lesseq(all_768_0, all_768_3) & matrix_to_iarray$(a$) = all_768_2 &
% 154.44/20.93 | rank_iarray$(all_768_2) = all_768_1 & fun_app$d(of_nat$, all_768_1) =
% 154.44/20.93 | all_768_0 & fun_app$d(of_nat$, i$) = all_768_3 & Nat$(all_768_1) &
% 154.44/20.93 | A_iarray_iarray$(all_768_2)
% 154.44/20.93 |
% 154.44/20.93 | ALPHA: (60) implies:
% 154.44/20.93 | (61) $lesseq(all_768_0, all_768_3)
% 154.44/20.93 | (62) Nat$(all_768_1)
% 154.44/20.93 | (63) fun_app$d(of_nat$, i$) = all_768_3
% 154.44/20.93 | (64) fun_app$d(of_nat$, all_768_1) = all_768_0
% 154.44/20.93 | (65) rank_iarray$(all_768_2) = all_768_1
% 154.44/20.93 | (66) matrix_to_iarray$(a$) = all_768_2
% 154.44/20.93 |
% 154.44/20.93 | DELTA: instantiating (3) with fresh symbols all_771_0, all_771_1, all_771_2,
% 154.44/20.93 | all_771_3 gives:
% 154.44/20.93 | (67) $lesseq(1, $difference(all_771_1, all_771_0)) &
% 154.44/20.93 | ncols_iarray$(all_771_3) = all_771_2 & matrix_to_iarray$(a$) =
% 154.44/20.93 | all_771_3 & fun_app$d(of_nat$, all_771_2) = all_771_1 &
% 154.44/20.93 | fun_app$d(of_nat$, i$) = all_771_0 & Nat$(all_771_2) &
% 154.44/20.93 | A_iarray_iarray$(all_771_3)
% 154.44/20.93 |
% 154.44/20.93 | ALPHA: (67) implies:
% 154.44/20.93 | (68) Nat$(all_771_2)
% 154.44/20.93 | (69) fun_app$d(of_nat$, i$) = all_771_0
% 154.44/20.93 | (70) fun_app$d(of_nat$, all_771_2) = all_771_1
% 154.44/20.93 | (71) matrix_to_iarray$(a$) = all_771_3
% 154.44/20.93 |
% 154.44/20.93 | DELTA: instantiating (8) with fresh symbols all_776_0, all_776_1 gives:
% 154.44/20.93 | (72) card$(top$) = all_776_1 & fun_app$d(of_nat$, all_776_1) = all_776_0 &
% 154.44/20.93 | Nat$(all_776_1) & ! [v0: Cols$] : ! [v1: Nat$] : ( ~ (to_nat$(v0) =
% 154.44/20.93 | v1) | ~ Cols$(v0) | ? [v2: int] : ($lesseq(1,
% 154.44/20.93 | $difference(all_776_0, v2)) & fun_app$d(of_nat$, v1) = v2))
% 154.44/20.93 |
% 154.44/20.93 | ALPHA: (72) implies:
% 154.44/20.93 | (73) fun_app$d(of_nat$, all_776_1) = all_776_0
% 154.44/20.93 | (74) card$(top$) = all_776_1
% 154.44/20.93 | (75) ! [v0: Cols$] : ! [v1: Nat$] : ( ~ (to_nat$(v0) = v1) | ~ Cols$(v0)
% 154.44/20.93 | | ? [v2: int] : ($lesseq(1, $difference(all_776_0, v2)) &
% 154.44/20.93 | fun_app$d(of_nat$, v1) = v2))
% 154.44/20.93 |
% 154.44/20.93 | DELTA: instantiating (7) with fresh symbols all_782_0, all_782_1 gives:
% 154.44/20.93 | (76) card$(top$) = all_782_1 & fun_app$d(of_nat$, all_782_1) = all_782_0 &
% 154.44/20.93 | Nat$(all_782_1) & ! [v0: A_cols_vec_rows_vec$] : ! [v1:
% 154.44/20.93 | A_iarray_iarray$] : ( ~ (matrix_to_iarray$(v0) = v1) | ~
% 154.44/20.93 | A_cols_vec_rows_vec$(v0) | ? [v2: Nat$] : (ncols_iarray$(v1) = v2 &
% 154.44/20.93 | fun_app$d(of_nat$, v2) = all_782_0 & Nat$(v2)))
% 154.44/20.93 |
% 154.44/20.93 | ALPHA: (76) implies:
% 154.50/20.93 | (77) fun_app$d(of_nat$, all_782_1) = all_782_0
% 154.50/20.93 | (78) card$(top$) = all_782_1
% 154.50/20.93 |
% 154.50/20.93 | DELTA: instantiating (15) with fresh symbols all_785_0, all_785_1 gives:
% 154.50/20.93 | (79) card$a(top$a) = all_785_1 & fun_app$d(of_nat$, all_785_1) = all_785_0
% 154.50/20.93 | & Nat$(all_785_1) & ! [v0: A_cols_vec_rows_vec$] : ! [v1:
% 154.50/20.93 | A_iarray_iarray$] : ( ~ (matrix_to_iarray$(v0) = v1) | ~
% 154.50/20.93 | A_cols_vec_rows_vec$(v0) | ? [v2: Nat$] : (nrows_iarray$(v1) = v2 &
% 154.50/20.94 | fun_app$d(of_nat$, v2) = all_785_0 & Nat$(v2)))
% 154.50/20.94 |
% 154.50/20.94 | ALPHA: (79) implies:
% 154.50/20.94 | (80) fun_app$d(of_nat$, all_785_1) = all_785_0
% 154.50/20.94 | (81) card$a(top$a) = all_785_1
% 154.50/20.94 |
% 154.50/20.94 | DELTA: instantiating (16) with fresh symbols all_788_0, all_788_1 gives:
% 154.50/20.94 | (82) card$a(top$a) = all_788_1 & fun_app$d(of_nat$, all_788_1) = all_788_0
% 154.50/20.94 | & Nat$(all_788_1) & ! [v0: A_cols_vec_rows_vec$] : ! [v1:
% 154.50/20.94 | A_iarray_iarray$] : ( ~ (matrix_to_iarray$(v0) = v1) | ~
% 154.50/20.94 | A_cols_vec_rows_vec$(v0) | ? [v2: Nat$] : (length$(v1) = v2 &
% 154.50/20.94 | fun_app$d(of_nat$, v2) = all_788_0 & Nat$(v2)))
% 154.50/20.94 |
% 154.50/20.94 | ALPHA: (82) implies:
% 154.50/20.94 | (83) Nat$(all_788_1)
% 154.50/20.94 | (84) fun_app$d(of_nat$, all_788_1) = all_788_0
% 154.50/20.94 | (85) card$a(top$a) = all_788_1
% 154.50/20.94 |
% 154.50/20.94 | DELTA: instantiating (11) with fresh symbols all_800_0, all_800_1 gives:
% 154.50/20.94 | (86) card$(top$) = all_800_1 & fun_app$d(of_nat$, all_800_1) = all_800_0 &
% 154.50/20.94 | Nat$(all_800_1) & ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(1,
% 154.50/20.94 | $difference(all_800_0, v1))) | ~ (fun_app$d(of_nat$, v0) = v1)
% 154.50/20.94 | | ~ Nat$(v0) | ? [v2: Cols$] : ? [v3: Nat$] : (fun_app$d(of_nat$,
% 154.50/20.94 | v3) = v1 & to_nat$(v2) = v3 & from_nat$(v0) = v2 & Cols$(v2) &
% 154.50/20.94 | Nat$(v3)))
% 154.50/20.94 |
% 154.50/20.94 | ALPHA: (86) implies:
% 154.50/20.94 | (87) fun_app$d(of_nat$, all_800_1) = all_800_0
% 154.50/20.94 | (88) card$(top$) = all_800_1
% 154.50/20.94 | (89) ! [v0: Nat$] : ! [v1: int] : ( ~ ($lesseq(1, $difference(all_800_0,
% 154.50/20.94 | v1))) | ~ (fun_app$d(of_nat$, v0) = v1) | ~ Nat$(v0) | ?
% 154.50/20.94 | [v2: Cols$] : ? [v3: Nat$] : (fun_app$d(of_nat$, v3) = v1 &
% 154.50/20.94 | to_nat$(v2) = v3 & from_nat$(v0) = v2 & Cols$(v2) & Nat$(v3)))
% 154.50/20.94 |
% 154.50/20.94 | DELTA: instantiating (12) with fresh symbols all_808_0, all_808_1 gives:
% 154.50/20.94 | (90) card$(top$) = all_808_1 & fun_app$d(of_nat$, all_808_1) = all_808_0 &
% 154.50/20.94 | Nat$(all_808_1) & ! [v0: Nat$] : ! [v1: Cols$] : ! [v2: int] : !
% 154.50/20.94 | [v3: Nat$] : ( ~ ($lesseq(1, $difference(all_808_0, v2))) | ~
% 154.50/20.94 | (fun_app$d(of_nat$, v0) = v2) | ~ (to_nat$(v1) = v3) | ~ Cols$(v1)
% 154.50/20.94 | | ~ Nat$(v0) | ? [v4: Cols$] : ? [v5: int] : (fun_app$d(of_nat$,
% 154.50/20.94 | v3) = v5 & from_nat$(v0) = v4 & Cols$(v4) & ( ~ (v4 = v1) | v5 =
% 154.50/20.94 | v2)))
% 154.50/20.94 |
% 154.50/20.94 | ALPHA: (90) implies:
% 154.50/20.94 | (91) fun_app$d(of_nat$, all_808_1) = all_808_0
% 154.50/20.94 | (92) card$(top$) = all_808_1
% 154.50/20.94 |
% 154.50/20.94 | DELTA: instantiating (13) with fresh symbols all_811_0, all_811_1 gives:
% 154.50/20.94 | (93) card$(top$) = all_811_1 & fun_app$d(of_nat$, all_811_1) = all_811_0 &
% 154.50/20.94 | Nat$(all_811_1) & ! [v0: Nat$] : ! [v1: Cols$] : ! [v2: int] : !
% 154.50/20.94 | [v3: Nat$] : ( ~ ($lesseq(1, $difference(all_811_0, v2))) | ~
% 154.50/20.94 | (fun_app$d(of_nat$, v0) = v2) | ~ (to_nat$(v1) = v3) | ~ Cols$(v1)
% 154.50/20.94 | | ~ Nat$(v0) | ? [v4: int] : ? [v5: Cols$] : (fun_app$d(of_nat$,
% 154.50/20.94 | v3) = v4 & from_nat$(v0) = v5 & Cols$(v5) & ( ~ (v5 = v1) | v4 =
% 154.50/20.94 | v2)))
% 154.50/20.94 |
% 154.50/20.94 | ALPHA: (93) implies:
% 154.50/20.94 | (94) fun_app$d(of_nat$, all_811_1) = all_811_0
% 154.50/20.94 | (95) card$(top$) = all_811_1
% 154.50/20.94 |
% 154.50/20.94 | DELTA: instantiating (17) with fresh symbols all_817_0, all_817_1, all_817_2
% 154.50/20.94 | gives:
% 154.50/20.94 | (96) nat$(0) = all_817_2 & card$(top$) = all_817_1 & fun_app$d(of_nat$,
% 154.50/20.94 | all_817_1) = all_817_0 & Nat$(all_817_1) & Nat$(all_817_2) & ! [v0:
% 154.50/20.94 | A_cols_vec_rows_vec$] : ! [v1: A_iarray_iarray$] : ( ~
% 154.50/20.94 | (matrix_to_iarray$(v0) = v1) | ~ A_cols_vec_rows_vec$(v0) | ? [v2:
% 154.50/20.94 | Nat_a_iarray_fun$] : ? [v3: A_iarray$] : ? [v4: Nat$] :
% 154.50/20.94 | (length$a(v3) = v4 & sub$(v1) = v2 & fun_app$ac(v2, all_817_2) = v3
% 154.50/20.94 | & fun_app$d(of_nat$, v4) = all_817_0 & A_iarray$(v3) & Nat$(v4) &
% 154.50/20.94 | Nat_a_iarray_fun$(v2)))
% 154.50/20.94 |
% 154.50/20.94 | ALPHA: (96) implies:
% 154.50/20.94 | (97) fun_app$d(of_nat$, all_817_1) = all_817_0
% 154.50/20.94 | (98) card$(top$) = all_817_1
% 154.50/20.94 |
% 154.50/20.94 | DELTA: instantiating (14) with fresh symbols all_820_0, all_820_1 gives:
% 154.50/20.94 | (99) card$(top$) = all_820_1 & fun_app$d(of_nat$, all_820_1) = all_820_0 &
% 154.50/20.94 | Nat$(all_820_1) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Cols$] : !
% 154.50/20.94 | [v3: Cols_bool_fun$] : ! [v4: Cols$] : ! [v5: int] : (v5 = 0 | ~
% 154.50/20.94 | (fun_app$f(less_eq$a, v2) = v3) | ~ (fun_app$e(v3, v4) = v5) | ~
% 154.50/20.94 | (from_nat$(v1) = v4) | ~ (from_nat$(v0) = v2) | ~ Nat$(v1) | ~
% 154.50/20.94 | Nat$(v0) | ? [v6: int] : ? [v7: int] : (fun_app$d(of_nat$, v1) =
% 154.50/20.94 | v6 & fun_app$d(of_nat$, v0) = v7 & ( ~ ($lesseq(v7, v6)) | ~
% 154.50/20.94 | ($lesseq(1, $difference(all_820_0, v6))))))
% 154.50/20.94 |
% 154.50/20.94 | ALPHA: (99) implies:
% 154.50/20.94 | (100) fun_app$d(of_nat$, all_820_1) = all_820_0
% 154.50/20.94 | (101) card$(top$) = all_820_1
% 154.50/20.94 |
% 154.50/20.94 | DELTA: instantiating (10) with fresh symbols all_823_0, all_823_1 gives:
% 154.50/20.94 | (102) card$(top$) = all_823_1 & fun_app$d(of_nat$, all_823_1) = all_823_0 &
% 154.50/20.94 | Nat$(all_823_1) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Cols$] : !
% 154.50/20.94 | [v3: Cols_bool_fun$] : ! [v4: Cols$] : ! [v5: int] : (v5 = 0 | ~
% 154.50/20.94 | (fun_app$f(less$, v2) = v3) | ~ (fun_app$e(v3, v4) = v5) | ~
% 154.50/20.94 | (from_nat$(v1) = v4) | ~ (from_nat$(v0) = v2) | ~ Nat$(v1) | ~
% 154.50/20.94 | Nat$(v0) | ? [v6: int] : ? [v7: int] : (fun_app$d(of_nat$, v1) =
% 154.50/20.94 | v6 & fun_app$d(of_nat$, v0) = v7 & ( ~ ($lesseq(1,
% 154.50/20.94 | $difference(v6, v7))) | ~ ($lesseq(1,
% 154.50/20.94 | $difference(all_823_0, v6))))))
% 154.50/20.94 |
% 154.50/20.94 | ALPHA: (102) implies:
% 154.50/20.94 | (103) fun_app$d(of_nat$, all_823_1) = all_823_0
% 154.50/20.94 | (104) card$(top$) = all_823_1
% 154.50/20.94 |
% 154.50/20.94 | DELTA: instantiating (9) with fresh symbols all_829_0, all_829_1 gives:
% 154.50/20.94 | (105) card$(top$) = all_829_1 & fun_app$d(of_nat$, all_829_1) = all_829_0 &
% 154.50/20.94 | Nat$(all_829_1) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : !
% 154.50/20.94 | [v3: int] : (v3 = v2 | ~ ($lesseq(1, $difference(all_829_0, v3))) |
% 154.50/20.94 | ~ ($lesseq(1, $difference(all_829_0, v2))) | ~ (fun_app$d(of_nat$,
% 154.50/20.94 | v1) = v3) | ~ (fun_app$d(of_nat$, v0) = v2) | ~ Nat$(v1) | ~
% 154.50/20.94 | Nat$(v0) | ? [v4: Cols$] : ? [v5: Cols$] : ( ~ (v5 = v4) &
% 154.50/20.94 | from_nat$(v1) = v5 & from_nat$(v0) = v4 & Cols$(v5) & Cols$(v4)))
% 154.50/20.94 |
% 154.50/20.94 | ALPHA: (105) implies:
% 154.50/20.94 | (106) fun_app$d(of_nat$, all_829_1) = all_829_0
% 154.50/20.94 | (107) card$(top$) = all_829_1
% 154.50/20.94 | (108) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : ! [v3: int] : (v3 =
% 154.50/20.94 | v2 | ~ ($lesseq(1, $difference(all_829_0, v3))) | ~ ($lesseq(1,
% 154.50/20.94 | $difference(all_829_0, v2))) | ~ (fun_app$d(of_nat$, v1) = v3)
% 154.50/20.94 | | ~ (fun_app$d(of_nat$, v0) = v2) | ~ Nat$(v1) | ~ Nat$(v0) | ?
% 154.50/20.94 | [v4: Cols$] : ? [v5: Cols$] : ( ~ (v5 = v4) & from_nat$(v1) = v5 &
% 154.50/20.94 | from_nat$(v0) = v4 & Cols$(v5) & Cols$(v4)))
% 154.50/20.94 |
% 154.50/20.94 | DELTA: instantiating (27) with fresh symbols all_845_0, all_845_1, all_845_2,
% 154.50/20.94 | all_845_3, all_845_4, all_845_5 gives:
% 154.50/20.95 | (109) p_Gauss_Jordan$(all_845_4) = all_845_3 & row$(all_845_5, all_845_3) =
% 154.50/20.95 | all_845_2 & rank$(a$) = all_845_1 & transpose$(a$) = all_845_4 &
% 154.50/20.95 | fun_app$d(of_nat$, all_845_1) = all_845_0 & from_nat$(i$) = all_845_5
% 154.50/20.95 | & A_cols_vec_cols_vec$(all_845_3) & Cols$(all_845_5) &
% 154.50/20.95 | A_cols_vec$(all_845_2) & Nat$(all_845_1) &
% 154.50/20.95 | A_rows_vec_cols_vec$(all_845_4) & ! [v0: Cols$] : ( ~ (row$(v0,
% 154.50/20.95 | all_845_3) = all_845_2) | ~ Cols$(v0) | ? [v1: Nat$] : ?
% 154.50/20.95 | [v2: int] : ($lesseq(1, $difference(all_845_0, v2)) &
% 154.50/20.95 | fun_app$d(of_nat$, v1) = v2 & to_nat$(v0) = v1 & Nat$(v1)))
% 154.50/20.95 |
% 154.50/20.95 | ALPHA: (109) implies:
% 154.50/20.95 | (110) Nat$(all_845_1)
% 154.50/20.95 | (111) Cols$(all_845_5)
% 154.50/20.95 | (112) from_nat$(i$) = all_845_5
% 154.50/20.95 | (113) fun_app$d(of_nat$, all_845_1) = all_845_0
% 154.50/20.95 | (114) transpose$(a$) = all_845_4
% 154.50/20.95 | (115) rank$(a$) = all_845_1
% 154.50/20.95 | (116) row$(all_845_5, all_845_3) = all_845_2
% 154.50/20.95 | (117) ! [v0: Cols$] : ( ~ (row$(v0, all_845_3) = all_845_2) | ~ Cols$(v0)
% 154.50/20.95 | | ? [v1: Nat$] : ? [v2: int] : ($lesseq(1, $difference(all_845_0,
% 154.50/20.95 | v2)) & fun_app$d(of_nat$, v1) = v2 & to_nat$(v0) = v1 &
% 154.50/20.95 | Nat$(v1)))
% 154.50/20.95 |
% 154.50/20.95 | DELTA: instantiating (6) with fresh symbols all_859_0, all_859_1 gives:
% 154.50/20.95 | (118) card$(top$) = all_859_1 & fun_app$d(of_nat$, all_859_1) = all_859_0 &
% 154.50/20.95 | Nat$(all_859_1) & ? [v0: Cols_bool_fun$] : ( ~ Cols_bool_fun$(v0) |
% 154.50/20.95 | ? [v1: Cols$] : ? [v2: Nat$] : ? [v3: int] : ? [v4: int] : ( ~
% 154.50/20.95 | (v4 = 0) & $lesseq(1, $difference(all_859_0, v3)) & fun_app$e(v0,
% 154.50/20.95 | v1) = v4 & fun_app$d(of_nat$, v2) = v3 & to_nat$(v1) = v2 &
% 154.50/20.95 | Cols$(v1) & Nat$(v2)) | ! [v1: Cols$] : ! [v2: int] : (v2 = 0 |
% 154.50/20.95 | ~ (fun_app$e(v0, v1) = v2) | ~ Cols$(v1))) & ? [v0:
% 154.50/20.95 | Cols_bool_fun$] : ( ~ Cols_bool_fun$(v0) | ? [v1: Cols$] : ? [v2:
% 154.50/20.95 | int] : ( ~ (v2 = 0) & fun_app$e(v0, v1) = v2 & Cols$(v1)) | !
% 154.50/20.95 | [v1: Cols$] : ! [v2: Nat$] : ( ~ (to_nat$(v1) = v2) | ~ Cols$(v1)
% 154.50/20.95 | | ? [v3: int] : ? [v4: any] : (fun_app$e(v0, v1) = v4 &
% 154.50/20.95 | fun_app$d(of_nat$, v2) = v3 & (v4 = 0 | ~ ($lesseq(1,
% 154.50/20.95 | $difference(all_859_0, v3)))))))
% 154.50/20.95 |
% 154.50/20.95 | ALPHA: (118) implies:
% 154.50/20.95 | (119) fun_app$d(of_nat$, all_859_1) = all_859_0
% 154.50/20.95 | (120) card$(top$) = all_859_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (34) with all_768_3, all_771_0, i$, of_nat$,
% 154.50/20.95 | simplifying with (63), (69) gives:
% 154.50/20.95 | (121) all_771_0 = all_768_3
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (34) with all_762_0, all_771_0, i$, of_nat$,
% 154.50/20.95 | simplifying with (57), (69) gives:
% 154.50/20.95 | (122) all_771_0 = all_762_0
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (31) with all_768_2, all_771_3, a$, simplifying
% 154.50/20.95 | with (66), (71) gives:
% 154.50/20.95 | (123) all_771_3 = all_768_2
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_741_0, all_776_1, top$, simplifying
% 154.50/20.95 | with (36), (74) gives:
% 154.50/20.95 | (124) all_776_1 = all_741_0
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_776_1, all_782_1, top$, simplifying
% 154.50/20.95 | with (74), (78) gives:
% 154.50/20.95 | (125) all_782_1 = all_776_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_754_1, all_782_1, top$, simplifying
% 154.50/20.95 | with (54), (78) gives:
% 154.50/20.95 | (126) all_782_1 = all_754_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_776_1, all_800_1, top$, simplifying
% 154.50/20.95 | with (74), (88) gives:
% 154.50/20.95 | (127) all_800_1 = all_776_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_800_1, all_817_1, top$, simplifying
% 154.50/20.95 | with (88), (98) gives:
% 154.50/20.95 | (128) all_817_1 = all_800_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_751_1, all_817_1, top$, simplifying
% 154.50/20.95 | with (51), (98) gives:
% 154.50/20.95 | (129) all_817_1 = all_751_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_817_1, all_820_1, top$, simplifying
% 154.50/20.95 | with (98), (101) gives:
% 154.50/20.95 | (130) all_820_1 = all_817_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_823_1, all_829_1, top$, simplifying
% 154.50/20.95 | with (104), (107) gives:
% 154.50/20.95 | (131) all_829_1 = all_823_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_811_1, all_829_1, top$, simplifying
% 154.50/20.95 | with (95), (107) gives:
% 154.50/20.95 | (132) all_829_1 = all_811_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_776_1, all_829_1, top$, simplifying
% 154.50/20.95 | with (74), (107) gives:
% 154.50/20.95 | (133) all_829_1 = all_776_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_762_2, all_829_1, top$, simplifying
% 154.50/20.95 | with (59), (107) gives:
% 154.50/20.95 | (134) all_829_1 = all_762_2
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_820_1, all_859_1, top$, simplifying
% 154.50/20.95 | with (101), (120) gives:
% 154.50/20.95 | (135) all_859_1 = all_820_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (32) with all_808_1, all_859_1, top$, simplifying
% 154.50/20.95 | with (92), (120) gives:
% 154.50/20.95 | (136) all_859_1 = all_808_1
% 154.50/20.95 |
% 154.50/20.95 | GROUND_INST: instantiating (33) with all_785_1, all_788_1, top$a, simplifying
% 154.50/20.95 | with (81), (85) gives:
% 154.50/20.95 | (137) all_788_1 = all_785_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (135), (136) imply:
% 154.50/20.95 | (138) all_820_1 = all_808_1
% 154.50/20.95 |
% 154.50/20.95 | SIMP: (138) implies:
% 154.50/20.95 | (139) all_820_1 = all_808_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (131), (132) imply:
% 154.50/20.95 | (140) all_823_1 = all_811_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (131), (134) imply:
% 154.50/20.95 | (141) all_823_1 = all_762_2
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (131), (133) imply:
% 154.50/20.95 | (142) all_823_1 = all_776_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (140), (141) imply:
% 154.50/20.95 | (143) all_811_1 = all_762_2
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (140), (142) imply:
% 154.50/20.95 | (144) all_811_1 = all_776_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (130), (139) imply:
% 154.50/20.95 | (145) all_817_1 = all_808_1
% 154.50/20.95 |
% 154.50/20.95 | SIMP: (145) implies:
% 154.50/20.95 | (146) all_817_1 = all_808_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (128), (146) imply:
% 154.50/20.95 | (147) all_808_1 = all_800_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (129), (146) imply:
% 154.50/20.95 | (148) all_808_1 = all_751_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (143), (144) imply:
% 154.50/20.95 | (149) all_776_1 = all_762_2
% 154.50/20.95 |
% 154.50/20.95 | SIMP: (149) implies:
% 154.50/20.95 | (150) all_776_1 = all_762_2
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (147), (148) imply:
% 154.50/20.95 | (151) all_800_1 = all_751_1
% 154.50/20.95 |
% 154.50/20.95 | SIMP: (151) implies:
% 154.50/20.95 | (152) all_800_1 = all_751_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (127), (152) imply:
% 154.50/20.95 | (153) all_776_1 = all_751_1
% 154.50/20.95 |
% 154.50/20.95 | SIMP: (153) implies:
% 154.50/20.95 | (154) all_776_1 = all_751_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (125), (126) imply:
% 154.50/20.95 | (155) all_776_1 = all_754_1
% 154.50/20.95 |
% 154.50/20.95 | SIMP: (155) implies:
% 154.50/20.95 | (156) all_776_1 = all_754_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (124), (150) imply:
% 154.50/20.95 | (157) all_762_2 = all_741_0
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (150), (156) imply:
% 154.50/20.95 | (158) all_762_2 = all_754_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (150), (154) imply:
% 154.50/20.95 | (159) all_762_2 = all_751_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (121), (122) imply:
% 154.50/20.95 | (160) all_768_3 = all_762_0
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (157), (158) imply:
% 154.50/20.95 | (161) all_754_1 = all_741_0
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (158), (159) imply:
% 154.50/20.95 | (162) all_754_1 = all_751_1
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (161), (162) imply:
% 154.50/20.95 | (163) all_751_1 = all_741_0
% 154.50/20.95 |
% 154.50/20.95 | COMBINE_EQS: (126), (161) imply:
% 154.50/20.95 | (164) all_782_1 = all_741_0
% 154.50/20.95 |
% 154.50/20.96 | COMBINE_EQS: (152), (163) imply:
% 154.50/20.96 | (165) all_800_1 = all_741_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (148), (163) imply:
% 154.50/20.96 | (166) all_808_1 = all_741_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (143), (157) imply:
% 154.50/20.96 | (167) all_811_1 = all_741_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (146), (166) imply:
% 154.50/20.96 | (168) all_817_1 = all_741_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (139), (166) imply:
% 154.50/20.96 | (169) all_820_1 = all_741_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (140), (167) imply:
% 154.50/20.96 | (170) all_823_1 = all_741_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (131), (170) imply:
% 154.50/20.96 | (171) all_829_1 = all_741_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (136), (166) imply:
% 154.50/20.96 | (172) all_859_1 = all_741_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (61), (160) imply:
% 154.50/20.96 | (173) $lesseq(all_768_0, all_762_0)
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (119), (172) imply:
% 154.50/20.96 | (174) fun_app$d(of_nat$, all_741_0) = all_859_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (106), (171) imply:
% 154.50/20.96 | (175) fun_app$d(of_nat$, all_741_0) = all_829_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (103), (170) imply:
% 154.50/20.96 | (176) fun_app$d(of_nat$, all_741_0) = all_823_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (100), (169) imply:
% 154.50/20.96 | (177) fun_app$d(of_nat$, all_741_0) = all_820_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (97), (168) imply:
% 154.50/20.96 | (178) fun_app$d(of_nat$, all_741_0) = all_817_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (94), (167) imply:
% 154.50/20.96 | (179) fun_app$d(of_nat$, all_741_0) = all_811_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (91), (166) imply:
% 154.50/20.96 | (180) fun_app$d(of_nat$, all_741_0) = all_808_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (87), (165) imply:
% 154.50/20.96 | (181) fun_app$d(of_nat$, all_741_0) = all_800_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (84), (137) imply:
% 154.50/20.96 | (182) fun_app$d(of_nat$, all_785_1) = all_788_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (77), (164) imply:
% 154.50/20.96 | (183) fun_app$d(of_nat$, all_741_0) = all_782_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (73), (124) imply:
% 154.50/20.96 | (184) fun_app$d(of_nat$, all_741_0) = all_776_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (58), (157) imply:
% 154.50/20.96 | (185) fun_app$d(of_nat$, all_741_0) = all_762_1
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (53), (161) imply:
% 154.50/20.96 | (186) fun_app$d(of_nat$, all_741_0) = all_754_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (50), (163) imply:
% 154.50/20.96 | (187) fun_app$d(of_nat$, all_741_0) = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (83), (137) imply:
% 154.50/20.96 | (188) Nat$(all_785_1)
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (49), (163) imply:
% 154.50/20.96 | (189) Nat$(all_741_0)
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_754_0, all_762_1, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (185), (186) gives:
% 154.50/20.96 | (190) all_762_1 = all_754_0
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_762_1, all_808_0, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (180), (185) gives:
% 154.50/20.96 | (191) all_808_0 = all_762_1
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_808_0, all_817_0, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (178), (180) gives:
% 154.50/20.96 | (192) all_817_0 = all_808_0
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_776_0, all_817_0, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (178), (184) gives:
% 154.50/20.96 | (193) all_817_0 = all_776_0
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_811_0, all_820_0, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (177), (179) gives:
% 154.50/20.96 | (194) all_820_0 = all_811_0
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_808_0, all_820_0, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (177), (180) gives:
% 154.50/20.96 | (195) all_820_0 = all_808_0
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_800_0, all_820_0, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (177), (181) gives:
% 154.50/20.96 | (196) all_820_0 = all_800_0
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_782_0, all_820_0, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (177), (183) gives:
% 154.50/20.96 | (197) all_820_0 = all_782_0
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_800_0, all_823_0, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (176), (181) gives:
% 154.50/20.96 | (198) all_823_0 = all_800_0
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_823_0, all_829_0, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (175), (176) gives:
% 154.50/20.96 | (199) all_829_0 = all_823_0
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_829_0, all_859_0, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (174), (175) gives:
% 154.50/20.96 | (200) all_859_0 = all_829_0
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_751_0, all_859_0, all_741_0, of_nat$,
% 154.50/20.96 | simplifying with (174), (187) gives:
% 154.50/20.96 | (201) all_859_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (34) with all_785_0, all_788_0, all_785_1, of_nat$,
% 154.50/20.96 | simplifying with (80), (182) gives:
% 154.50/20.96 | (202) all_788_0 = all_785_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (200), (201) imply:
% 154.50/20.96 | (203) all_829_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | SIMP: (203) implies:
% 154.50/20.96 | (204) all_829_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (199), (204) imply:
% 154.50/20.96 | (205) all_823_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | SIMP: (205) implies:
% 154.50/20.96 | (206) all_823_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (198), (206) imply:
% 154.50/20.96 | (207) all_800_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | SIMP: (207) implies:
% 154.50/20.96 | (208) all_800_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (194), (197) imply:
% 154.50/20.96 | (209) all_811_0 = all_782_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (194), (196) imply:
% 154.50/20.96 | (210) all_811_0 = all_800_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (194), (195) imply:
% 154.50/20.96 | (211) all_811_0 = all_808_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (192), (193) imply:
% 154.50/20.96 | (212) all_808_0 = all_776_0
% 154.50/20.96 |
% 154.50/20.96 | SIMP: (212) implies:
% 154.50/20.96 | (213) all_808_0 = all_776_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (209), (210) imply:
% 154.50/20.96 | (214) all_800_0 = all_782_0
% 154.50/20.96 |
% 154.50/20.96 | SIMP: (214) implies:
% 154.50/20.96 | (215) all_800_0 = all_782_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (209), (211) imply:
% 154.50/20.96 | (216) all_808_0 = all_782_0
% 154.50/20.96 |
% 154.50/20.96 | SIMP: (216) implies:
% 154.50/20.96 | (217) all_808_0 = all_782_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (191), (213) imply:
% 154.50/20.96 | (218) all_776_0 = all_762_1
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (213), (217) imply:
% 154.50/20.96 | (219) all_782_0 = all_776_0
% 154.50/20.96 |
% 154.50/20.96 | SIMP: (219) implies:
% 154.50/20.96 | (220) all_782_0 = all_776_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (208), (215) imply:
% 154.50/20.96 | (221) all_782_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | SIMP: (221) implies:
% 154.50/20.96 | (222) all_782_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (220), (222) imply:
% 154.50/20.96 | (223) all_776_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | SIMP: (223) implies:
% 154.50/20.96 | (224) all_776_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (218), (224) imply:
% 154.50/20.96 | (225) all_762_1 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | SIMP: (225) implies:
% 154.50/20.96 | (226) all_762_1 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | COMBINE_EQS: (190), (226) imply:
% 154.50/20.96 | (227) all_754_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | SIMP: (227) implies:
% 154.50/20.96 | (228) all_754_0 = all_751_0
% 154.50/20.96 |
% 154.50/20.96 | REDUCE: (56), (226) imply:
% 154.50/20.96 | (229) $lesseq(1, $difference(all_751_0, all_762_0))
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (75) with one$, all_747_0, simplifying with (22),
% 154.50/20.96 | (42) gives:
% 154.50/20.96 | (230) ? [v0: int] : ($lesseq(1, $difference(all_776_0, v0)) &
% 154.50/20.96 | fun_app$d(of_nat$, all_747_0) = v0)
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (2) with zero$, i$, all_749_0, all_762_0,
% 154.50/20.96 | simplifying with (19), (25), (46), (57) gives:
% 154.50/20.96 | (231) ? [v0: int] : ? [v1: Cols$] : (fun_app$d(of_nat$, all_749_0) = v0 &
% 154.50/20.96 | from_nat$(i$) = v1 & Cols$(v1) & ( ~ (v0 = all_762_0) | v1 =
% 154.50/20.96 | zero$))
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (2) with one$, i$, all_747_0, all_762_0,
% 154.50/20.96 | simplifying with (22), (25), (42), (57) gives:
% 154.50/20.96 | (232) ? [v0: int] : ? [v1: Cols$] : (fun_app$d(of_nat$, all_747_0) = v0 &
% 154.50/20.96 | from_nat$(i$) = v1 & Cols$(v1) & ( ~ (v0 = all_762_0) | v1 = one$))
% 154.50/20.96 |
% 154.50/20.96 | GROUND_INST: instantiating (89) with i$, all_762_0, simplifying with (25),
% 154.50/20.96 | (57) gives:
% 154.50/20.97 | (233) ~ ($lesseq(1, $difference(all_800_0, all_762_0))) | ? [v0: Cols$] :
% 154.50/20.97 | ? [v1: Nat$] : (fun_app$d(of_nat$, v1) = all_762_0 & to_nat$(v0) =
% 154.50/20.97 | v1 & from_nat$(i$) = v0 & Cols$(v0) & Nat$(v1))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (2) with one$, all_741_0, all_747_0, all_751_0,
% 154.50/20.97 | simplifying with (22), (42), (187), (189) gives:
% 154.50/20.97 | (234) ? [v0: int] : ? [v1: Cols$] : (fun_app$d(of_nat$, all_747_0) = v0 &
% 154.50/20.97 | from_nat$(all_741_0) = v1 & Cols$(v1) & ( ~ (v0 = all_751_0) | v1 =
% 154.50/20.97 | one$))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (2) with one$, all_745_0, all_747_0, 0, simplifying
% 154.50/20.97 | with (22), (38), (39), (42) gives:
% 154.50/20.97 | (235) ? [v0: int] : ? [v1: Cols$] : (fun_app$d(of_nat$, all_747_0) = v0 &
% 154.50/20.97 | from_nat$(all_745_0) = v1 & Cols$(v1) & ( ~ (v0 = 0) | v1 = one$))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (108) with all_745_0, all_747_0, 0, 1, simplifying
% 154.50/20.97 | with (38), (39), (41), (43) gives:
% 154.50/20.97 | (236) ~ ($lesseq(2, all_829_0)) | ? [v0: Cols$] : ? [v1: Cols$] : ( ~
% 154.50/20.97 | (v1 = v0) & from_nat$(all_747_0) = v1 & from_nat$(all_745_0) = v0 &
% 154.50/20.97 | Cols$(v1) & Cols$(v0))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (2) with one$, all_747_0, all_747_0, 1, simplifying
% 154.50/20.97 | with (22), (41), (42), (43) gives:
% 154.50/20.97 | (237) ? [v0: int] : ? [v1: Cols$] : (fun_app$d(of_nat$, all_747_0) = v0 &
% 154.50/20.97 | from_nat$(all_747_0) = v1 & Cols$(v1) & ( ~ (v0 = 1) | v1 = one$))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (2) with one$, all_749_0, all_747_0, 0, simplifying
% 154.50/20.97 | with (22), (42), (45), (47) gives:
% 154.50/20.97 | (238) ? [v0: int] : ? [v1: Cols$] : (fun_app$d(of_nat$, all_747_0) = v0 &
% 154.50/20.97 | from_nat$(all_749_0) = v1 & Cols$(v1) & ( ~ (v0 = 0) | v1 = one$))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (2) with one$, all_768_1, all_747_0, all_768_0,
% 154.50/20.97 | simplifying with (22), (42), (62), (64) gives:
% 154.50/20.97 | (239) ? [v0: int] : ? [v1: Cols$] : (fun_app$d(of_nat$, all_747_0) = v0 &
% 154.50/20.97 | from_nat$(all_768_1) = v1 & Cols$(v1) & ( ~ (v0 = all_768_0) | v1 =
% 154.50/20.97 | one$))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (2) with one$, all_771_2, all_747_0, all_771_1,
% 154.50/20.97 | simplifying with (22), (42), (68), (70) gives:
% 154.50/20.97 | (240) ? [v0: int] : ? [v1: Cols$] : (fun_app$d(of_nat$, all_747_0) = v0 &
% 154.50/20.97 | from_nat$(all_771_2) = v1 & Cols$(v1) & ( ~ (v0 = all_771_1) | v1 =
% 154.50/20.97 | one$))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (2) with one$, all_785_1, all_747_0, all_785_0,
% 154.50/20.97 | simplifying with (22), (42), (80), (188) gives:
% 154.50/20.97 | (241) ? [v0: int] : ? [v1: Cols$] : (fun_app$d(of_nat$, all_747_0) = v0 &
% 154.50/20.97 | from_nat$(all_785_1) = v1 & Cols$(v1) & ( ~ (v0 = all_785_0) | v1 =
% 154.50/20.97 | one$))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (2) with one$, all_845_1, all_747_0, all_845_0,
% 154.50/20.97 | simplifying with (22), (42), (110), (113) gives:
% 154.50/20.97 | (242) ? [v0: int] : ? [v1: Cols$] : (fun_app$d(of_nat$, all_747_0) = v0 &
% 154.50/20.97 | from_nat$(all_845_1) = v1 & Cols$(v1) & ( ~ (v0 = all_845_0) | v1 =
% 154.50/20.97 | one$))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (axiom415) with a$, all_845_4, simplifying with
% 154.50/20.97 | (26), (114) gives:
% 154.50/20.97 | (243) ? [v0: A_iarray_iarray$] : ? [v1: A_iarray_iarray$] :
% 154.50/20.97 | (matrix_to_iarray$a(all_845_4) = v0 & transpose_iarray$(v1) = v0 &
% 154.50/20.97 | matrix_to_iarray$(a$) = v1 & A_iarray_iarray$(v1) &
% 154.50/20.97 | A_iarray_iarray$(v0))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (4) with a$, all_845_1, simplifying with (26),
% 154.50/20.97 | (115) gives:
% 154.50/20.97 | (244) ? [v0: int] : ? [v1: A_iarray_iarray$] : ? [v2: Nat$] :
% 154.50/20.97 | (matrix_to_iarray$(a$) = v1 & rank_iarray$(v1) = v2 &
% 154.50/20.97 | fun_app$d(of_nat$, v2) = v0 & fun_app$d(of_nat$, all_845_1) = v0 &
% 154.50/20.97 | Nat$(v2) & A_iarray_iarray$(v1))
% 154.50/20.97 |
% 154.50/20.97 | GROUND_INST: instantiating (117) with all_845_5, simplifying with (111), (116)
% 154.50/20.97 | gives:
% 154.50/20.97 | (245) ? [v0: Nat$] : ? [v1: int] : ($lesseq(1, $difference(all_845_0,
% 154.50/20.97 | v1)) & fun_app$d(of_nat$, v0) = v1 & to_nat$(all_845_5) = v0 &
% 154.50/20.97 | Nat$(v0))
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (230) with fresh symbol all_898_0 gives:
% 154.50/20.97 | (246) $lesseq(1, $difference(all_776_0, all_898_0)) & fun_app$d(of_nat$,
% 154.50/20.97 | all_747_0) = all_898_0
% 154.50/20.97 |
% 154.50/20.97 | ALPHA: (246) implies:
% 154.50/20.97 | (247) $lesseq(1, $difference(all_776_0, all_898_0))
% 154.50/20.97 | (248) fun_app$d(of_nat$, all_747_0) = all_898_0
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (245) with fresh symbols all_970_0, all_970_1 gives:
% 154.50/20.97 | (249) $lesseq(1, $difference(all_845_0, all_970_0)) & fun_app$d(of_nat$,
% 154.50/20.97 | all_970_1) = all_970_0 & to_nat$(all_845_5) = all_970_1 &
% 154.50/20.97 | Nat$(all_970_1)
% 154.50/20.97 |
% 154.50/20.97 | ALPHA: (249) implies:
% 154.50/20.97 | (250) $lesseq(1, $difference(all_845_0, all_970_0))
% 154.50/20.97 | (251) to_nat$(all_845_5) = all_970_1
% 154.50/20.97 | (252) fun_app$d(of_nat$, all_970_1) = all_970_0
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (243) with fresh symbols all_985_0, all_985_1 gives:
% 154.50/20.97 | (253) matrix_to_iarray$a(all_845_4) = all_985_1 &
% 154.50/20.97 | transpose_iarray$(all_985_0) = all_985_1 & matrix_to_iarray$(a$) =
% 154.50/20.97 | all_985_0 & A_iarray_iarray$(all_985_0) & A_iarray_iarray$(all_985_1)
% 154.50/20.97 |
% 154.50/20.97 | ALPHA: (253) implies:
% 154.50/20.97 | (254) matrix_to_iarray$(a$) = all_985_0
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (235) with fresh symbols all_991_0, all_991_1 gives:
% 154.50/20.97 | (255) fun_app$d(of_nat$, all_747_0) = all_991_1 & from_nat$(all_745_0) =
% 154.50/20.97 | all_991_0 & Cols$(all_991_0) & ( ~ (all_991_1 = 0) | all_991_0 =
% 154.50/20.97 | one$)
% 154.50/20.97 |
% 154.50/20.97 | ALPHA: (255) implies:
% 154.50/20.97 | (256) fun_app$d(of_nat$, all_747_0) = all_991_1
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (242) with fresh symbols all_995_0, all_995_1 gives:
% 154.50/20.97 | (257) fun_app$d(of_nat$, all_747_0) = all_995_1 & from_nat$(all_845_1) =
% 154.50/20.97 | all_995_0 & Cols$(all_995_0) & ( ~ (all_995_1 = all_845_0) |
% 154.50/20.97 | all_995_0 = one$)
% 154.50/20.97 |
% 154.50/20.97 | ALPHA: (257) implies:
% 154.50/20.97 | (258) fun_app$d(of_nat$, all_747_0) = all_995_1
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (238) with fresh symbols all_997_0, all_997_1 gives:
% 154.50/20.97 | (259) fun_app$d(of_nat$, all_747_0) = all_997_1 & from_nat$(all_749_0) =
% 154.50/20.97 | all_997_0 & Cols$(all_997_0) & ( ~ (all_997_1 = 0) | all_997_0 =
% 154.50/20.97 | one$)
% 154.50/20.97 |
% 154.50/20.97 | ALPHA: (259) implies:
% 154.50/20.97 | (260) fun_app$d(of_nat$, all_747_0) = all_997_1
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (231) with fresh symbols all_999_0, all_999_1 gives:
% 154.50/20.97 | (261) fun_app$d(of_nat$, all_749_0) = all_999_1 & from_nat$(i$) = all_999_0
% 154.50/20.97 | & Cols$(all_999_0) & ( ~ (all_999_1 = all_762_0) | all_999_0 = zero$)
% 154.50/20.97 |
% 154.50/20.97 | ALPHA: (261) implies:
% 154.50/20.97 | (262) from_nat$(i$) = all_999_0
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (241) with fresh symbols all_1001_0, all_1001_1 gives:
% 154.50/20.97 | (263) fun_app$d(of_nat$, all_747_0) = all_1001_1 & from_nat$(all_785_1) =
% 154.50/20.97 | all_1001_0 & Cols$(all_1001_0) & ( ~ (all_1001_1 = all_785_0) |
% 154.50/20.97 | all_1001_0 = one$)
% 154.50/20.97 |
% 154.50/20.97 | ALPHA: (263) implies:
% 154.50/20.97 | (264) fun_app$d(of_nat$, all_747_0) = all_1001_1
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (232) with fresh symbols all_1005_0, all_1005_1 gives:
% 154.50/20.97 | (265) fun_app$d(of_nat$, all_747_0) = all_1005_1 & from_nat$(i$) =
% 154.50/20.97 | all_1005_0 & Cols$(all_1005_0) & ( ~ (all_1005_1 = all_762_0) |
% 154.50/20.97 | all_1005_0 = one$)
% 154.50/20.97 |
% 154.50/20.97 | ALPHA: (265) implies:
% 154.50/20.97 | (266) from_nat$(i$) = all_1005_0
% 154.50/20.97 | (267) fun_app$d(of_nat$, all_747_0) = all_1005_1
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (237) with fresh symbols all_1007_0, all_1007_1 gives:
% 154.50/20.97 | (268) fun_app$d(of_nat$, all_747_0) = all_1007_1 & from_nat$(all_747_0) =
% 154.50/20.97 | all_1007_0 & Cols$(all_1007_0) & ( ~ (all_1007_1 = 1) | all_1007_0 =
% 154.50/20.97 | one$)
% 154.50/20.97 |
% 154.50/20.97 | ALPHA: (268) implies:
% 154.50/20.97 | (269) fun_app$d(of_nat$, all_747_0) = all_1007_1
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (240) with fresh symbols all_1011_0, all_1011_1 gives:
% 154.50/20.97 | (270) fun_app$d(of_nat$, all_747_0) = all_1011_1 & from_nat$(all_771_2) =
% 154.50/20.97 | all_1011_0 & Cols$(all_1011_0) & ( ~ (all_1011_1 = all_771_1) |
% 154.50/20.97 | all_1011_0 = one$)
% 154.50/20.97 |
% 154.50/20.97 | ALPHA: (270) implies:
% 154.50/20.97 | (271) fun_app$d(of_nat$, all_747_0) = all_1011_1
% 154.50/20.97 |
% 154.50/20.97 | DELTA: instantiating (234) with fresh symbols all_1019_0, all_1019_1 gives:
% 154.50/20.98 | (272) fun_app$d(of_nat$, all_747_0) = all_1019_1 & from_nat$(all_741_0) =
% 154.50/20.98 | all_1019_0 & Cols$(all_1019_0) & ( ~ (all_1019_1 = all_751_0) |
% 154.50/20.98 | all_1019_0 = one$)
% 154.50/20.98 |
% 154.50/20.98 | ALPHA: (272) implies:
% 154.50/20.98 | (273) fun_app$d(of_nat$, all_747_0) = all_1019_1
% 154.50/20.98 |
% 154.50/20.98 | DELTA: instantiating (239) with fresh symbols all_1021_0, all_1021_1 gives:
% 154.50/20.98 | (274) fun_app$d(of_nat$, all_747_0) = all_1021_1 & from_nat$(all_768_1) =
% 154.50/20.98 | all_1021_0 & Cols$(all_1021_0) & ( ~ (all_1021_1 = all_768_0) |
% 154.50/20.98 | all_1021_0 = one$)
% 154.50/20.98 |
% 154.50/20.98 | ALPHA: (274) implies:
% 154.50/20.98 | (275) fun_app$d(of_nat$, all_747_0) = all_1021_1
% 154.50/20.98 |
% 154.50/20.98 | DELTA: instantiating (244) with fresh symbols all_1031_0, all_1031_1,
% 154.50/20.98 | all_1031_2 gives:
% 154.50/20.98 | (276) matrix_to_iarray$(a$) = all_1031_1 & rank_iarray$(all_1031_1) =
% 154.50/20.98 | all_1031_0 & fun_app$d(of_nat$, all_1031_0) = all_1031_2 &
% 154.50/20.98 | fun_app$d(of_nat$, all_845_1) = all_1031_2 & Nat$(all_1031_0) &
% 154.50/20.98 | A_iarray_iarray$(all_1031_1)
% 154.50/20.98 |
% 154.50/20.98 | ALPHA: (276) implies:
% 154.50/20.98 | (277) fun_app$d(of_nat$, all_845_1) = all_1031_2
% 154.50/20.98 | (278) fun_app$d(of_nat$, all_1031_0) = all_1031_2
% 154.50/20.98 | (279) rank_iarray$(all_1031_1) = all_1031_0
% 154.50/20.98 | (280) matrix_to_iarray$(a$) = all_1031_1
% 154.50/20.98 |
% 154.50/20.98 | REDUCE: (224), (247) imply:
% 154.50/20.98 | (281) $lesseq(1, $difference(all_751_0, all_898_0))
% 154.50/20.98 |
% 154.50/20.98 | BETA: splitting (233) gives:
% 154.50/20.98 |
% 154.50/20.98 | Case 1:
% 154.50/20.98 | |
% 154.50/20.98 | | (282) $lesseq(all_800_0, all_762_0)
% 154.50/20.98 | |
% 154.50/20.98 | | REDUCE: (208), (282) imply:
% 154.50/20.98 | | (283) $lesseq(all_751_0, all_762_0)
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_INEQS: (229), (283) imply:
% 154.50/20.98 | | (284) $false
% 154.50/20.98 | |
% 154.50/20.98 | | CLOSE: (284) is inconsistent.
% 154.50/20.98 | |
% 154.50/20.98 | Case 2:
% 154.50/20.98 | |
% 154.50/20.98 | | (285) ? [v0: Cols$] : ? [v1: Nat$] : (fun_app$d(of_nat$, v1) =
% 154.50/20.98 | | all_762_0 & to_nat$(v0) = v1 & from_nat$(i$) = v0 & Cols$(v0) &
% 154.50/20.98 | | Nat$(v1))
% 154.50/20.98 | |
% 154.50/20.98 | | DELTA: instantiating (285) with fresh symbols all_1117_0, all_1117_1 gives:
% 154.50/20.98 | | (286) fun_app$d(of_nat$, all_1117_0) = all_762_0 & to_nat$(all_1117_1) =
% 154.50/20.98 | | all_1117_0 & from_nat$(i$) = all_1117_1 & Cols$(all_1117_1) &
% 154.50/20.98 | | Nat$(all_1117_0)
% 154.50/20.98 | |
% 154.50/20.98 | | ALPHA: (286) implies:
% 154.50/20.98 | | (287) from_nat$(i$) = all_1117_1
% 154.50/20.98 | | (288) to_nat$(all_1117_1) = all_1117_0
% 154.50/20.98 | | (289) fun_app$d(of_nat$, all_1117_0) = all_762_0
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (28) with all_845_5, all_1005_0, i$, simplifying
% 154.50/20.98 | | with (112), (266) gives:
% 154.50/20.98 | | (290) all_1005_0 = all_845_5
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (28) with all_1005_0, all_1117_1, i$, simplifying
% 154.50/20.98 | | with (266), (287) gives:
% 154.50/20.98 | | (291) all_1117_1 = all_1005_0
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (28) with all_999_0, all_1117_1, i$, simplifying
% 154.50/20.98 | | with (262), (287) gives:
% 154.50/20.98 | | (292) all_1117_1 = all_999_0
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (34) with all_991_1, all_995_1, all_747_0,
% 154.50/20.98 | | of_nat$, simplifying with (256), (258) gives:
% 154.50/20.98 | | (293) all_995_1 = all_991_1
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (34) with all_1007_1, all_1011_1, all_747_0,
% 154.50/20.98 | | of_nat$, simplifying with (269), (271) gives:
% 154.50/20.98 | | (294) all_1011_1 = all_1007_1
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (34) with all_1005_1, all_1011_1, all_747_0,
% 154.50/20.98 | | of_nat$, simplifying with (267), (271) gives:
% 154.50/20.98 | | (295) all_1011_1 = all_1005_1
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (34) with all_1001_1, all_1011_1, all_747_0,
% 154.50/20.98 | | of_nat$, simplifying with (264), (271) gives:
% 154.50/20.98 | | (296) all_1011_1 = all_1001_1
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (34) with all_997_1, all_1011_1, all_747_0,
% 154.50/20.98 | | of_nat$, simplifying with (260), (271) gives:
% 154.50/20.98 | | (297) all_1011_1 = all_997_1
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (34) with all_995_1, all_1011_1, all_747_0,
% 154.50/20.98 | | of_nat$, simplifying with (258), (271) gives:
% 154.50/20.98 | | (298) all_1011_1 = all_995_1
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (34) with all_1001_1, all_1019_1, all_747_0,
% 154.50/20.98 | | of_nat$, simplifying with (264), (273) gives:
% 154.50/20.98 | | (299) all_1019_1 = all_1001_1
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (34) with all_898_0, all_1019_1, all_747_0,
% 154.50/20.98 | | of_nat$, simplifying with (248), (273) gives:
% 154.50/20.98 | | (300) all_1019_1 = all_898_0
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (34) with 1, all_1021_1, all_747_0, of_nat$,
% 154.50/20.98 | | simplifying with (43), (275) gives:
% 154.50/20.98 | | (301) all_1021_1 = 1
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (34) with all_995_1, all_1021_1, all_747_0,
% 154.50/20.98 | | of_nat$, simplifying with (258), (275) gives:
% 154.50/20.98 | | (302) all_1021_1 = all_995_1
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (34) with all_845_0, all_1031_2, all_845_1,
% 154.50/20.98 | | of_nat$, simplifying with (113), (277) gives:
% 154.50/20.98 | | (303) all_1031_2 = all_845_0
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (31) with all_768_2, all_1031_1, a$, simplifying
% 154.50/20.98 | | with (66), (280) gives:
% 154.50/20.98 | | (304) all_1031_1 = all_768_2
% 154.50/20.98 | |
% 154.50/20.98 | | GROUND_INST: instantiating (31) with all_985_0, all_1031_1, a$, simplifying
% 154.50/20.98 | | with (254), (280) gives:
% 154.50/20.98 | | (305) all_1031_1 = all_985_0
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (291), (292) imply:
% 154.50/20.98 | | (306) all_1005_0 = all_999_0
% 154.50/20.98 | |
% 154.50/20.98 | | SIMP: (306) implies:
% 154.50/20.98 | | (307) all_1005_0 = all_999_0
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (304), (305) imply:
% 154.50/20.98 | | (308) all_985_0 = all_768_2
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (301), (302) imply:
% 154.50/20.98 | | (309) all_995_1 = 1
% 154.50/20.98 | |
% 154.50/20.98 | | SIMP: (309) implies:
% 154.50/20.98 | | (310) all_995_1 = 1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (299), (300) imply:
% 154.50/20.98 | | (311) all_1001_1 = all_898_0
% 154.50/20.98 | |
% 154.50/20.98 | | SIMP: (311) implies:
% 154.50/20.98 | | (312) all_1001_1 = all_898_0
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (294), (298) imply:
% 154.50/20.98 | | (313) all_1007_1 = all_995_1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (294), (296) imply:
% 154.50/20.98 | | (314) all_1007_1 = all_1001_1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (294), (295) imply:
% 154.50/20.98 | | (315) all_1007_1 = all_1005_1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (294), (297) imply:
% 154.50/20.98 | | (316) all_1007_1 = all_997_1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (315), (316) imply:
% 154.50/20.98 | | (317) all_1005_1 = all_997_1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (313), (315) imply:
% 154.50/20.98 | | (318) all_1005_1 = all_995_1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (314), (315) imply:
% 154.50/20.98 | | (319) all_1005_1 = all_1001_1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (290), (307) imply:
% 154.50/20.98 | | (320) all_999_0 = all_845_5
% 154.50/20.98 | |
% 154.50/20.98 | | SIMP: (320) implies:
% 154.50/20.98 | | (321) all_999_0 = all_845_5
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (317), (319) imply:
% 154.50/20.98 | | (322) all_1001_1 = all_997_1
% 154.50/20.98 | |
% 154.50/20.98 | | SIMP: (322) implies:
% 154.50/20.98 | | (323) all_1001_1 = all_997_1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (317), (318) imply:
% 154.50/20.98 | | (324) all_997_1 = all_995_1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (312), (323) imply:
% 154.50/20.98 | | (325) all_997_1 = all_898_0
% 154.50/20.98 | |
% 154.50/20.98 | | SIMP: (325) implies:
% 154.50/20.98 | | (326) all_997_1 = all_898_0
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (324), (326) imply:
% 154.50/20.98 | | (327) all_995_1 = all_898_0
% 154.50/20.98 | |
% 154.50/20.98 | | SIMP: (327) implies:
% 154.50/20.98 | | (328) all_995_1 = all_898_0
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (293), (310) imply:
% 154.50/20.98 | | (329) all_991_1 = 1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (293), (328) imply:
% 154.50/20.98 | | (330) all_991_1 = all_898_0
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (329), (330) imply:
% 154.50/20.98 | | (331) all_898_0 = 1
% 154.50/20.98 | |
% 154.50/20.98 | | SIMP: (331) implies:
% 154.50/20.98 | | (332) all_898_0 = 1
% 154.50/20.98 | |
% 154.50/20.98 | | COMBINE_EQS: (292), (321) imply:
% 154.50/20.98 | | (333) all_1117_1 = all_845_5
% 154.50/20.98 | |
% 154.50/20.98 | | REDUCE: (281), (332) imply:
% 154.50/20.98 | | (334) $lesseq(2, all_751_0)
% 154.50/20.98 | |
% 154.50/20.98 | | REDUCE: (279), (304) imply:
% 154.50/20.98 | | (335) rank_iarray$(all_768_2) = all_1031_0
% 154.50/20.98 | |
% 154.50/20.98 | | REDUCE: (278), (303) imply:
% 154.50/20.98 | | (336) fun_app$d(of_nat$, all_1031_0) = all_845_0
% 154.50/20.99 | |
% 154.50/20.99 | | REDUCE: (288), (333) imply:
% 154.50/20.99 | | (337) to_nat$(all_845_5) = all_1117_0
% 154.50/20.99 | |
% 154.50/20.99 | | BETA: splitting (236) gives:
% 154.50/20.99 | |
% 154.50/20.99 | | Case 1:
% 154.50/20.99 | | |
% 154.50/20.99 | | | (338) $lesseq(all_829_0, 1)
% 154.50/20.99 | | |
% 154.50/20.99 | | | REDUCE: (204), (338) imply:
% 154.50/20.99 | | | (339) $lesseq(all_751_0, 1)
% 154.50/20.99 | | |
% 154.50/20.99 | | | COMBINE_INEQS: (334), (339) imply:
% 154.50/20.99 | | | (340) $false
% 154.50/20.99 | | |
% 154.50/20.99 | | | CLOSE: (340) is inconsistent.
% 154.50/20.99 | | |
% 154.50/20.99 | | Case 2:
% 154.50/20.99 | | |
% 154.50/20.99 | | |
% 154.50/20.99 | | | GROUND_INST: instantiating (29) with all_970_1, all_1117_0, all_845_5,
% 154.50/20.99 | | | simplifying with (251), (337) gives:
% 154.50/20.99 | | | (341) all_1117_0 = all_970_1
% 154.50/20.99 | | |
% 154.50/20.99 | | | GROUND_INST: instantiating (30) with all_768_1, all_1031_0, all_768_2,
% 154.50/20.99 | | | simplifying with (65), (335) gives:
% 154.50/20.99 | | | (342) all_1031_0 = all_768_1
% 154.50/20.99 | | |
% 154.50/20.99 | | | REDUCE: (289), (341) imply:
% 154.50/20.99 | | | (343) fun_app$d(of_nat$, all_970_1) = all_762_0
% 154.50/20.99 | | |
% 154.50/20.99 | | | REDUCE: (336), (342) imply:
% 154.50/20.99 | | | (344) fun_app$d(of_nat$, all_768_1) = all_845_0
% 154.50/20.99 | | |
% 154.50/20.99 | | | GROUND_INST: instantiating (34) with all_768_0, all_845_0, all_768_1,
% 154.50/20.99 | | | of_nat$, simplifying with (64), (344) gives:
% 154.50/20.99 | | | (345) all_845_0 = all_768_0
% 154.50/20.99 | | |
% 154.50/20.99 | | | GROUND_INST: instantiating (34) with all_970_0, all_762_0, all_970_1,
% 154.50/20.99 | | | of_nat$, simplifying with (252), (343) gives:
% 154.50/20.99 | | | (346) all_970_0 = all_762_0
% 154.50/20.99 | | |
% 154.50/20.99 | | | REDUCE: (250), (345), (346) imply:
% 154.50/20.99 | | | (347) $lesseq(1, $difference(all_768_0, all_762_0))
% 154.50/20.99 | | |
% 154.50/20.99 | | | COMBINE_INEQS: (173), (347) imply:
% 154.50/20.99 | | | (348) $false
% 154.50/20.99 | | |
% 154.50/20.99 | | | CLOSE: (348) is inconsistent.
% 154.50/20.99 | | |
% 154.50/20.99 | | End of split
% 154.50/20.99 | |
% 154.50/20.99 | End of split
% 154.50/20.99 |
% 154.50/20.99 End of proof
% 154.50/20.99 % SZS output end Proof for theBenchmark
% 154.50/20.99
% 154.50/20.99 20372ms
%------------------------------------------------------------------------------